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##The following is written by Savanna van Mesdag, going through the relevant coding and analyses for CCAs and ANOSIMs for the plant and substrate data for the six study sites.

#setwd#

#To run the following code to carry out the analyses, the following packages must be installed#

install.packages("vegan", repos = "https://github.com/vegandevs/vegan")
## Installing package into 'C:/Users/Savanna/AppData/Local/R/win-library/4.4'
## (as 'lib' is unspecified)
## Warning: unable to access index for repository https://github.com/vegandevs/vegan/src/contrib:
##   cannot open URL 'https://github.com/vegandevs/vegan/src/contrib/PACKAGES'
## Warning: package 'vegan' is not available for this version of R
## 
## A version of this package for your version of R might be available elsewhere,
## see the ideas at
## https://cran.r-project.org/doc/manuals/r-patched/R-admin.html#Installing-packages
## Warning: unable to access index for repository https://github.com/vegandevs/vegan/bin/windows/contrib/4.4:
##   cannot open URL 'https://github.com/vegandevs/vegan/bin/windows/contrib/4.4/PACKAGES'
install.packages("ggplot2", repos = "https://github.com/tidyverse/ggplot2")
## Installing package into 'C:/Users/Savanna/AppData/Local/R/win-library/4.4'
## (as 'lib' is unspecified)
## Warning: unable to access index for repository https://github.com/tidyverse/ggplot2/src/contrib:
##   cannot open URL 'https://github.com/tidyverse/ggplot2/src/contrib/PACKAGES'
## Warning: package 'ggplot2' is not available for this version of R
## 
## A version of this package for your version of R might be available elsewhere,
## see the ideas at
## https://cran.r-project.org/doc/manuals/r-patched/R-admin.html#Installing-packages
## Warning: unable to access index for repository https://github.com/tidyverse/ggplot2/bin/windows/contrib/4.4:
##   cannot open URL 'https://github.com/tidyverse/ggplot2/bin/windows/contrib/4.4/PACKAGES'

#Once installed, then need to load these r packages…

library(vegan)
## Warning: package 'vegan' was built under R version 4.4.1
## Loading required package: permute
## Loading required package: lattice
## This is vegan 2.6-8
library(ggplot2)

#Loading the data files…

urlfile1 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/Plant_Species_BD.csv'

PlantSpecies <-read.csv(urlfile1)

urlfile2 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/PLANT_CHEMISTRY_MG_KG.csv'

PlantChemistry <-read.csv(urlfile2)

#Need to do this to make sure the datasets are good to go.

col_sums     <- apply(X = PlantSpecies, MARGIN = 2, FUN = sum);
rm           <- which(is.na(col_sums) == TRUE);
PlantSpecies <- PlantSpecies[, -rm];

print(PlantSpecies)
##    Agrostis.spp. Agrostis.canina Alchemilla.mollis Alopercus.pratensis
## 1              0               0                 0                   0
## 2              9               0                 0                   0
## 3              1               0                 0                   0
## 4              0               0                 0                   0
## 5              0               0                 0                   0
## 6              1               0                 0                   0
## 7              0               0                 0                   0
## 8              0               0                 0                   0
## 9              0               0                 0                   0
## 10            14               0                 0                   0
## 11             5               3                 0                   0
## 12             3               0                 1                   0
## 13            32               0                 0                   0
## 14            39               0                 0                   0
## 15             0               0                 0                   0
## 16             0               0                 0                   0
## 17             0               0                 0                   0
## 18             0               0                 0                   0
## 19             0               0                 0                   0
## 20             0               0                 0                   0
## 21             0               0                 0                  27
## 22             0               0                 0                   0
## 23             0               0                 0                   0
## 24             0               0                 0                   0
## 25             0               0                 0                   0
## 26             0               0                 0                   0
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## 37             0               0                 0                   0
## 38             0               0                 0                   0
## 39             0               0                 0                   0
## 40             0               0                 0                   0
## 41             0               0                 0                   0
##    Angelica.sylvestris Anthoxanthum.odoratum Anthyllis.vulneraria
## 1                    0                    81                    0
## 2                    0                    18                    0
## 3                    0                     8                    0
## 4                    0                    82                    0
## 5                    0                    55                    0
## 6                    0                     0                    0
## 7                    0                     0                    0
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## 23                   0                     0                    0
## 24                   0                     0                    4
## 25                   0                     0                    0
## 26                   0                     0                  127
## 27                   0                     0                    0
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## 34                   0                     0                    0
## 35                   0                     0                    0
## 36                   0                     0                   70
## 37                   0                     0                  189
## 38                   0                     7                    0
## 39                   0                     0                    0
## 40                   0                     0                    0
## 41                   0                     0                    0
##    Aphanes.arvensis Arrhenatherum.elatius Atrichum.undulatum Avenula.pratensis
## 1                 0                     0                  0                 0
## 2                 0                     0                  0                 0
## 3                 0                     0                  0                 0
## 4                 0                     2                  0                 0
## 5                 0                    42                 10                 0
## 6                 0                     0                  0                 0
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## 25                0                     0                  0                 0
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## 28                0                     0                  0                 0
## 29                0                     8                  0                 0
## 30                1                     0                  0                 0
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## 37                0                     0                  0                 0
## 38                0                     0                  0                 0
## 39                0                     0                  0                 0
## 40                0                     0                  0                 0
## 41                0                     0                  0                 0
##    Bellis.perennis Betula.pubescens Blackstonia.perfoliata
## 1                1                0                      0
## 2                0                0                      0
## 3                8               12                      0
## 4               16                0                      0
## 5                0                0                      0
## 6                0                0                      0
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##    Brachythecium.albicans Brachythecium.glareosum Brachythecium.mildeanum
## 1                       0                       0                       0
## 2                       0                       0                       0
## 3                       0                       0                       0
## 4                       0                       0                       0
## 5                       0                       0                       0
## 6                       0                      10                      10
## 7                       0                       0                      80
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## 10                      0                       0                     150
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## 41                      0                       0                       0
##    Brachythecium.rutabulum Briza.media Bromus.hordeaceus
## 1                        0           0                 0
## 2                        0           0                 0
## 3                        0           0                 0
## 4                        0           0                 0
## 5                        0           0                 0
## 6                       10           0                 0
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## 26                       0         138                 0
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## 29                       0           0                 1
## 30                       0           0                 0
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##    Bryum.c.f..caespiticium Bryum.c.f..pallescens Bryum.capillare Bryum.spp.
## 1                        0                     0               0          0
## 2                        0                     0              10          0
## 3                       10                    10               0          0
## 4                        0                     0               0          0
## 5                        0                     0               0          0
## 6                        0                     0               0          0
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## 19                       0                     0               0         20
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##    Calliergonella.cupsidata Campanula.rotundifolia Carex.distans Carex.flacca
## 1                         0                      0             0            0
## 2                         0                      0             0            0
## 3                        10                      0             0            0
## 4                        10                      0             0            0
## 5                        30                      0             0            0
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## 8                       150                      0             0            1
## 9                        90                      0             0            0
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## 19                      120                      0             0           24
## 20                        0                      0             0            0
## 21                       10                      0             0            0
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## 23                        0                      0            52            0
## 24                        0                      0             0            0
## 25                       30                      0             0            0
## 26                       20                      0             0            0
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##    Carex.panicea Carlina.vulgaris Centaurea.nigra Centaurium.erythraea
## 1              0                0               0                    0
## 2              0                0               0                    0
## 3              0                0               0                    0
## 4              0                0               0                    0
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##    Centaurium.littorale Centaurium.pulchellum Cerastium.fontanum
## 1                     0                     0                  0
## 2                     0                     0                  6
## 3                     0                     0                  0
## 4                     0                     0                  0
## 5                     0                     0                  0
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##    Chamaenerion.angustifolium Cirriphyllum.piliferum Cirsium.arvense
## 1                           0                      0               0
## 2                           0                      0               0
## 3                           0                     10               0
## 4                           0                      0               0
## 5                           0                      0               0
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## 39                          0                      0               0
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## 41                          0                      0               0
##    Cirsium.palustre Crepis.capillaris Cynosurus.cristatus Dactylis.glomerata
## 1                 0                 4                   0                  1
## 2                 0                 0                   0                  0
## 3                 0                 0                   0                  0
## 4                 0                 1                   0                  0
## 5                 0                 0                   0                  0
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## 10                0                 0                  16                 12
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## 40                0                 0                   0                  0
## 41                0                 0                   0                 10
##    Danthonia.decumbens Daucus.carrota Dicranella.spp. Dicranum.scoparium
## 1                    0              0               0                 30
## 2                    0              0               0                 20
## 3                    0              0               0                  0
## 4                    0              0               0                 10
## 5                    0              0               0                 16
## 6                    0              0               0                  0
## 7                    0              0               0                  0
## 8                    0              0               0                  0
## 9                    0              0               0                 50
## 10                   1              0               0                  0
## 11                   0              0               0                  0
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## 40                   0              0               0                  0
## 41                   0              0               0                  0
##    Epilobium.montanum Equisetum.arvense Equisteum.variegatum Erigeron.acer
## 1                   0                 0                    0             0
## 2                   0                 0                    0             0
## 3                   0                 0                    0             0
## 4                   0                 0                    0             0
## 5                   0                 0                    0             0
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##    Euphrasia.agg Festuca.ovina Festuca.rubra Festuca.rubra.agg.
## 1              3             0             0                  0
## 2              0             0             0                  5
## 3              6             0             0                  0
## 4              0             0             0                  0
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## 25             0             0            19                  0
## 26            14             0             1                  0
## 27             0             0            39                  0
## 28             0             2             2                  0
## 29             0             0            54                  0
## 30             0             0            42                  0
## 31             7             0            19                  0
## 32             2             0            22                  0
## 33             1             0            41                  0
## 34             4             0            44                  0
## 35             0             0            10                  0
## 36             0             0             0                  0
## 37             0             0             4                  0
## 38             0             0             2                  0
## 39            36             0            44                  0
## 40             0             0             0                  0
## 41            31             0            33                  0
##    Filipendula.ulmaria Fissidens.adianthoides Fissidens.dubius Fissidens.exilis
## 1                    0                      0                0                0
## 2                    0                      0                0                0
## 3                    0                     10               10                0
## 4                    0                      0                0                0
## 5                    0                      0                0                0
## 6                   27                      0                0                0
## 7                    0                      0                0                0
## 8                    0                      0                0                0
## 9                    0                      0                0                0
## 10                   0                      0                0                0
## 11                   3                      0                0                0
## 12                   3                      0                0                0
## 13                   0                      0                0                0
## 14                   0                      0                0                0
## 15                   0                      0                0                0
## 16                   0                      0                0                0
## 17                   0                      0                0                0
## 18                   0                      0                0                0
## 19                   0                      0               20                0
## 20                   0                      0                0                0
## 21                   0                      0                0                0
## 22                   0                      0                0               60
## 23                   0                      0                0                0
## 24                   0                      0                0                0
## 25                   0                      0                0                0
## 26                   0                      0                0                0
## 27                   0                      0                0                0
## 28                   0                      0                0                0
## 29                   0                      0                0                0
## 30                   0                      0                0                0
## 31                   0                      0                0                0
## 32                   0                      0                0                0
## 33                   0                      0                0                0
## 34                   0                      0                0                0
## 35                   0                      0                0                0
## 36                   0                      0                0                0
## 37                   0                      0                0                0
## 38                   0                      0                0                0
## 39                   0                      0                0                0
## 40                   0                      0                0                0
## 41                   0                      0                0                0
##    Fragaria.vesca Galium.aparine Galium.arvense Galium.saxatile Galium.verum
## 1              67              0              0               0            0
## 2              38              0              0               0            0
## 3              65              0              0               0            0
## 4             117              0              0               0            0
## 5              68              0              0               0            0
## 6               0              0              0               0            0
## 7               0              0              0               0            0
## 8               0              0              0               0            0
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## 12              0              0              0               0            0
## 13              0              0              0               0            0
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## 15              0             47              0               0            0
## 16              0              0              0               0            0
## 17              0              0              0               0            0
## 18              0              0              0               0            0
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## 21              0              0              0               0            0
## 22              0              0              0               0            0
## 23              0              0              0               0            0
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## 26              0              0              0               0           88
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## 38              0              0              0               0            0
## 39              0              0              0               0            0
## 40              0              0              0               0            0
## 41              0              0              0               0            0
##    Geum.urbanum Glechoma.hederacea Helicotrichon.spp. Heracleum.sphondylium
## 1             0                  0                  0                     0
## 2             0                  0                  0                     0
## 3             0                  0                  0                     0
## 4             0                  0                  0                     0
## 5             0                  0                  0                     0
## 6             0                  0                  0                     0
## 7             0                  0                  0                     8
## 8             0                  0                  0                     0
## 9             0                  0                  0                     0
## 10            0                  0                  0                     1
## 11            0                  0                  0                     0
## 12            0                  0                  0                     0
## 13            0                  0                  0                     0
## 14           48                  5                  0                     0
## 15            0                  0                  0                     1
## 16            0                  0                  0                     0
## 17            0                  0                  0                     0
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## 19            0                  0                  0                     0
## 20            0                  0                  0                     0
## 21            0                  0                  0                     0
## 22            0                  0                  0                     0
## 23            0                  0                  0                     0
## 24            0                  0                  0                     0
## 25            0                  0                  0                     0
## 26            0                  0                  0                     0
## 27            0                  0                  0                     0
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## 30            0                  0                  0                     0
## 31            0                  0                  0                     0
## 32            0                  0                  0                     0
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## 35            0                  0                  0                     0
## 36            0                  0                  0                     0
## 37            0                  0                  0                     0
## 38            0                  0                  0                     0
## 39            0                  0                  0                     0
## 40            0                  0                  0                     0
## 41            0                  0                  0                     0
##    Hieracium.spp. Holcus.spp. Holcus.lanatus Holcus.mollis
## 1               0           0             30             0
## 2               0           0             80             0
## 3               0           0              0             0
## 4               0           0             28             0
## 5               0           0             36             0
## 6               0           5              0             0
## 7               0          14              0             0
## 8               0          36              0             0
## 9               0           0              0           143
## 10              0           0              0             1
## 11              0           0              0            56
## 12              0           0              0            17
## 13              0           0              0             4
## 14              0           0              0             0
## 15              0           0              0             0
## 16              0          42              0             0
## 17              0           0              0             0
## 18              0          40              8             0
## 19              0          58              3             0
## 20              0          70              0             0
## 21              0          23              0             0
## 22              0           0              0             0
## 23              0          13              0             0
## 24              0           0              0             0
## 25              0          55              5             0
## 26              0           0              1             0
## 27              0          50             25             0
## 28              1           3              2             0
## 29              0         169              0             0
## 30              0          10              0             0
## 31              0          30              0             0
## 32              0           0              0             0
## 33              0          82              5            10
## 34              0           4              0             0
## 35              0          47              0             0
## 36              0           0              0             0
## 37              0           0              0             0
## 38              0           0             18             0
## 39              0          23              0             0
## 40              0          78              0             0
## 41              0          10              0             0
##    Homalothecium.lutescens Hylocomium.splendens Hypericum.perforatum
## 1                        0                   50                   11
## 2                        0                   80                   24
## 3                        0                  110                    2
## 4                        0                  160                    4
## 5                        0                   90                    1
## 6                        0                    0                    0
## 7                        0                    0                    0
## 8                        0                    1                    0
## 9                        0                   90                    0
## 10                       0                    0                    0
## 11                       0                    0                    0
## 12                       0                    0                    0
## 13                       0                    0                    0
## 14                       0                    0                    0
## 15                       0                    0                    0
## 16                       0                    0                    0
## 17                       0                    0                    0
## 18                       0                    0                    0
## 19                       0                    0                    0
## 20                     160                    0                    0
## 21                      10                    0                    0
## 22                       0                    0                    0
## 23                       0                    0                    0
## 24                       0                    0                    0
## 25                       0                    0                    0
## 26                       0                    0                    0
## 27                       0                    0                    0
## 28                       0                    0                    0
## 29                       0                    0                    0
## 30                       0                    0                    0
## 31                       0                    0                    0
## 32                       0                    0                    0
## 33                       0                    0                    0
## 34                       0                    0                   22
## 35                       0                    0                    0
## 36                       0                    0                    0
## 37                       0                    0                    0
## 38                       0                    0                    0
## 39                       0                    0                    0
## 40                       0                    0                    0
## 41                       0                    0                    0
##    Hypnum.cupressiforme Hypnum.imponens Hypnum.jutlandicum Hypochaeris.radicata
## 1                     0               0                  0                    0
## 2                    10               0                 20                    0
## 3                    60               0                  0                    0
## 4                    10               0                  0                    0
## 5                    20               0                120                    0
## 6                     0               0                  0                    0
## 7                     0               0                  0                    0
## 8                     0               0                  0                    0
## 9                    20              60                  0                    0
## 10                   50               0                 10                    0
## 11                    0               0                  0                    0
## 12                    0               0                  0                    0
## 13                    0               0                  0                    0
## 14                    0               0                  0                    0
## 15                    0               0                  0                    0
## 16                   60               0                  0                    0
## 17                  150               0                  0                    0
## 18                   60               0                  0                    0
## 19                    0               0                  0                    0
## 20                    0               0                  0                    0
## 21                    0               0                  0                    0
## 22                    0               0                  0                    0
## 23                    0               0                  0                    0
## 24                    0               0                  0                    0
## 25                    0               0                  0                    0
## 26                    0               0                  0                    0
## 27                    0               0                  0                    1
## 28                    0               0                  0                    0
## 29                    0               0                  0                    0
## 30                    0               0                  0                    0
## 31                    0               0                  0                    0
## 32                    0               0                  0                    0
## 33                    0               0                  0                    0
## 34                    0               0                  0                    0
## 35                    0               0                  0                    0
## 36                    0               0                  0                    0
## 37                    0               0                  0                    0
## 38                  160               0                  0                    0
## 39                    0               0                  0                    0
## 40                    0               0                  0                    0
## 41                    0               0                  0                    0
##    Kindbergia.praelonga Lathyrus.pratensis Leontodon.hispidus
## 1                     0                  0                  0
## 2                     0                  0                  0
## 3                     0                  0                  0
## 4                     0                  0                  0
## 5                     0                  0                  0
## 6                    10                  0                  0
## 7                    60                  0                  0
## 8                     0                 30                  0
## 9                    30                  0                  0
## 10                   10                 18                  0
## 11                    0                  0                  0
## 12                    0                  0                  0
## 13                   50                  0                  0
## 14                   50                  0                  0
## 15                    0                  0                  0
## 16                    0                  0                  0
## 17                    0                  0                  0
## 18                    0                  0                  0
## 19                    0                  0                  0
## 20                    0                  0                  0
## 21                    0                  0                  0
## 22                    0                  0                  0
## 23                    0                  0                  0
## 24                    0                  0                 18
## 25                    0                  0                  0
## 26                    0                  0                  0
## 27                    0                  0                  0
## 28                    0                  0                 30
## 29                    0                  0                  0
## 30                    0                 42                  0
## 31                    0                  0                  0
## 32                    0                  0                  0
## 33                    0                  0                  0
## 34                    0                  0                  0
## 35                    0                  0                  0
## 36                    0                  0                  0
## 37                    0                  0                  0
## 38                    0                  0                  0
## 39                    0                  0                 16
## 40                    0                  0                  2
## 41                    0                  0                 43
##    Leontodon.saxatilis Leucanthemum.vulgare Linum.catharticum Lolium.perenne
## 1                    0                   20                 0              0
## 2                    0                   15                 0              0
## 3                    0                    0                 0              0
## 4                    0                    7                 0              0
## 5                    0                    1                 0              0
## 6                    0                    0                 0              0
## 7                    0                    0                 0              0
## 8                    0                    0                 0              0
## 9                    0                    0                 0              0
## 10                   0                    0                 0              0
## 11                   0                    0                 0              0
## 12                   0                    0                 0              0
## 13                   0                    0                 0              0
## 14                   0                    0                 0              0
## 15                   0                    0                 0              0
## 16                   0                    0                 5              0
## 17                   0                    0                 0              0
## 18                   0                    0                 0              0
## 19                   0                    0                 0              0
## 20                   0                    0                 0              0
## 21                   0                    0                 0              0
## 22                   0                    0                 0              0
## 23                   0                    0                 0              0
## 24                   1                    0                 0              0
## 25                   0                   12                 0              0
## 26                   0                    0                 0              0
## 27                   0                    1                 0              0
## 28                   0                    3                 0              0
## 29                   0                    2                 0             85
## 30                   0                    0                 0              2
## 31                   0                    0                 0              0
## 32                   0                    2                 0              2
## 33                   0                    0                 0              5
## 34                   0                   24                 0              0
## 35                   0                    2                 0              0
## 36                   0                    0                 2              0
## 37                   0                    2                 0              0
## 38                   0                    1                 0              0
## 39                   0                    6                 1              0
## 40                   0                    0                 6              0
## 41                   0                    0                 6              0
##    Lophocolea.semiteres Lotus.corniculatus Luzula.multiflora
## 1                     0                 69                 0
## 2                     0                120                 0
## 3                    10                 92                 0
## 4                     0                  1                 0
## 5                     0                  0                 0
## 6                     0                  0                 0
## 7                     0                  0                 0
## 8                     0                  0                 1
## 9                     0                  0                 0
## 10                    0                  0                 0
## 11                    0                  0                 0
## 12                    0                  0                 0
## 13                    0                 12                 0
## 14                    0                  0                 0
## 15                    0                  0                 0
## 16                    0                  0                 0
## 17                    0                  0                 0
## 18                    0                220                 0
## 19                    0                 19                 0
## 20                    0                  0                 0
## 21                    0                  0                 0
## 22                    0                  0                 0
## 23                    0                  0                 0
## 24                    0                  0                 0
## 25                    0                 67                 0
## 26                    0                 18                 0
## 27                    0                 31                 0
## 28                    0                 12                 0
## 29                    0                140                 0
## 30                    0                  0                 0
## 31                    0                 14                 0
## 32                    0                  2                 0
## 33                    0                 98                 0
## 34                    0                 17                 0
## 35                    0                  0                 0
## 36                    0                  0                 0
## 37                    0                  0                 0
## 38                    0                  0                 0
## 39                    0                 57                 0
## 40                    0                  0                 0
## 41                    0                 20                 0
##    Lysimachia.maritima Medicago.lupulina Myosotis.arvensis Ononis.repens
## 1                    0                 0                 0             0
## 2                    0                 0                 0             0
## 3                    0                 0                 0             0
## 4                    0                 0                 0             0
## 5                    0                 0                 0             0
## 6                    0                 0                 0             0
## 7                    0                 0                 0             0
## 8                    0                 0                 2             0
## 9                    0                 0                 0             0
## 10                   0                 0                 0             2
## 11                   0                 0                 0             0
## 12                   0                 0                 0             0
## 13                   0                 0                 0             0
## 14                   0                 0                 0             0
## 15                   0                 0                 3             0
## 16                   0                 0                 0             0
## 17                   0                 0                 1             0
## 18                   0                 5                 0             0
## 19                   0                 0                 0             0
## 20                   0                 0                 6             2
## 21                   0                 0                 4            63
## 22                   0                 0                 0             0
## 23                  80                 0                 0             0
## 24                   0                 3                 0             0
## 25                   0                 3                 0             0
## 26                   0                 0                 0             0
## 27                   0                 0                 0             0
## 28                   0                 0                 0             0
## 29                   0                 0                 0             0
## 30                   0                 0                 0             0
## 31                   0                 0                 0           153
## 32                   0                 3                 0             0
## 33                   0                 0                 0             0
## 34                   0                 0                 0             0
## 35                   2                 0                 0             0
## 36                   0                 0                 0             5
## 37                   0                 0                 0             1
## 38                   0                91                 0           111
## 39                   0                 0                 0             2
## 40                   0                 0                 0             0
## 41                   0                 0                 0             0
##    Oxalis.acetosella Pastinaca.sativa Pentaglottis.sempervirens
## 1                  0                0                         0
## 2                  0                0                         0
## 3                  0                0                         0
## 4                  0                0                         0
## 5                  0                0                         0
## 6                  0                0                         0
## 7                  0                0                         0
## 8                  0                0                         0
## 9                  0                0                         0
## 10                 0                0                         0
## 11                 0                0                         0
## 12                 0                0                         0
## 13                 0                0                         0
## 14               113                0                         0
## 15                 0                0                         4
## 16                 0                0                         0
## 17                 0                0                         0
## 18                 0                0                         0
## 19                 0                0                         0
## 20                 0                0                         0
## 21                 0                0                         0
## 22                 0                0                         0
## 23                 0                0                         0
## 24                 0                0                         0
## 25                 0                0                         0
## 26                 0                0                         0
## 27                 0                0                         0
## 28                 0                0                         0
## 29                 0                0                         0
## 30                 0                0                         0
## 31                 0                0                         0
## 32                 0                1                         0
## 33                 0                0                         0
## 34                 0                0                         0
## 35                 0                0                         0
## 36                 0                0                         0
## 37                 0                0                         0
## 38                 0                0                         0
## 39                 0                0                         0
## 40                 0                0                         0
## 41                 0                0                         0
##    Pillosella.officinarum Plantago.coronopus Plantago.lanceolata
## 1                       0                  0                  13
## 2                       0                  0                   0
## 3                       0                  0                   0
## 4                       0                  0                  22
## 5                       0                  0                  36
## 6                       0                  0                   0
## 7                       0                  0                   0
## 8                       0                  0                   0
## 9                       0                  0                   0
## 10                      0                  0                   8
## 11                      0                  0                   0
## 12                      0                  0                   0
## 13                      0                  0                   0
## 14                      0                  0                   0
## 15                      0                  0                   0
## 16                     33                  0                   1
## 17                    286                  0                   0
## 18                      2                  0                   0
## 19                      0                  1                   0
## 20                     54                 19                   0
## 21                      0                  0                   1
## 22                      1                  0                   0
## 23                      0                114                   0
## 24                     22                  0                   0
## 25                      0                  0                   0
## 26                      0                  0                   0
## 27                      0                  0                   0
## 28                      4                  0                   3
## 29                      0                  0                   0
## 30                      0                  0                   1
## 31                      0                  0                   3
## 32                      3                  0                   0
## 33                      0                  0                   0
## 34                     14                  0                   3
## 35                      2                  0                   0
## 36                      0                  0                   0
## 37                      0                  0                   0
## 38                     91                  0                   5
## 39                     39                 50                  20
## 40                      0                  0                   0
## 41                      0                  0                  29
##    Pleurozium.schreberi Poa.annua Poa.spp. Polytrichum.commune
## 1                   110         0        0                   0
## 2                    10         0        0                   0
## 3                     0         0        0                   0
## 4                     0         0        0                   0
## 5                   120         0        0                   0
## 6                     0         0        0                   0
## 7                     0         0        0                   0
## 8                     0         0        0                   0
## 9                    60         0        0                  10
## 10                    0         0        0                   0
## 11                    0         0        0                   0
## 12                    0         0        0                   0
## 13                    0         0        0                   0
## 14                    0         0        0                   0
## 15                    0         0        0                   0
## 16                    0         0        0                   0
## 17                    0         0        0                   0
## 18                    0         0        0                   0
## 19                    0         0        0                   0
## 20                    0         0        0                   0
## 21                    0         0        0                   0
## 22                    0         0        0                   0
## 23                    0         0        0                   0
## 24                    0         0        0                   0
## 25                    0         0        0                   0
## 26                    0         0        0                   0
## 27                    0         0        0                   0
## 28                    0         0        0                   0
## 29                    0         0        3                   0
## 30                    0         0        0                   0
## 31                    0         0        0                   0
## 32                    0         0        0                   0
## 33                    0         0        0                   0
## 34                    0         0        0                   0
## 35                    0         0        0                   0
## 36                    0        69        0                   0
## 37                    0        46        0                   0
## 38                    0         0        0                   0
## 39                    0        55        0                   0
## 40                    0         0        0                   0
## 41                    0         0        0                   0
##    Polytrichum.commune.agg. Polytrichum.formosum Potentilla.reptans
## 1                         0                    0                  0
## 2                         0                   40                  0
## 3                         0                    0                  0
## 4                         0                    0                  0
## 5                         0                    0                  0
## 6                         0                    0                  0
## 7                         0                    0                  0
## 8                         0                    0                  0
## 9                        10                    0                  0
## 10                        0                    0                  4
## 11                        0                    0                  0
## 12                        0                    0                  0
## 13                        0                    0                  0
## 14                        0                    0                  0
## 15                        0                    0                  0
## 16                        0                    0                  0
## 17                        0                    0                  0
## 18                        0                    0                  0
## 19                        0                    0                  0
## 20                        0                    0                  0
## 21                        0                    0                  0
## 22                        0                    0                  0
## 23                        0                    0                  0
## 24                        0                    0                  0
## 25                        0                    0                  0
## 26                        0                    0                  0
## 27                        0                    0                  0
## 28                        0                    0                  0
## 29                        0                    0                  0
## 30                        0                    0                 37
## 31                        0                    0                  1
## 32                        0                    0                  0
## 33                        0                    0                  0
## 34                        0                    0                  2
## 35                        0                    0                  0
## 36                        0                    0                  0
## 37                        0                    0                  0
## 38                        0                    0                  0
## 39                        0                    0                  0
## 40                        0                    0                  0
## 41                        0                    0                  0
##    Prunella.vulgaris Pseudoscleropidum.purum Pteridium.aquilinum
## 1                  1                      40                   0
## 2                  0                       0                   0
## 3                  2                     150                   0
## 4                  0                     150                   0
## 5                  0                      90                   0
## 6                  0                       0                   8
## 7                  0                       0                   4
## 8                  0                       0                   0
## 9                  0                      10                   0
## 10                 0                       0                   0
## 11                 0                       0                   0
## 12                 0                       0                   0
## 13                 0                       0                   0
## 14                 0                       0                   4
## 15                 0                       0                   0
## 16                 0                       0                   0
## 17                 0                       0                   0
## 18                 0                       0                   0
## 19                 0                       0                   0
## 20                 0                      30                   0
## 21                 0                       0                   0
## 22                 0                       0                   0
## 23                 0                      20                   0
## 24                 0                       0                   0
## 25                 0                       0                   0
## 26                 0                       0                   0
## 27                 0                       0                   0
## 28                 0                     160                   0
## 29                 0                       0                   0
## 30                 2                       0                   0
## 31                 0                       0                   0
## 32                 5                       0                   0
## 33                 0                       0                   0
## 34                 0                       0                   0
## 35                 0                       0                   0
## 36                 0                       0                   0
## 37                 0                       0                   0
## 38                 0                       0                   0
## 39                 0                       0                   0
## 40                 0                       0                   0
## 41                 2                       0                   0
##    Ranunculus.acris Ranunculus.repens Reseda.lutea Rhinanthus.minor
## 1                 0                 0            0                0
## 2                 0                 0            0                0
## 3                 0                 0            0                0
## 4                 0                 0            0                0
## 5                 2                 0            0                0
## 6                 0                 5            0                0
## 7                 0                 0            0                0
## 8                 0                23            0                0
## 9                 0                 0            0                0
## 10                0                 0            0                4
## 11                0                 0            0                0
## 12                0                 0            0                0
## 13                0                 0            0                0
## 14                0                 0            0                0
## 15                0                 0            0                0
## 16                0                 0            0                0
## 17                0                 0            0                0
## 18                0                 0            0                0
## 19                0                 0            0                0
## 20                0                 0            0                0
## 21                0                 0            0                0
## 22                0                 0            0                0
## 23                0                 0            0                0
## 24                0                 0            0                0
## 25                0                 0            0                0
## 26                0                 0            0                0
## 27                0                 1            0                0
## 28                0                 0            0                0
## 29                0                 0            0                0
## 30                0                 0            0                0
## 31                0                 0            0                0
## 32                0                 0            1                0
## 33                0                 0            0                0
## 34                0                 0            0                0
## 35                0                 0            0                0
## 36                0                 0            0                0
## 37                0                 0            0                0
## 38                0                 0            0                0
## 39                0                 0            0                0
## 40                0                 0            0                0
## 41                0                 0            0                0
##    Rhizomnium.punctatum Rhytidadelphus.squarrosus Rhytidadelphus.triquetris
## 1                     0                       160                        20
## 2                     0                         0                         0
## 3                     0                        30                         0
## 4                     0                       150                        20
## 5                     0                        30                         0
## 6                     0                       130                         0
## 7                     0                       160                         0
## 8                     4                       110                         0
## 9                     0                       110                         0
## 10                    0                         0                         0
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## 40                    0                         0                         0
## 41                    0                         0                         0
##    Rubus.fruticosus Sanguisorba.minor.spp.minor Saniona.uncinata Sedum.anglicum
## 1                 0                           0                0              0
## 2                 0                           0                0              0
## 3                 1                           0                0              0
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## 39                0                           0                0              0
## 40                0                           0                0              0
## 41                0                           0                0              0
##    Senecio.jacobaea Senecio.vulgaris Sonchus.arvensis Stachys.sylvatica
## 1                 0                0                0                 0
## 2                 0                0                0                 0
## 3                 0                0                0                 0
## 4                 0                0                0                 0
## 5                 0                0                0                 0
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## 9                 0                0                0                 0
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## 41                0                0                0                 0
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## 1                  0              0                     0                  0
## 2                  0              0                     0                  0
## 3                  0              0                     0                  0
## 4                  0              0                    30                  0
## 5                  0              0                     0                  0
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## 38                 0              0                     0                  0
## 39                 0              0                     0                  0
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## 41                 0              1                     0                  0
##    Trichostomum.crispulum Trifolium.campestre Trifolium.dubium
## 1                       0                   0                0
## 2                       0                   0                0
## 3                       0                   0                0
## 4                       0                   0                0
## 5                       0                   0                0
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## 36                     30                   0                0
## 37                     60                   0                0
## 38                      0                   0                0
## 39                     70                   0                0
## 40                      0                   0                0
## 41                      0                   0                0
##    Trifolium.pratense Trifolium.repens Trisetum.flavescens Tussilago.farfara
## 1                   0                0                   0                 0
## 2                   0                0                   0                 0
## 3                   0                0                   0                 0
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## 41                 21                0                   0                 0
##    Urtica.diocia Veronica.officinalis Vicia.sativa Viola.riviniana
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#Now to do some ANOSIM tests to assess any significant differences #between plant species in different chemical variables.

anoSiO2 <- anosim(PlantSpecies, PlantChemistry$SiO2, distance = "bray", permutations = 9999)

anoSiO2
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$SiO2, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.7017 
##       Significance: 0.0445 
## 
## Permutation: free
## Number of permutations: 9999

#This initial test demonstrates significant differences between plants in different SiO2 #concentrations, with a high ANOSIM statistic, 0.7017, and a low p value of 0.0423.

anoAl2O3 <- anosim(PlantSpecies, PlantChemistry$Al2O3, distance = "bray", permutations = 9999)

anoAl2O3
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Al2O3, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.1367 
##       Significance: 0.6525 
## 
## Permutation: free
## Number of permutations: 9999

#We do not see significant differences for the Al2O3 concentrations. Further significant #differences highlighted for each relevant test…

anoCaO <- anosim(PlantSpecies, PlantChemistry$CaO, distance = "bray", permutations = 9999)

anoCaO
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$CaO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.8535 
##       Significance: 0.0758 
## 
## Permutation: free
## Number of permutations: 9999
anoMgO <- anosim(PlantSpecies, PlantChemistry$MgO, distance = "bray", permutations = 9999)

anoMgO
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$MgO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1708 
##       Significance: 0.2269 
## 
## Permutation: free
## Number of permutations: 9999
anoNa2O <- anosim(PlantSpecies, PlantChemistry$Na2O, distance = "bray", permutations = 9999)

anoNa2O
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Na2O, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.2471 
##       Significance: 0.194 
## 
## Permutation: free
## Number of permutations: 9999
anoK2O <- anosim(PlantSpecies, PlantChemistry$K2O, distance = "bray", permutations = 9999)

anoK2O
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$K2O, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.3112 
##       Significance: 0.0877 
## 
## Permutation: free
## Number of permutations: 9999
anoCr2O3 <- anosim(PlantSpecies, PlantChemistry$Cr2O3, distance = "bray", permutations = 9999)

anoCr2O3
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Cr2O3, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.2463 
##       Significance: 0.0016 
## 
## Permutation: free
## Number of permutations: 9999

#ANOSIM statistic of 0.2463, with low p value of 0.0015. Significant differences between # plants on different Cr2O3 concentrations.

anoTiO2 <- anosim(PlantSpecies, PlantChemistry$TiO2, distance = "bray", permutations = 9999)

anoTiO2
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$TiO2, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1572 
##       Significance: 0.1873 
## 
## Permutation: free
## Number of permutations: 9999
anoMnO <- anosim(PlantSpecies, PlantChemistry$MnO, distance = "bray", permutations = 9999)

anoMnO
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$MnO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1542 
##       Significance: 0.0969 
## 
## Permutation: free
## Number of permutations: 9999
anoP2O5 <- anosim(PlantSpecies, PlantChemistry$P2O5, distance = "bray", permutations = 9999)

anoP2O5
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$P2O5, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.2941 
##       Significance: 0.009 
## 
## Permutation: free
## Number of permutations: 9999

#ANOSIM statistic of 0.2941, with a low p value of 0.0078.There are significant differences #between plants in different P2O5 concentrations.

anoSrO <- anosim(PlantSpecies, PlantChemistry$SrO, distance = "bray", permutations = 9999)

anoSrO
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$SrO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1214 
##       Significance: 0.0402 
## 
## Permutation: free
## Number of permutations: 9999
anoBaO <- anosim(PlantSpecies, PlantChemistry$BaO, distance = "bray", permutations = 9999)

anoBaO
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$BaO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.2961 
##       Significance: 0.0019 
## 
## Permutation: free
## Number of permutations: 9999

#ANOSIM statistic of 0.2961, with a low p value of 0.0031.There are significant differences #between plants in different BaO concentrations.

anoAs <- anosim(PlantSpecies, PlantChemistry$As, distance = "bray", permutations = 9999)

anoAs
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$As, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.01814 
##       Significance: 0.4119 
## 
## Permutation: free
## Number of permutations: 9999
anoAg <- anosim(PlantSpecies, PlantChemistry$Ag, distance = "bray", permutations = 9999)

anoAg
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Ag, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.006394 
##       Significance: 0.4446 
## 
## Permutation: free
## Number of permutations: 9999
anoB <- anosim(PlantSpecies, PlantChemistry$B, distance = "bray", permutations = 9999)

anoB
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$B, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.06893 
##       Significance: 0.2197 
## 
## Permutation: free
## Number of permutations: 9999
anoBe <- anosim(PlantSpecies, PlantChemistry$Be, distance = "bray", permutations = 9999)

anoBe
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Be, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1811 
##       Significance: 0.1193 
## 
## Permutation: free
## Number of permutations: 9999

#Skipping Bi as the values are all so similar and small.

anoCd <- anosim(PlantSpecies, PlantChemistry$Cd, distance = "bray", permutations = 9999)

anoCd
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Cd, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.04405 
##       Significance: 0.6631 
## 
## Permutation: free
## Number of permutations: 9999
anoCo <- anosim(PlantSpecies, PlantChemistry$Co, distance = "bray", permutations = 9999)

anoCo
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Co, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.2712 
##       Significance: 0.0087 
## 
## Permutation: free
## Number of permutations: 9999

#ANOSIM statistic of 0.2712, with a low p value of 0.0087.There are significant differences #between plants in different Co concentrations.

anoCu <- anosim(PlantSpecies, PlantChemistry$Cu, distance = "bray", permutations = 9999)

anoCu
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Cu, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.132 
##       Significance: 0.2152 
## 
## Permutation: free
## Number of permutations: 9999

#Skipped Ga, Hg, La and Li due to similarity in values.

anoMo <- anosim(PlantSpecies, PlantChemistry$Mo, distance = "bray", permutations = 9999)

anoMo
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Mo, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.0447 
##       Significance: 0.2147 
## 
## Permutation: free
## Number of permutations: 9999
anoNi <- anosim(PlantSpecies, PlantChemistry$Ni, distance = "bray", permutations = 9999)

anoNi
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Ni, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.2407 
##       Significance: 0.0337 
## 
## Permutation: free
## Number of permutations: 9999

#ANOSIM statistic of 0.2407, with a low p value of 0.0351. There are significant differences #between plants in different Ni concentrations.

anoPb <- anosim(PlantSpecies, PlantChemistry$Pb, distance = "bray", permutations = 9999)

anoPb
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Pb, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.05781 
##       Significance: 0.5952 
## 
## Permutation: free
## Number of permutations: 9999
anoS <- anosim(PlantSpecies, PlantChemistry$S, distance = "bray", permutations = 9999)

anoS
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$S, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.2388 
##       Significance: 0.0635 
## 
## Permutation: free
## Number of permutations: 9999
anoSb <- anosim(PlantSpecies, PlantChemistry$Sb, distance = "bray", permutations = 9999)

anoSb
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Sb, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.009027 
##       Significance: 0.4473 
## 
## Permutation: free
## Number of permutations: 9999
anoSc <- anosim(PlantSpecies, PlantChemistry$Sc, distance = "bray", permutations = 9999)

anoSc
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Sc, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.0786 
##       Significance: 0.1702 
## 
## Permutation: free
## Number of permutations: 9999

#Skipping Th, Tl and U because of similarities in values

anoV <- anosim(PlantSpecies, PlantChemistry$V, distance = "bray", permutations = 9999)

anoV
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$V, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1315 
##       Significance: 0.1873 
## 
## Permutation: free
## Number of permutations: 9999

#Skipping W because of similarities in values

anoZn <- anosim(PlantSpecies, PlantChemistry$Zn, distance = "bray", permutations = 9999)

anoZn
## 
## Call:
## anosim(x = PlantSpecies, grouping = PlantChemistry$Zn, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.1196 
##       Significance: 0.6694 
## 
## Permutation: free
## Number of permutations: 9999

#6 out of 27 substrate variables show statistically significant differences #for plant species growing in those same sample locations. #Will do CCA for the whole dataset, but will then do analysis with those #6 substrate variables only.

#The initial CCA with the basic parameters and without specific substrate variables #selected. The dataset used includes too many variables for an anova P value to be #generated, as shown when attempting an anova below.

plant_cca <- cca(PlantSpecies, PlantChemistry, na.action = na.omit);
## 
## Some constraints or conditions were aliased because they were redundant. This
## can happen if terms are linearly dependent (collinear): 'Tl', 'W', 'Anhydrite',
## 'Aragonite', 'Augite', 'Biotite', 'Birnessite', 'Calcite', 'Clinochlore',
## 'Cuspidine', 'Diaspore', 'Dickite', 'Gehlenite', 'Goethite', 'Haematite',
## 'Illite', 'Kaolinite', 'Langite', 'Linnaeite', 'Magnesioferrite', 'Melilite',
## 'Merwinite', 'Microcline', 'Mullite', 'Muscovite', 'Nitratine', 'Orthoclase',
## 'Orthopyroxene', 'Periclase', 'Phengite', 'Pigeonite', 'Pseudowollastonite',
## 'Quartz', 'Spinel', 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component
print(plant_cca);
## Call: cca(X = PlantSpecies, Y = PlantChemistry, na.action = na.omit)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total           11.91       1.00     
## Constrained     11.91       1.00   40
## Unconstrained    0.00       0.00    0
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## Some constraints or conditions were aliased because they were redundant.
## This can happen if terms are linearly dependent (collinear): 'Tl', 'W',
## 'Anhydrite', 'Aragonite', 'Augite', 'Biotite', 'Birnessite', 'Calcite',
## 'Clinochlore', 'Cuspidine', 'Diaspore', 'Dickite', 'Gehlenite', 'Goethite',
## 'Haematite', 'Illite', 'Kaolinite', 'Langite', 'Linnaeite',
## 'Magnesioferrite', 'Melilite', 'Merwinite', 'Microcline', 'Mullite',
## 'Muscovite', 'Nitratine', 'Orthoclase', 'Orthopyroxene', 'Periclase',
## 'Phengite', 'Pigeonite', 'Pseudowollastonite', 'Quartz', 'Spinel',
## 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6   CCA7   CCA8   CCA9  CCA10  CCA11 
## 0.7967 0.7491 0.7151 0.6758 0.6347 0.6060 0.5689 0.5477 0.4941 0.4578 0.4288 
##  CCA12  CCA13  CCA14  CCA15  CCA16  CCA17  CCA18  CCA19  CCA20  CCA21  CCA22 
## 0.4119 0.3872 0.3604 0.3428 0.3059 0.2836 0.2740 0.2664 0.2527 0.2289 0.2185 
##  CCA23  CCA24  CCA25  CCA26  CCA27  CCA28  CCA29  CCA30  CCA31  CCA32  CCA33 
## 0.2083 0.2045 0.1893 0.1571 0.1504 0.1473 0.1268 0.1095 0.1065 0.0938 0.0869 
##  CCA34  CCA35  CCA36  CCA37  CCA38  CCA39  CCA40 
## 0.0777 0.0661 0.0557 0.0472 0.0396 0.0286 0.0130
plot(plant_cca)

summary(plant_cca)
## 
## Call:
## cca(X = PlantSpecies, Y = PlantChemistry, na.action = na.omit) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           11.92          1
## Constrained     11.92          1
## Unconstrained    0.00          0
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.79674 0.74908 0.71514 0.67576 0.63467 0.60596 0.56889
## Proportion Explained  0.06687 0.06287 0.06002 0.05671 0.05327 0.05086 0.04775
## Cumulative Proportion 0.06687 0.12974 0.18975 0.24647 0.29973 0.35059 0.39834
##                          CCA8    CCA9   CCA10   CCA11   CCA12  CCA13   CCA14
## Eigenvalue            0.54769 0.49408 0.45782 0.42883 0.41191 0.3872 0.36037
## Proportion Explained  0.04597 0.04147 0.03842 0.03599 0.03457 0.0325 0.03024
## Cumulative Proportion 0.44430 0.48577 0.52419 0.56018 0.59475 0.6273 0.65750
##                         CCA15   CCA16   CCA17   CCA18   CCA19   CCA20   CCA21
## Eigenvalue            0.34279 0.30587 0.28365 0.27397 0.26637 0.25273 0.22885
## Proportion Explained  0.02877 0.02567 0.02381 0.02299 0.02236 0.02121 0.01921
## Cumulative Proportion 0.68627 0.71194 0.73574 0.75874 0.78109 0.80230 0.82151
##                         CCA22   CCA23   CCA24   CCA25   CCA26   CCA27   CCA28
## Eigenvalue            0.21849 0.20831 0.20450 0.18934 0.15715 0.15042 0.14726
## Proportion Explained  0.01834 0.01748 0.01716 0.01589 0.01319 0.01262 0.01236
## Cumulative Proportion 0.83985 0.85733 0.87449 0.89038 0.90357 0.91620 0.92855
##                         CCA29    CCA30    CCA31    CCA32    CCA33    CCA34
## Eigenvalue            0.12681 0.109450 0.106459 0.093799 0.086888 0.077678
## Proportion Explained  0.01064 0.009186 0.008935 0.007872 0.007292 0.006519
## Cumulative Proportion 0.93920 0.948383 0.957318 0.965190 0.972482 0.979001
##                          CCA35    CCA36    CCA37    CCA38  CCA39    CCA40
## Eigenvalue            0.066101 0.055728 0.047200 0.039574 0.0286 0.013006
## Proportion Explained  0.005548 0.004677 0.003961 0.003321 0.0024 0.001092
## Cumulative Proportion 0.984549 0.989226 0.993187 0.996509 0.9989 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.79674 0.74908 0.71514 0.67576 0.63467 0.60596 0.56889
## Proportion Explained  0.06687 0.06287 0.06002 0.05671 0.05327 0.05086 0.04775
## Cumulative Proportion 0.06687 0.12974 0.18975 0.24647 0.29973 0.35059 0.39834
##                          CCA8    CCA9   CCA10   CCA11   CCA12  CCA13   CCA14
## Eigenvalue            0.54769 0.49408 0.45782 0.42883 0.41191 0.3872 0.36037
## Proportion Explained  0.04597 0.04147 0.03842 0.03599 0.03457 0.0325 0.03024
## Cumulative Proportion 0.44430 0.48577 0.52419 0.56018 0.59475 0.6273 0.65750
##                         CCA15   CCA16   CCA17   CCA18   CCA19   CCA20   CCA21
## Eigenvalue            0.34279 0.30587 0.28365 0.27397 0.26637 0.25273 0.22885
## Proportion Explained  0.02877 0.02567 0.02381 0.02299 0.02236 0.02121 0.01921
## Cumulative Proportion 0.68627 0.71194 0.73574 0.75874 0.78109 0.80230 0.82151
##                         CCA22   CCA23   CCA24   CCA25   CCA26   CCA27   CCA28
## Eigenvalue            0.21849 0.20831 0.20450 0.18934 0.15715 0.15042 0.14726
## Proportion Explained  0.01834 0.01748 0.01716 0.01589 0.01319 0.01262 0.01236
## Cumulative Proportion 0.83985 0.85733 0.87449 0.89038 0.90357 0.91620 0.92855
##                         CCA29    CCA30    CCA31    CCA32    CCA33    CCA34
## Eigenvalue            0.12681 0.109450 0.106459 0.093799 0.086888 0.077678
## Proportion Explained  0.01064 0.009186 0.008935 0.007872 0.007292 0.006519
## Cumulative Proportion 0.93920 0.948383 0.957318 0.965190 0.972482 0.979001
##                          CCA35    CCA36    CCA37    CCA38  CCA39    CCA40
## Eigenvalue            0.066101 0.055728 0.047200 0.039574 0.0286 0.013006
## Proportion Explained  0.005548 0.004677 0.003961 0.003321 0.0024 0.001092
## Cumulative Proportion 0.984549 0.989226 0.993187 0.996509 0.9989 1.000000
anova(plant_cca)
## No residual component
## 
## Model: cca(X = PlantSpecies, Y = PlantChemistry, na.action = na.omit)
##          Df ChiSquare F Pr(>F)
## Model    40    11.915         
## Residual  0     0.000

#Now to do a CCA with the 7 statistically significant variables as #determined by the ANOSIM tests

Plant_CCA_Chem <- cca(PlantSpecies ~ SiO2 + Cr2O3 + P2O5 +
                        BaO + Co + Ni, 
                      data = PlantChemistry)

plot(Plant_CCA_Chem)

summary(Plant_CCA_Chem)
## 
## Call:
## cca(formula = PlantSpecies ~ SiO2 + Cr2O3 + P2O5 + BaO + Co +      Ni, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.161     0.1814
## Unconstrained   9.754     0.8186
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4   CCA5    CCA6     CA1
## Eigenvalue            0.59649 0.44091 0.37329 0.30020 0.2692 0.18130 0.72033
## Proportion Explained  0.05006 0.03700 0.03133 0.02519 0.0226 0.01522 0.06046
## Cumulative Proportion 0.05006 0.08707 0.11839 0.14359 0.1662 0.18140 0.24186
##                           CA2     CA3     CA4     CA5     CA6     CA7     CA8
## Eigenvalue            0.68949 0.65378 0.59795 0.55559 0.54561 0.47844 0.44733
## Proportion Explained  0.05787 0.05487 0.05018 0.04663 0.04579 0.04015 0.03754
## Cumulative Proportion 0.29972 0.35459 0.40478 0.45141 0.49720 0.53735 0.57489
##                           CA9    CA10    CA11    CA12    CA13    CA14    CA15
## Eigenvalue            0.41372 0.39002 0.38418 0.36494 0.33578 0.28911 0.27257
## Proportion Explained  0.03472 0.03273 0.03224 0.03063 0.02818 0.02426 0.02288
## Cumulative Proportion 0.60962 0.64235 0.67459 0.70522 0.73340 0.75766 0.78054
##                         CA16    CA17    CA18    CA19    CA20    CA21    CA22
## Eigenvalue            0.2574 0.24237 0.21760 0.20842 0.20541 0.19132 0.18527
## Proportion Explained  0.0216 0.02034 0.01826 0.01749 0.01724 0.01606 0.01555
## Cumulative Proportion 0.8021 0.82248 0.84074 0.85824 0.87548 0.89153 0.90708
##                          CA23    CA24    CA25    CA26     CA27     CA28
## Eigenvalue            0.16350 0.14617 0.13304 0.12325 0.115441 0.102612
## Proportion Explained  0.01372 0.01227 0.01117 0.01034 0.009689 0.008612
## Cumulative Proportion 0.92080 0.93307 0.94424 0.95458 0.964269 0.972881
##                           CA29     CA30     CA31     CA32     CA33     CA34
## Eigenvalue            0.082128 0.069360 0.062230 0.050843 0.034782 0.023781
## Proportion Explained  0.006893 0.005821 0.005223 0.004267 0.002919 0.001996
## Cumulative Proportion 0.979774 0.985595 0.990818 0.995085 0.998004 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6
## Eigenvalue            0.5965 0.4409 0.3733 0.3002 0.2692 0.18130
## Proportion Explained  0.2760 0.2040 0.1727 0.1389 0.1246 0.08388
## Cumulative Proportion 0.2760 0.4800 0.6527 0.7916 0.9161 1.00000
anova(Plant_CCA_Chem)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ SiO2 + Cr2O3 + P2O5 + BaO + Co + Ni, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)   
## Model     6    2.1614 1.2557   0.01 **
## Residual 34    9.7537                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Generating a CCA plot with the 6 significant varibles from the ANOSIMS produces a very #good-looking graph, except for the fact that Cr2O3 has a very short arrow. The F statistic #for the anova for this CCA is 1.2557 and the p value is 0.028. The p value indicates #statistical significance for this CCA, but the F statistic is fairly low. It will be #useful to carry out additional CCAs with different combinations of substrate variables to #see if there is one that is more statistically significant, with a higher F statistic.

#The following CCAs were carried out to determine which chemistry variables #most strongly influenced plant species presence, which included removing variables #with particularly short arrows, especially compared with variables with much longer arrows.

Plant_CCA_Chem1 <- cca(PlantSpecies ~ pH + SiO2 + Al2O3 + Fe2O3, data = 
PlantChemistry)

plot(Plant_CCA_Chem1)

summary(Plant_CCA_Chem1)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + SiO2 + Al2O3 + Fe2O3, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915      1.000
## Constrained     1.691      0.142
## Unconstrained  10.224      0.858
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4     CA1     CA2     CA3
## Eigenvalue            0.66033 0.44210 0.36238 0.22657 0.73836 0.69904 0.66956
## Proportion Explained  0.05542 0.03710 0.03041 0.01902 0.06197 0.05867 0.05619
## Cumulative Proportion 0.05542 0.09252 0.12294 0.14195 0.20392 0.26259 0.31878
##                           CA4   CA5     CA6     CA7     CA8     CA9    CA10
## Eigenvalue            0.62275 0.560 0.52466 0.51159 0.45951 0.44148 0.41715
## Proportion Explained  0.05227 0.047 0.04403 0.04294 0.03856 0.03705 0.03501
## Cumulative Proportion 0.37105 0.418 0.46208 0.50501 0.54358 0.58063 0.61564
##                          CA11    CA12    CA13    CA14    CA15    CA16    CA17
## Eigenvalue            0.40486 0.34284 0.31916 0.31656 0.28850 0.27093 0.26671
## Proportion Explained  0.03398 0.02877 0.02679 0.02657 0.02421 0.02274 0.02238
## Cumulative Proportion 0.64962 0.67839 0.70518 0.73175 0.75596 0.77870 0.80108
##                          CA18    CA19    CA20    CA21    CA22    CA23    CA24
## Eigenvalue            0.24923 0.22491 0.21064 0.19291 0.18026 0.16528 0.15953
## Proportion Explained  0.02092 0.01888 0.01768 0.01619 0.01513 0.01387 0.01339
## Cumulative Proportion 0.82200 0.84088 0.85855 0.87474 0.88987 0.90374 0.91713
##                         CA25    CA26     CA27     CA28     CA29     CA30
## Eigenvalue            0.1489 0.14274 0.119108 0.107805 0.093070 0.087145
## Proportion Explained  0.0125 0.01198 0.009996 0.009048 0.007811 0.007314
## Cumulative Proportion 0.9296 0.94161 0.951608 0.960655 0.968467 0.975780
##                           CA31     CA32     CA33     CA34     CA35     CA36
## Eigenvalue            0.071814 0.057604 0.053815 0.049415 0.038050 0.017885
## Proportion Explained  0.006027 0.004835 0.004516 0.004147 0.003193 0.001501
## Cumulative Proportion 0.981807 0.986642 0.991158 0.995306 0.998499 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4
## Eigenvalue            0.6603 0.4421 0.3624 0.2266
## Proportion Explained  0.3904 0.2614 0.2143 0.1340
## Cumulative Proportion 0.3904 0.6518 0.8660 1.0000
anova(Plant_CCA_Chem1)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + SiO2 + Al2O3 + Fe2O3, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     4    1.6914 1.4889  0.001 ***
## Residual 36   10.2238                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#We now have an F statistic of 1.4889 and a p value of 0.001, which is our lowest p value #so far. It is worth testing further because 1.4889 is not an especially high F statistic #and the graph does not look ideal, especially as some of the variables have very short #arrows in comparison to, say, Al2O3.

Plant_CCA_Chem2.2 <-cca(PlantSpecies ~ Quartz + Gehlenite + Dickite +
Aluminium.oxide.hydroxide, data = PlantChemistry)

plot(Plant_CCA_Chem2.2)

summary(Plant_CCA_Chem2.2)
## 
## Call:
## cca(formula = PlantSpecies ~ Quartz + Gehlenite + Dickite + Aluminium.oxide.hydroxide,      data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total         11.9152    1.00000
## Constrained    0.9727    0.08163
## Unconstrained 10.9425    0.91837
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3     CCA4     CA1     CA2     CA3
## Eigenvalue            0.35042 0.29305 0.24102 0.088199 0.73982 0.73340 0.68814
## Proportion Explained  0.02941 0.02459 0.02023 0.007402 0.06209 0.06155 0.05775
## Cumulative Proportion 0.02941 0.05400 0.07423 0.081634 0.14372 0.20528 0.26303
##                           CA4     CA5     CA6     CA7     CA8     CA9   CA10
## Eigenvalue            0.66867 0.61205 0.58169 0.56418 0.52152 0.45349 0.4420
## Proportion Explained  0.05612 0.05137 0.04882 0.04735 0.04377 0.03806 0.0371
## Cumulative Proportion 0.31915 0.37052 0.41934 0.46669 0.51045 0.54851 0.5856
##                          CA11    CA12    CA13    CA14    CA15   CA16    CA17
## Eigenvalue            0.41083 0.39639 0.38398 0.32309 0.29993 0.2823 0.27179
## Proportion Explained  0.03448 0.03327 0.03223 0.02712 0.02517 0.0237 0.02281
## Cumulative Proportion 0.62009 0.65336 0.68558 0.71270 0.73787 0.7616 0.78438
##                          CA18   CA19    CA20    CA21    CA22    CA23    CA24
## Eigenvalue            0.25217 0.2502 0.22497 0.21583 0.21018 0.18269 0.17026
## Proportion Explained  0.02116 0.0210 0.01888 0.01811 0.01764 0.01533 0.01429
## Cumulative Proportion 0.80554 0.8265 0.84542 0.86353 0.88117 0.89650 0.91079
##                          CA25    CA26    CA27     CA28     CA29     CA30
## Eigenvalue            0.15223 0.14701 0.12405 0.114539 0.107792 0.102907
## Proportion Explained  0.01278 0.01234 0.01041 0.009613 0.009047 0.008637
## Cumulative Proportion 0.92357 0.93591 0.94632 0.955932 0.964979 0.973616
##                           CA31     CA32     CA33     CA34     CA35     CA36
## Eigenvalue            0.084548 0.066974 0.060738 0.048160 0.030887 0.023067
## Proportion Explained  0.007096 0.005621 0.005098 0.004042 0.002592 0.001936
## Cumulative Proportion 0.980711 0.986332 0.991430 0.995472 0.998064 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3    CCA4
## Eigenvalue            0.3504 0.2931 0.2410 0.08820
## Proportion Explained  0.3603 0.3013 0.2478 0.09068
## Cumulative Proportion 0.3603 0.6615 0.9093 1.00000
anova(Plant_CCA_Chem2.2)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ Quartz + Gehlenite + Dickite + Aluminium.oxide.hydroxide, data = PlantChemistry)
##          Df ChiSquare   F Pr(>F)
## Model     4    0.9727 0.8   0.89
## Residual 36   10.9425

#F statistic of 0.8, p value of 0.862.

Plant_CCA_Chem3 <- cca(PlantSpecies ~ pH + SiO2 + Al2O3 +Fe2O3 + CaO, 
data = PlantChemistry)

plot(Plant_CCA_Chem3)

summary(Plant_CCA_Chem3)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + SiO2 + Al2O3 + Fe2O3 + CaO,      data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.101     0.1764
## Unconstrained   9.814     0.8236
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2   CCA3   CCA4    CCA5     CA1    CA2
## Eigenvalue            0.66033 0.47885 0.3777 0.3598 0.22471 0.73380 0.6982
## Proportion Explained  0.05542 0.04019 0.0317 0.0302 0.01886 0.06159 0.0586
## Cumulative Proportion 0.05542 0.09561 0.1273 0.1575 0.17636 0.23795 0.2965
##                           CA3     CA4     CA5     CA6    CA7    CA8     CA9
## Eigenvalue            0.65383 0.59140 0.54642 0.51940 0.4671 0.4575 0.41717
## Proportion Explained  0.05487 0.04963 0.04586 0.04359 0.0392 0.0384 0.03501
## Cumulative Proportion 0.35142 0.40105 0.44691 0.49050 0.5297 0.5681 0.60312
##                          CA10    CA11    CA12    CA13    CA14    CA15    CA16
## Eigenvalue            0.40524 0.34859 0.32924 0.31657 0.30043 0.27994 0.26847
## Proportion Explained  0.03401 0.02926 0.02763 0.02657 0.02521 0.02349 0.02253
## Cumulative Proportion 0.63713 0.66638 0.69401 0.72058 0.74580 0.76929 0.79182
##                          CA17    CA18   CA19    CA20   CA21    CA22    CA23
## Eigenvalue            0.26142 0.23774 0.2120 0.21019 0.1918 0.17188 0.16405
## Proportion Explained  0.02194 0.01995 0.0178 0.01764 0.0161 0.01443 0.01377
## Cumulative Proportion 0.81376 0.83372 0.8515 0.86915 0.8852 0.89967 0.91344
##                          CA24    CA25    CA26     CA27     CA28     CA29
## Eigenvalue            0.15869 0.14713 0.12008 0.114805 0.093077 0.092361
## Proportion Explained  0.01332 0.01235 0.01008 0.009635 0.007812 0.007752
## Cumulative Proportion 0.92676 0.93911 0.94919 0.958820 0.966632 0.974384
##                           CA30     CA31     CA32     CA33     CA34     CA35
## Eigenvalue            0.071874 0.069234 0.055205 0.050173 0.040844 0.017894
## Proportion Explained  0.006032 0.005811 0.004633 0.004211 0.003428 0.001502
## Cumulative Proportion 0.980416 0.986226 0.990859 0.995070 0.998498 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5
## Eigenvalue            0.6603 0.4788 0.3777 0.3598 0.2247
## Proportion Explained  0.3142 0.2279 0.1797 0.1712 0.1069
## Cumulative Proportion 0.3142 0.5421 0.7219 0.8931 1.0000
anova(Plant_CCA_Chem3)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + SiO2 + Al2O3 + Fe2O3 + CaO, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     5    2.1014 1.4989  0.001 ***
## Residual 35    9.8138                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4989 and p value of 0.001, still worth doing more tests.

Plant_CCA_Chem4 <- cca(PlantSpecies ~ pH + SiO2 + Al2O3 +Fe2O3 + CaO + Cd,
data = PlantChemistry)

plot(Plant_CCA_Chem4)

summary(Plant_CCA_Chem4)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + SiO2 + Al2O3 + Fe2O3 + CaO +      Cd, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.341     0.1965
## Unconstrained   9.574     0.8035
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CA1
## Eigenvalue            0.66142 0.48385 0.39029 0.36331 0.22751 0.21478 0.7316
## Proportion Explained  0.05551 0.04061 0.03276 0.03049 0.01909 0.01803 0.0614
## Cumulative Proportion 0.05551 0.09612 0.12887 0.15937 0.17846 0.19649 0.2579
##                           CA2     CA3     CA4     CA5     CA6     CA7     CA8
## Eigenvalue            0.69807 0.65363 0.58832 0.54247 0.51701 0.46090 0.43394
## Proportion Explained  0.05859 0.05486 0.04938 0.04553 0.04339 0.03868 0.03642
## Cumulative Proportion 0.31648 0.37133 0.42071 0.46624 0.50963 0.54831 0.58473
##                           CA9    CA10    CA11    CA12    CA13    CA14    CA15
## Eigenvalue            0.41716 0.37974 0.34857 0.32923 0.31515 0.29477 0.27982
## Proportion Explained  0.03501 0.03187 0.02925 0.02763 0.02645 0.02474 0.02348
## Cumulative Proportion 0.61974 0.65161 0.68086 0.70850 0.73494 0.75968 0.78317
##                          CA16    CA17    CA18    CA19    CA20    CA21    CA22
## Eigenvalue            0.26847 0.25546 0.23062 0.21148 0.19998 0.17464 0.16692
## Proportion Explained  0.02253 0.02144 0.01936 0.01775 0.01678 0.01466 0.01401
## Cumulative Proportion 0.80570 0.82714 0.84650 0.86424 0.88103 0.89568 0.90969
##                          CA23    CA24    CA25     CA26     CA27     CA28
## Eigenvalue            0.16166 0.15865 0.14126 0.116481 0.098711 0.092362
## Proportion Explained  0.01357 0.01331 0.01186 0.009776 0.008284 0.007752
## Cumulative Proportion 0.92326 0.93658 0.94843 0.958207 0.966492 0.974243
##                           CA29     CA30     CA31     CA32     CA33     CA34
## Eigenvalue            0.072021 0.069779 0.055388 0.050176 0.041637 0.017895
## Proportion Explained  0.006044 0.005856 0.004649 0.004211 0.003494 0.001502
## Cumulative Proportion 0.980288 0.986144 0.990793 0.995004 0.998498 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4    CCA5    CCA6
## Eigenvalue            0.6614 0.4839 0.3903 0.3633 0.22751 0.21478
## Proportion Explained  0.2825 0.2067 0.1667 0.1552 0.09718 0.09174
## Cumulative Proportion 0.2825 0.4892 0.6559 0.8111 0.90826 1.00000
anova(Plant_CCA_Chem4)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + SiO2 + Al2O3 + Fe2O3 + CaO + Cd, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     6    2.3412 1.3857  0.001 ***
## Residual 34    9.5740                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.3857, p value of 0.002. This one has a lower p value and a somewhat higher F statistic than some of the ones generated so far, but it is still worth doing further tests.

Plant_CCA_Chem5 <- cca(PlantSpecies ~ pH + SiO2 + Al2O3 + Fe2O3 + CaO + Cr2O3,
data = PlantChemistry)
plot(Plant_CCA_Chem5)

summary(Plant_CCA_Chem5)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + SiO2 + Al2O3 + Fe2O3 + CaO +      Cr2O3, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.341     0.1964
## Unconstrained   9.575     0.8036
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CA1
## Eigenvalue            0.66121 0.47959 0.37899 0.36228 0.24681 0.21171 0.7327
## Proportion Explained  0.05549 0.04025 0.03181 0.03041 0.02071 0.01777 0.0615
## Cumulative Proportion 0.05549 0.09574 0.12755 0.15796 0.17867 0.19644 0.2579
##                           CA2     CA3     CA4     CA5     CA6     CA7     CA8
## Eigenvalue            0.69766 0.63669 0.58694 0.54118 0.51436 0.46632 0.44554
## Proportion Explained  0.05855 0.05343 0.04926 0.04542 0.04317 0.03914 0.03739
## Cumulative Proportion 0.31649 0.36992 0.41918 0.46460 0.50777 0.54691 0.58430
##                           CA9    CA10   CA11   CA12    CA13    CA14    CA15
## Eigenvalue            0.41170 0.40402 0.3456 0.3241 0.31633 0.29631 0.27925
## Proportion Explained  0.03455 0.03391 0.0290 0.0272 0.02655 0.02487 0.02344
## Cumulative Proportion 0.61885 0.65276 0.6818 0.7090 0.73551 0.76038 0.78382
##                          CA16   CA17    CA18    CA19   CA20    CA21    CA22
## Eigenvalue            0.26823 0.2514 0.23575 0.21107 0.2062 0.18555 0.16425
## Proportion Explained  0.02251 0.0211 0.01979 0.01771 0.0173 0.01557 0.01378
## Cumulative Proportion 0.80633 0.8274 0.84721 0.86493 0.8822 0.89780 0.91159
##                         CA23   CA24    CA25     CA26     CA27     CA28     CA29
## Eigenvalue            0.1608 0.1585 0.12161 0.115396 0.095511 0.092427 0.072529
## Proportion Explained  0.0135 0.0133 0.01021 0.009685 0.008016 0.007757 0.006087
## Cumulative Proportion 0.9251 0.9384 0.94859 0.958278 0.966294 0.974051 0.980139
##                          CA30     CA31     CA32     CA33     CA34
## Eigenvalue            0.07078 0.056031 0.050495 0.040972 0.018376
## Proportion Explained  0.00594 0.004702 0.004238 0.003439 0.001542
## Cumulative Proportion 0.98608 0.990781 0.995019 0.998458 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6
## Eigenvalue            0.6612 0.4796 0.3790 0.3623 0.2468 0.21171
## Proportion Explained  0.2825 0.2049 0.1619 0.1548 0.1054 0.09045
## Cumulative Proportion 0.2825 0.4874 0.6493 0.8041 0.9095 1.00000
anova(Plant_CCA_Chem5)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + SiO2 + Al2O3 + Fe2O3 + CaO + Cr2O3, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)   
## Model     6    2.3406 1.3853  0.003 **
## Residual 34    9.5746                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.3853, p value of 0.006

Plant_CCA_Chem6 <- cca(PlantSpecies ~ pH + SiO2 + Al2O3 + CaO + Cr2O3 + K2O, 
data = PlantChemistry)
plot(Plant_CCA_Chem6)

summary(Plant_CCA_Chem6)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + SiO2 + Al2O3 + CaO + Cr2O3 +      K2O, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.489     0.2089
## Unconstrained   9.427     0.7911
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6     CA1
## Eigenvalue            0.66909 0.55955 0.38429 0.36058 0.30514 0.20993 0.73458
## Proportion Explained  0.05615 0.04696 0.03225 0.03026 0.02561 0.01762 0.06165
## Cumulative Proportion 0.05615 0.10312 0.13537 0.16563 0.19124 0.20886 0.27051
##                          CA2     CA3    CA4     CA5     CA6     CA7     CA8
## Eigenvalue            0.6863 0.63777 0.5707 0.52446 0.47890 0.46650 0.43833
## Proportion Explained  0.0576 0.05353 0.0479 0.04402 0.04019 0.03915 0.03679
## Cumulative Proportion 0.3281 0.38164 0.4295 0.47355 0.51374 0.55289 0.58968
##                           CA9    CA10   CA11    CA12    CA13    CA14    CA15
## Eigenvalue            0.40464 0.38949 0.3515 0.32679 0.31756 0.28584 0.26889
## Proportion Explained  0.03396 0.03269 0.0295 0.02743 0.02665 0.02399 0.02257
## Cumulative Proportion 0.62364 0.65633 0.6858 0.71325 0.73991 0.76390 0.78646
##                          CA16    CA17    CA18    CA19    CA20    CA21    CA22
## Eigenvalue            0.25475 0.24259 0.22336 0.20823 0.20036 0.18551 0.16488
## Proportion Explained  0.02138 0.02036 0.01875 0.01748 0.01682 0.01557 0.01384
## Cumulative Proportion 0.80784 0.82820 0.84695 0.86442 0.88124 0.89681 0.91065
##                          CA23    CA24    CA25     CA26     CA27     CA28
## Eigenvalue            0.16116 0.15793 0.12647 0.115798 0.095218 0.092042
## Proportion Explained  0.01353 0.01325 0.01061 0.009719 0.007991 0.007725
## Cumulative Proportion 0.92417 0.93743 0.94804 0.957760 0.965751 0.973476
##                           CA29     CA30    CA31     CA32     CA33    CA34
## Eigenvalue            0.074362 0.067986 0.05946 0.053478 0.041328 0.01942
## Proportion Explained  0.006241 0.005706 0.00499 0.004488 0.003469 0.00163
## Cumulative Proportion 0.979717 0.985423 0.99041 0.994901 0.998370 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6
## Eigenvalue            0.6691 0.5596 0.3843 0.3606 0.3051 0.20993
## Proportion Explained  0.2689 0.2248 0.1544 0.1449 0.1226 0.08436
## Cumulative Proportion 0.2689 0.4937 0.6481 0.7930 0.9156 1.00000
anova(Plant_CCA_Chem6)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + SiO2 + Al2O3 + CaO + Cr2O3 + K2O, data = PlantChemistry)
##          Df ChiSquare     F Pr(>F)    
## Model     6    2.4886 1.496  0.001 ***
## Residual 34    9.4266                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.496, p value of 0.001

Plant_CCA_Chem6.1 <- cca(PlantSpecies ~ pH + Al2O3 + MgO + Cr2O3 + K2O, 
data = PlantChemistry)

plot(Plant_CCA_Chem6.1)

summary(Plant_CCA_Chem6.1)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + MgO + Cr2O3 + K2O,      data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.046     0.1718
## Unconstrained   9.869     0.8282
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CA1     CA2
## Eigenvalue            0.67625 0.50981 0.35582 0.29587 0.20875 0.7423 0.67221
## Proportion Explained  0.05676 0.04279 0.02986 0.02483 0.01752 0.0623 0.05642
## Cumulative Proportion 0.05676 0.09954 0.12940 0.15424 0.17176 0.2341 0.29047
##                           CA3     CA4     CA5     CA6     CA7     CA8    CA9
## Eigenvalue            0.64761 0.59801 0.56416 0.51704 0.49243 0.44888 0.4206
## Proportion Explained  0.05435 0.05019 0.04735 0.04339 0.04133 0.03767 0.0353
## Cumulative Proportion 0.34482 0.39501 0.44236 0.48575 0.52708 0.56475 0.6000
##                         CA10    CA11    CA12    CA13    CA14    CA15    CA16
## Eigenvalue            0.4051 0.38374 0.34570 0.32892 0.29877 0.27562 0.26107
## Proportion Explained  0.0340 0.03221 0.02901 0.02761 0.02507 0.02313 0.02191
## Cumulative Proportion 0.6340 0.66625 0.69527 0.72287 0.74795 0.77108 0.79299
##                          CA17    CA18    CA19    CA20    CA21    CA22    CA23
## Eigenvalue            0.24919 0.23977 0.22152 0.20781 0.19052 0.16942 0.16629
## Proportion Explained  0.02091 0.02012 0.01859 0.01744 0.01599 0.01422 0.01396
## Cumulative Proportion 0.81390 0.83403 0.85262 0.87006 0.88605 0.90027 0.91422
##                          CA24    CA25    CA26    CA27     CA28     CA29
## Eigenvalue            0.15984 0.13778 0.12759 0.11248 0.095346 0.088723
## Proportion Explained  0.01341 0.01156 0.01071 0.00944 0.008002 0.007446
## Cumulative Proportion 0.92764 0.93920 0.94991 0.95935 0.967353 0.974800
##                           CA30     CA31    CA32     CA33     CA34     CA35
## Eigenvalue            0.076104 0.060542 0.05528 0.051254 0.035962 0.021123
## Proportion Explained  0.006387 0.005081 0.00464 0.004302 0.003018 0.001773
## Cumulative Proportion 0.981187 0.986268 0.99091 0.995209 0.998227 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5
## Eigenvalue            0.6762 0.5098 0.3558 0.2959 0.2088
## Proportion Explained  0.3304 0.2491 0.1739 0.1446 0.1020
## Cumulative Proportion 0.3304 0.5796 0.7534 0.8980 1.0000
anova(Plant_CCA_Chem6.1)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + MgO + Cr2O3 + K2O, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     5    2.0465 1.4516  0.001 ***
## Residual 35    9.8687                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4516, p value of 0.001

Plant_CCA_Chem6.2 <- cca(PlantSpecies ~ pH + Al2O3 + CaO + Cr2O3 + K2O + BaO, 
data = PlantChemistry)
plot(Plant_CCA_Chem6.2)

summary(Plant_CCA_Chem6.2)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + CaO + Cr2O3 + K2O +      BaO, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.363     0.1983
## Unconstrained   9.552     0.8017
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6     CA1
## Eigenvalue            0.67050 0.53091 0.37822 0.31297 0.28974 0.18037 0.73979
## Proportion Explained  0.05627 0.04456 0.03174 0.02627 0.02432 0.01514 0.06209
## Cumulative Proportion 0.05627 0.10083 0.13257 0.15884 0.18316 0.19829 0.26038
##                           CA2     CA3     CA4    CA5     CA6     CA7     CA8
## Eigenvalue            0.68382 0.64426 0.59908 0.5433 0.51670 0.46512 0.43660
## Proportion Explained  0.05739 0.05407 0.05028 0.0456 0.04336 0.03904 0.03664
## Cumulative Proportion 0.31777 0.37184 0.42212 0.4677 0.51109 0.55012 0.58676
##                           CA9   CA10    CA11    CA12    CA13    CA14    CA15
## Eigenvalue            0.41911 0.4016 0.37755 0.34539 0.31158 0.28410 0.27597
## Proportion Explained  0.03517 0.0337 0.03169 0.02899 0.02615 0.02384 0.02316
## Cumulative Proportion 0.62194 0.6556 0.68733 0.71631 0.74246 0.76631 0.78947
##                          CA16   CA17    CA18    CA19    CA20    CA21    CA22
## Eigenvalue            0.25578 0.2324 0.22008 0.20909 0.20603 0.16839 0.16257
## Proportion Explained  0.02147 0.0195 0.01847 0.01755 0.01729 0.01413 0.01364
## Cumulative Proportion 0.81094 0.8304 0.84891 0.86646 0.88375 0.89788 0.91152
##                          CA23    CA24    CA25     CA26     CA27     CA28
## Eigenvalue            0.15871 0.14570 0.13084 0.112995 0.102767 0.092826
## Proportion Explained  0.01332 0.01223 0.01098 0.009483 0.008625 0.007791
## Cumulative Proportion 0.92484 0.93707 0.94805 0.957538 0.966163 0.973953
##                           CA29     CA30    CA31    CA32     CA33     CA34
## Eigenvalue            0.075967 0.060043 0.05660 0.05338 0.041425 0.022937
## Proportion Explained  0.006376 0.005039 0.00475 0.00448 0.003477 0.001925
## Cumulative Proportion 0.980329 0.985368 0.99012 0.99460 0.998075 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6
## Eigenvalue            0.6705 0.5309 0.3782 0.3130 0.2897 0.18037
## Proportion Explained  0.2838 0.2247 0.1601 0.1325 0.1226 0.07634
## Cumulative Proportion 0.2838 0.5085 0.6686 0.8010 0.9237 1.00000
anova(Plant_CCA_Chem6.2)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + CaO + Cr2O3 + K2O + BaO, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     6    2.3627 1.4016  0.001 ***
## Residual 34    9.5525                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4016, p value of 0.004

Plant_CCA_Chem6.3 <- cca(PlantSpecies ~ pH + Al2O3 + Fe2O3 + CaO + SrO + K2O, 
data = PlantChemistry)

plot(Plant_CCA_Chem6.3)

summary(Plant_CCA_Chem6.3)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + Fe2O3 + CaO + SrO +      K2O, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.376     0.1994
## Unconstrained   9.539     0.8006
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6     CA1
## Eigenvalue            0.67187 0.51988 0.38774 0.34342 0.25050 0.20285 0.74161
## Proportion Explained  0.05639 0.04363 0.03254 0.02882 0.02102 0.01702 0.06224
## Cumulative Proportion 0.05639 0.10002 0.13256 0.16138 0.18241 0.19943 0.26167
##                           CA2     CA3     CA4     CA5    CA6     CA7     CA8
## Eigenvalue            0.68475 0.65732 0.56467 0.53273 0.5243 0.46221 0.45089
## Proportion Explained  0.05747 0.05517 0.04739 0.04471 0.0440 0.03879 0.03784
## Cumulative Proportion 0.31914 0.37431 0.42170 0.46641 0.5104 0.54920 0.58704
##                           CA9    CA10    CA11    CA12    CA13    CA14    CA15
## Eigenvalue            0.41523 0.40304 0.36964 0.34403 0.29863 0.28856 0.27151
## Proportion Explained  0.03485 0.03383 0.03102 0.02887 0.02506 0.02422 0.02279
## Cumulative Proportion 0.62189 0.65572 0.68674 0.71561 0.74068 0.76489 0.78768
##                          CA16    CA17    CA18    CA19   CA20    CA21    CA22
## Eigenvalue            0.25202 0.24479 0.22774 0.20422 0.1919 0.17030 0.16365
## Proportion Explained  0.02115 0.02054 0.01911 0.01714 0.0161 0.01429 0.01373
## Cumulative Proportion 0.80883 0.82938 0.84849 0.86563 0.8817 0.89603 0.90976
##                          CA23    CA24    CA25     CA26     CA27    CA28
## Eigenvalue            0.15261 0.14625 0.12703 0.112969 0.098321 0.09377
## Proportion Explained  0.01281 0.01227 0.01066 0.009481 0.008252 0.00787
## Cumulative Proportion 0.92257 0.93484 0.94550 0.954985 0.963236 0.97111
##                           CA29    CA30     CA31     CA32     CA33     CA34
## Eigenvalue            0.080200 0.07519 0.057766 0.053407 0.051623 0.026087
## Proportion Explained  0.006731 0.00631 0.004848 0.004482 0.004333 0.002189
## Cumulative Proportion 0.977837 0.98415 0.988996 0.993478 0.997811 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6
## Eigenvalue            0.6719 0.5199 0.3877 0.3434 0.2505 0.20285
## Proportion Explained  0.2827 0.2188 0.1632 0.1445 0.1054 0.08536
## Cumulative Proportion 0.2827 0.5015 0.6647 0.8092 0.9146 1.00000
anova(Plant_CCA_Chem6.3)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + Fe2O3 + CaO + SrO + K2O, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     6    2.3763 1.4116  0.001 ***
## Residual 34    9.5389                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4116, p value of 0.001

Plant_CCA_Chem6.4 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + SrO + K2O, 
data = PlantChemistry)

plot(Plant_CCA_Chem6.4)

summary(Plant_CCA_Chem6.4)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + SrO + K2O,      data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.421     0.2031
## Unconstrained   9.495     0.7969
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4   CCA5    CCA6     CA1
## Eigenvalue            0.67211 0.53559 0.39184 0.32871 0.2872 0.20510 0.74179
## Proportion Explained  0.05641 0.04495 0.03289 0.02759 0.0241 0.01721 0.06226
## Cumulative Proportion 0.05641 0.10136 0.13424 0.16183 0.1859 0.20315 0.26540
##                           CA2     CA3     CA4     CA5     CA6     CA7    CA8
## Eigenvalue            0.68259 0.65814 0.55451 0.53529 0.51313 0.45212 0.4206
## Proportion Explained  0.05729 0.05524 0.04654 0.04492 0.04307 0.03795 0.0353
## Cumulative Proportion 0.32269 0.37792 0.42446 0.46939 0.51245 0.55040 0.5857
##                           CA9    CA10    CA11    CA12    CA13    CA14    CA15
## Eigenvalue            0.41881 0.40348 0.37645 0.34577 0.30011 0.28993 0.27108
## Proportion Explained  0.03515 0.03386 0.03159 0.02902 0.02519 0.02433 0.02275
## Cumulative Proportion 0.62085 0.65471 0.68630 0.71532 0.74051 0.76484 0.78759
##                          CA16    CA17    CA18    CA19    CA20    CA21    CA22
## Eigenvalue            0.25185 0.24650 0.22919 0.20553 0.19160 0.17068 0.16331
## Proportion Explained  0.02114 0.02069 0.01924 0.01725 0.01608 0.01432 0.01371
## Cumulative Proportion 0.80873 0.82942 0.84865 0.86590 0.88198 0.89631 0.91001
##                          CA23   CA24    CA25     CA26     CA27     CA28
## Eigenvalue            0.15207 0.1489 0.12723 0.112333 0.098435 0.096695
## Proportion Explained  0.01276 0.0125 0.01068 0.009428 0.008261 0.008115
## Cumulative Proportion 0.92278 0.9353 0.94595 0.955377 0.963639 0.971754
##                           CA29     CA30     CA31     CA32     CA33     CA34
## Eigenvalue            0.076198 0.074787 0.056641 0.053319 0.049622 0.025988
## Proportion Explained  0.006395 0.006277 0.004754 0.004475 0.004165 0.002181
## Cumulative Proportion 0.978149 0.984426 0.989179 0.993654 0.997819 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6
## Eigenvalue            0.6721 0.5356 0.3918 0.3287 0.2872 0.20510
## Proportion Explained  0.2777 0.2213 0.1619 0.1358 0.1186 0.08473
## Cumulative Proportion 0.2777 0.4989 0.6608 0.7966 0.9153 1.00000
anova(Plant_CCA_Chem6.4)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + SrO + K2O, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     6    2.4205 1.4446  0.001 ***
## Residual 34    9.4947                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4446, p value of 0.001

Plant_CCA_Chem6.5 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + S + K2O, 
data = PlantChemistry)
plot(Plant_CCA_Chem6.5)

summary(Plant_CCA_Chem6.5)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + S + K2O,      data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.426     0.2036
## Unconstrained   9.489     0.7964
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6     CA1
## Eigenvalue            0.66957 0.53290 0.39979 0.34537 0.31078 0.16751 0.74120
## Proportion Explained  0.05619 0.04472 0.03355 0.02899 0.02608 0.01406 0.06221
## Cumulative Proportion 0.05619 0.10092 0.13447 0.16346 0.18954 0.20360 0.26581
##                           CA2     CA3    CA4     CA5     CA6     CA7     CA8
## Eigenvalue            0.68218 0.65665 0.5851 0.53674 0.50016 0.44234 0.42009
## Proportion Explained  0.05725 0.05511 0.0491 0.04505 0.04198 0.03712 0.03526
## Cumulative Proportion 0.32306 0.37817 0.4273 0.47232 0.51430 0.55142 0.58668
##                           CA9    CA10    CA11    CA12   CA13    CA14    CA15
## Eigenvalue            0.40666 0.39156 0.37745 0.33056 0.3074 0.28818 0.27210
## Proportion Explained  0.03413 0.03286 0.03168 0.02774 0.0258 0.02419 0.02284
## Cumulative Proportion 0.62081 0.65367 0.68535 0.71309 0.7389 0.76308 0.78591
##                          CA16    CA17    CA18    CA19   CA20    CA21    CA22
## Eigenvalue            0.26705 0.23929 0.22535 0.20478 0.1942 0.18487 0.16245
## Proportion Explained  0.02241 0.02008 0.01891 0.01719 0.0163 0.01552 0.01363
## Cumulative Proportion 0.80832 0.82841 0.84732 0.86451 0.8808 0.89632 0.90996
##                          CA23    CA24    CA25    CA26    CA27     CA28     CA29
## Eigenvalue            0.15857 0.14961 0.13268 0.12098 0.10568 0.093755 0.074928
## Proportion Explained  0.01331 0.01256 0.01114 0.01015 0.00887 0.007869 0.006288
## Cumulative Proportion 0.92327 0.93582 0.94696 0.95711 0.96598 0.973848 0.980136
##                           CA30     CA31     CA32     CA33     CA34
## Eigenvalue            0.064833 0.059530 0.050787 0.042218 0.019313
## Proportion Explained  0.005441 0.004996 0.004262 0.003543 0.001621
## Cumulative Proportion 0.985577 0.990574 0.994836 0.998379 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6
## Eigenvalue            0.6696 0.5329 0.3998 0.3454 0.3108 0.16751
## Proportion Explained  0.2760 0.2197 0.1648 0.1424 0.1281 0.06905
## Cumulative Proportion 0.2760 0.4957 0.6605 0.8028 0.9310 1.00000
anova(Plant_CCA_Chem6.5)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + S + K2O, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     6    2.4259 1.4487  0.001 ***
## Residual 34    9.4893                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4487, p value of 0.001

Plant_CCA_Chem6.5 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O, data = 
PlantChemistry)

plot(Plant_CCA_Chem6.5)

summary(Plant_CCA_Chem6.5)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O,      data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915        1.0
## Constrained     2.383        0.2
## Unconstrained   9.532        0.8
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6     CA1
## Eigenvalue            0.67370 0.53683 0.39668 0.32544 0.25798 0.19251 0.74167
## Proportion Explained  0.05654 0.04505 0.03329 0.02731 0.02165 0.01616 0.06225
## Cumulative Proportion 0.05654 0.10160 0.13489 0.16220 0.18385 0.20001 0.26225
##                           CA2     CA3     CA4     CA5     CA6     CA7    CA8
## Eigenvalue            0.68466 0.64723 0.57808 0.53692 0.49032 0.45570 0.4218
## Proportion Explained  0.05746 0.05432 0.04852 0.04506 0.04115 0.03825 0.0354
## Cumulative Proportion 0.31972 0.37403 0.42255 0.46761 0.50876 0.54701 0.5824
##                           CA9    CA10    CA11    CA12    CA13   CA14    CA15
## Eigenvalue            0.41161 0.40405 0.37934 0.32658 0.31469 0.2872 0.28156
## Proportion Explained  0.03455 0.03391 0.03184 0.02741 0.02641 0.0241 0.02363
## Cumulative Proportion 0.61695 0.65086 0.68270 0.71011 0.73652 0.7606 0.78425
##                          CA16    CA17    CA18    CA19    CA20   CA21   CA22
## Eigenvalue            0.25324 0.24731 0.21728 0.20788 0.19452 0.1871 0.1633
## Proportion Explained  0.02125 0.02076 0.01824 0.01745 0.01633 0.0157 0.0137
## Cumulative Proportion 0.80551 0.82626 0.84450 0.86195 0.87827 0.8940 0.9077
##                          CA23    CA24    CA25     CA26     CA27     CA28
## Eigenvalue            0.16217 0.15203 0.12842 0.117823 0.111618 0.096592
## Proportion Explained  0.01361 0.01276 0.01078 0.009888 0.009368 0.008107
## Cumulative Proportion 0.92129 0.93405 0.94482 0.954713 0.964081 0.972188
##                           CA29     CA30     CA31     CA32     CA33     CA34
## Eigenvalue            0.082024 0.074693 0.056649 0.053778 0.044759 0.019486
## Proportion Explained  0.006884 0.006269 0.004754 0.004513 0.003757 0.001635
## Cumulative Proportion 0.979072 0.985340 0.990095 0.994608 0.998365 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6
## Eigenvalue            0.6737 0.5368 0.3967 0.3254 0.2580 0.19251
## Proportion Explained  0.2827 0.2253 0.1665 0.1366 0.1083 0.08078
## Cumulative Proportion 0.2827 0.5080 0.6744 0.8110 0.9192 1.00000
anova(Plant_CCA_Chem6.5)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     6    2.3831 1.4167  0.001 ***
## Residual 34    9.5320                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4167, p value of 0.001

Plant_CCA_Chem7 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O, 
data = PlantChemistry)

plot(Plant_CCA_Chem7)

summary(Plant_CCA_Chem7)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O +      Na2O, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.784     0.2336
## Unconstrained   9.131     0.7664
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5   CCA6    CCA7
## Eigenvalue            0.67597 0.55216 0.41151 0.38813 0.31736 0.2490 0.18967
## Proportion Explained  0.05673 0.04634 0.03454 0.03257 0.02663 0.0209 0.01592
## Cumulative Proportion 0.05673 0.10307 0.13761 0.17018 0.19682 0.2177 0.23364
##                           CA1     CA2     CA3     CA4     CA5     CA6     CA7
## Eigenvalue            0.74146 0.66736 0.63538 0.56760 0.50076 0.47533 0.45320
## Proportion Explained  0.06223 0.05601 0.05333 0.04764 0.04203 0.03989 0.03804
## Cumulative Proportion 0.29587 0.35187 0.40520 0.45284 0.49486 0.53476 0.57279
##                           CA8     CA9    CA10    CA11    CA12    CA13    CA14
## Eigenvalue            0.41176 0.40656 0.38256 0.33833 0.32023 0.30939 0.28709
## Proportion Explained  0.03456 0.03412 0.03211 0.02839 0.02688 0.02597 0.02409
## Cumulative Proportion 0.60735 0.64147 0.67358 0.70197 0.72885 0.75481 0.77891
##                          CA15    CA16    CA17    CA18    CA19    CA20    CA21
## Eigenvalue            0.26443 0.25186 0.21769 0.20869 0.20463 0.19158 0.16671
## Proportion Explained  0.02219 0.02114 0.01827 0.01751 0.01717 0.01608 0.01399
## Cumulative Proportion 0.80110 0.82224 0.84051 0.85802 0.87520 0.89128 0.90527
##                          CA22    CA23    CA24     CA25   CA26     CA27     CA28
## Eigenvalue            0.16306 0.15391 0.13113 0.118251 0.1156 0.099443 0.084853
## Proportion Explained  0.01369 0.01292 0.01101 0.009924 0.0097 0.008346 0.007121
## Cumulative Proportion 0.91895 0.93187 0.94287 0.952799 0.9625 0.970845 0.977967
##                           CA29     CA30     CA31     CA32     CA33
## Eigenvalue            0.081960 0.057774 0.054370 0.048567 0.019858
## Proportion Explained  0.006879 0.004849 0.004563 0.004076 0.001667
## Cumulative Proportion 0.984845 0.989694 0.994257 0.998333 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.6760 0.5522 0.4115 0.3881 0.3174 0.24903 0.18967
## Proportion Explained  0.2428 0.1983 0.1478 0.1394 0.1140 0.08946 0.06813
## Cumulative Proportion 0.2428 0.4412 0.5890 0.7284 0.8424 0.93187 1.00000
anova(Plant_CCA_Chem7)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     7    2.7838 1.4372  0.001 ***
## Residual 33    9.1313                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4372, p value of 0.001

Plant_CCA_Chem8 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O +
SiO2, data = PlantChemistry)

plot(Plant_CCA_Chem8)

summary(Plant_CCA_Chem8)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O +      Na2O + SiO2, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     3.130     0.2627
## Unconstrained   8.785     0.7373
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2   CCA3    CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.67598 0.58272 0.4134 0.38864 0.3456 0.31717 0.22803
## Proportion Explained  0.05673 0.04891 0.0347 0.03262 0.0290 0.02662 0.01914
## Cumulative Proportion 0.05673 0.10564 0.1403 0.17295 0.2020 0.22858 0.24771
##                          CCA8    CA1     CA2    CA3    CA4     CA5     CA6
## Eigenvalue            0.17821 0.7268 0.66115 0.6339 0.5672 0.47986 0.46065
## Proportion Explained  0.01496 0.0610 0.05549 0.0532 0.0476 0.04027 0.03866
## Cumulative Proportion 0.26267 0.3237 0.37915 0.4324 0.4800 0.52023 0.55889
##                           CA7     CA8     CA9    CA10    CA11    CA12   CA13
## Eigenvalue            0.45319 0.40669 0.38513 0.35903 0.32200 0.31503 0.3003
## Proportion Explained  0.03803 0.03413 0.03232 0.03013 0.02702 0.02644 0.0252
## Cumulative Proportion 0.59693 0.63106 0.66338 0.69351 0.72054 0.74698 0.7722
##                          CA14    CA15    CA16    CA17    CA18    CA19    CA20
## Eigenvalue            0.27381 0.25916 0.24012 0.21084 0.20789 0.19166 0.17352
## Proportion Explained  0.02298 0.02175 0.02015 0.01769 0.01745 0.01608 0.01456
## Cumulative Proportion 0.79516 0.81691 0.83706 0.85476 0.87220 0.88829 0.90285
##                          CA21    CA22    CA23    CA24    CA25   CA26    CA27
## Eigenvalue            0.16434 0.15952 0.13117 0.12916 0.11629 0.1013 0.08603
## Proportion Explained  0.01379 0.01339 0.01101 0.01084 0.00976 0.0085 0.00722
## Cumulative Proportion 0.91664 0.93003 0.94104 0.95188 0.96164 0.9701 0.97736
##                           CA28     CA29     CA30     CA31     CA32
## Eigenvalue            0.082493 0.061051 0.054681 0.049216 0.022314
## Proportion Explained  0.006923 0.005124 0.004589 0.004131 0.001873
## Cumulative Proportion 0.984284 0.989407 0.993997 0.998127 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                        CCA1   CCA2   CCA3   CCA4   CCA5   CCA6    CCA7    CCA8
## Eigenvalue            0.676 0.5827 0.4134 0.3886 0.3456 0.3172 0.22803 0.17821
## Proportion Explained  0.216 0.1862 0.1321 0.1242 0.1104 0.1013 0.07286 0.05694
## Cumulative Proportion 0.216 0.4022 0.5343 0.6584 0.7689 0.8702 0.94306 1.00000
anova(Plant_CCA_Chem8)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O + SiO2, data = PlantChemistry)
##          Df ChiSquare     F Pr(>F)    
## Model     8    3.1298 1.425  0.001 ***
## Residual 32    8.7854                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.425, p value of 0.001

Plant_CCA_Chem9 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O +
                         BaO, data = PlantChemistry)

plot(Plant_CCA_Chem9)

summary(Plant_CCA_Chem9)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O +      Na2O + BaO, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915      1.000
## Constrained     3.062      0.257
## Unconstrained   8.853      0.743
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3   CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.67599 0.57025 0.41514 0.3896 0.33699 0.27554 0.21490
## Proportion Explained  0.05673 0.04786 0.03484 0.0327 0.02828 0.02312 0.01804
## Cumulative Proportion 0.05673 0.10459 0.13943 0.1721 0.20042 0.22354 0.24158
##                          CCA8     CA1    CA2     CA3     CA4     CA5     CA6
## Eigenvalue            0.18404 0.73947 0.6637 0.63353 0.56589 0.49146 0.47522
## Proportion Explained  0.01545 0.06206 0.0557 0.05317 0.04749 0.04125 0.03988
## Cumulative Proportion 0.25702 0.31909 0.3748 0.42796 0.47545 0.51670 0.55658
##                           CA7     CA8     CA9    CA10    CA11    CA12    CA13
## Eigenvalue            0.44848 0.41165 0.40604 0.36930 0.33459 0.31031 0.29162
## Proportion Explained  0.03764 0.03455 0.03408 0.03099 0.02808 0.02604 0.02448
## Cumulative Proportion 0.59422 0.62877 0.66284 0.69384 0.72192 0.74796 0.77244
##                          CA14    CA15   CA16    CA17    CA18    CA19    CA20
## Eigenvalue            0.27273 0.25661 0.2240 0.21541 0.20655 0.20176 0.16691
## Proportion Explained  0.02289 0.02154 0.0188 0.01808 0.01734 0.01693 0.01401
## Cumulative Proportion 0.79533 0.81686 0.8357 0.85374 0.87107 0.88801 0.90201
##                          CA21    CA22    CA23    CA24     CA25    CA26     CA27
## Eigenvalue            0.16377 0.16251 0.13373 0.12294 0.116095 0.10521 0.092032
## Proportion Explained  0.01375 0.01364 0.01122 0.01032 0.009743 0.00883 0.007724
## Cumulative Proportion 0.91576 0.92940 0.94062 0.95094 0.960683 0.96951 0.977237
##                          CA28    CA29     CA30     CA31     CA32
## Eigenvalue            0.08198 0.05779 0.055535 0.049133 0.026791
## Proportion Explained  0.00688 0.00485 0.004661 0.004124 0.002248
## Cumulative Proportion 0.98412 0.98897 0.993628 0.997752 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.6760 0.5703 0.4151 0.3896 0.3370 0.27554 0.21490
## Proportion Explained  0.2207 0.1862 0.1356 0.1272 0.1100 0.08997 0.07017
## Cumulative Proportion 0.2207 0.4069 0.5425 0.6697 0.7798 0.86974 0.93991
##                          CCA8
## Eigenvalue            0.18404
## Proportion Explained  0.06009
## Cumulative Proportion 1.00000
anova(Plant_CCA_Chem9)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O + BaO, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     8    3.0625 1.3838  0.001 ***
## Residual 32    8.8527                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.3838, p value of 0.001

Plant_CCA_Chem10 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O +
                          Cu, data = PlantChemistry)

plot(Plant_CCA_Chem10)

summary(Plant_CCA_Chem10)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O +      Na2O + Cu, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     3.136     0.2632
## Unconstrained   8.780     0.7368
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.67789 0.56069 0.45214 0.41072 0.35892 0.31135 0.19242
## Proportion Explained  0.05689 0.04706 0.03795 0.03447 0.03012 0.02613 0.01615
## Cumulative Proportion 0.05689 0.10395 0.14190 0.17637 0.20649 0.23262 0.24877
##                         CCA8     CA1     CA2     CA3     CA4     CA5     CA6
## Eigenvalue            0.1715 0.72511 0.66691 0.63538 0.54023 0.47599 0.46291
## Proportion Explained  0.0144 0.06086 0.05597 0.05333 0.04534 0.03995 0.03885
## Cumulative Proportion 0.2632 0.32402 0.37999 0.43332 0.47866 0.51861 0.55746
##                           CA7     CA8    CA9    CA10    CA11    CA12    CA13
## Eigenvalue            0.42037 0.40656 0.3837 0.37944 0.33691 0.31583 0.30651
## Proportion Explained  0.03528 0.03412 0.0322 0.03185 0.02828 0.02651 0.02572
## Cumulative Proportion 0.59274 0.62686 0.6591 0.69090 0.71918 0.74569 0.77141
##                          CA14    CA15    CA16    CA17   CA18    CA19    CA20
## Eigenvalue            0.27632 0.25186 0.23485 0.21499 0.2085 0.20303 0.18423
## Proportion Explained  0.02319 0.02114 0.01971 0.01804 0.0175 0.01704 0.01546
## Cumulative Proportion 0.79460 0.81574 0.83545 0.85349 0.8710 0.88803 0.90349
##                          CA21    CA22    CA23    CA24     CA25     CA26
## Eigenvalue            0.16367 0.15684 0.13571 0.12000 0.115608 0.102677
## Proportion Explained  0.01374 0.01316 0.01139 0.01007 0.009703 0.008617
## Cumulative Proportion 0.91723 0.93039 0.94178 0.95185 0.961551 0.970169
##                           CA27     CA28     CA29    CA30     CA31    CA32
## Eigenvalue            0.085126 0.082489 0.063095 0.05565 0.048947 0.02014
## Proportion Explained  0.007144 0.006923 0.005295 0.00467 0.004108 0.00169
## Cumulative Proportion 0.977313 0.984236 0.989531 0.99420 0.998310 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7   CCA8
## Eigenvalue            0.6779 0.5607 0.4521 0.4107 0.3589 0.31135 0.19242 0.1715
## Proportion Explained  0.2162 0.1788 0.1442 0.1310 0.1145 0.09929 0.06137 0.0547
## Cumulative Proportion 0.2162 0.3950 0.5392 0.6702 0.7846 0.88393 0.94530 1.0000
anova(Plant_CCA_Chem10)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O + Cu, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     8    3.1357 1.4286  0.001 ***
## Residual 32    8.7795                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4286, p value of 0.001

Plant_CCA_Chem11 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O +
                          Cu + Calcite, data = PlantChemistry)
                        
plot(Plant_CCA_Chem11)

summary(Plant_CCA_Chem11)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O +      Na2O + Cu + Calcite, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     3.442     0.2889
## Unconstrained   8.473     0.7111
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.67988 0.56085 0.48487 0.41268 0.36950 0.31674 0.25647
## Proportion Explained  0.05706 0.04707 0.04069 0.03463 0.03101 0.02658 0.02152
## Cumulative Proportion 0.05706 0.10413 0.14482 0.17946 0.21047 0.23705 0.25858
##                          CCA8   CCA9     CA1     CA2     CA3     CA4     CA5
## Eigenvalue            0.18996 0.1715 0.71405 0.66689 0.63247 0.53605 0.47385
## Proportion Explained  0.01594 0.0144 0.05993 0.05597 0.05308 0.04499 0.03977
## Cumulative Proportion 0.27452 0.2889 0.34884 0.40481 0.45789 0.50288 0.54265
##                           CA6     CA7     CA8     CA9    CA10    CA11    CA12
## Eigenvalue            0.42403 0.40659 0.40371 0.38122 0.35663 0.33331 0.31296
## Proportion Explained  0.03559 0.03412 0.03388 0.03199 0.02993 0.02797 0.02627
## Cumulative Proportion 0.57824 0.61236 0.64624 0.67824 0.70817 0.73614 0.76241
##                          CA13   CA14    CA15    CA16    CA17    CA18    CA19
## Eigenvalue            0.27798 0.2538 0.24456 0.21517 0.20961 0.20303 0.18928
## Proportion Explained  0.02333 0.0213 0.02053 0.01806 0.01759 0.01704 0.01589
## Cumulative Proportion 0.78574 0.8070 0.82757 0.84563 0.86322 0.88026 0.89614
##                          CA20    CA21    CA22    CA23     CA24     CA25
## Eigenvalue            0.18025 0.16332 0.14845 0.12164 0.116862 0.113372
## Proportion Explained  0.01513 0.01371 0.01246 0.01021 0.009808 0.009515
## Cumulative Proportion 0.91127 0.92498 0.93744 0.94765 0.957453 0.966968
##                           CA26     CA27     CA28     CA29     CA30     CA31
## Eigenvalue            0.102186 0.082606 0.063206 0.055656 0.050502 0.039426
## Proportion Explained  0.008576 0.006933 0.005305 0.004671 0.004238 0.003309
## Cumulative Proportion 0.975544 0.982477 0.987782 0.992453 0.996691 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6   CCA7    CCA8
## Eigenvalue            0.6799 0.5608 0.4849 0.4127 0.3695 0.31674 0.2565 0.18996
## Proportion Explained  0.1975 0.1629 0.1408 0.1199 0.1073 0.09201 0.0745 0.05518
## Cumulative Proportion 0.1975 0.3604 0.5013 0.6211 0.7285 0.82049 0.8950 0.95017
##                          CCA9
## Eigenvalue            0.17153
## Proportion Explained  0.04983
## Cumulative Proportion 1.00000
anova(Plant_CCA_Chem11)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O + Cu + Calcite, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     9    3.4425 1.3995  0.001 ***
## Residual 31    8.4727                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.3995, p value of 0.001

Plant_CCA_Chem12 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O +
                          Cu + TiO2, data = PlantChemistry)

plot(Plant_CCA_Chem12)  

summary(Plant_CCA_Chem12)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O +      Na2O + Cu + TiO2, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     3.468     0.2911
## Unconstrained   8.447     0.7089
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2   CCA3    CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.68143 0.59994 0.4802 0.41497 0.37513 0.32983 0.25097
## Proportion Explained  0.05719 0.05035 0.0403 0.03483 0.03148 0.02768 0.02106
## Cumulative Proportion 0.05719 0.10754 0.1478 0.18267 0.21415 0.24183 0.26290
##                          CCA8    CCA9     CA1    CA2    CA3     CA4     CA5
## Eigenvalue            0.17410 0.16194 0.72436 0.6613 0.6256 0.53815 0.46291
## Proportion Explained  0.01461 0.01359 0.06079 0.0555 0.0525 0.04516 0.03885
## Cumulative Proportion 0.27751 0.29110 0.35189 0.4074 0.4599 0.50506 0.54391
##                           CA6     CA7     CA8     CA9    CA10    CA11    CA12
## Eigenvalue            0.44391 0.42021 0.40603 0.37991 0.36371 0.32553 0.30947
## Proportion Explained  0.03726 0.03527 0.03408 0.03188 0.03053 0.02732 0.02597
## Cumulative Proportion 0.58116 0.61643 0.65051 0.68239 0.71292 0.74024 0.76621
##                          CA13    CA14    CA15   CA16    CA17    CA18    CA19
## Eigenvalue            0.28081 0.26265 0.24457 0.2192 0.20913 0.20368 0.18925
## Proportion Explained  0.02357 0.02204 0.02053 0.0184 0.01755 0.01709 0.01588
## Cumulative Proportion 0.78978 0.81182 0.83235 0.8507 0.86830 0.88539 0.90127
##                          CA20    CA21    CA22    CA23    CA24     CA25     CA26
## Eigenvalue            0.16384 0.15708 0.13575 0.12338 0.11979 0.107430 0.085624
## Proportion Explained  0.01375 0.01318 0.01139 0.01036 0.01005 0.009016 0.007186
## Cumulative Proportion 0.91502 0.92821 0.93960 0.94995 0.96001 0.969024 0.976210
##                           CA27     CA28     CA29     CA30     CA31
## Eigenvalue            0.083023 0.064795 0.062993 0.049031 0.023616
## Proportion Explained  0.006968 0.005438 0.005287 0.004115 0.001982
## Cumulative Proportion 0.983178 0.988616 0.993903 0.998018 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7   CCA8
## Eigenvalue            0.6814 0.5999 0.4802 0.4150 0.3751 0.32983 0.25097 0.1741
## Proportion Explained  0.1965 0.1730 0.1384 0.1196 0.1082 0.09509 0.07236 0.0502
## Cumulative Proportion 0.1965 0.3694 0.5079 0.6275 0.7357 0.83076 0.90311 0.9533
##                          CCA9
## Eigenvalue            0.16194
## Proportion Explained  0.04669
## Cumulative Proportion 1.00000
anova(Plant_CCA_Chem12)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O + Cu + TiO2, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     9    3.4685 1.4144  0.001 ***
## Residual 31    8.4467                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4144, p value of 0.001

Plant_CCA_Chem13 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O +
                Cu + TiO2 + P2O5, data = PlantChemistry)

plot(Plant_CCA_Chem13)  

summary(Plant_CCA_Chem13)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O +      Na2O + Cu + TiO2 + P2O5, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     3.803     0.3192
## Unconstrained   8.112     0.6808
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.68669 0.61521 0.51182 0.44195 0.38047 0.34212 0.27119
## Proportion Explained  0.05763 0.05163 0.04296 0.03709 0.03193 0.02871 0.02276
## Cumulative Proportion 0.05763 0.10926 0.15222 0.18931 0.22124 0.24996 0.27272
##                          CCA8    CCA9   CCA10     CA1     CA2     CA3     CA4
## Eigenvalue            0.22265 0.17403 0.15685 0.71187 0.65912 0.61690 0.52127
## Proportion Explained  0.01869 0.01461 0.01316 0.05974 0.05532 0.05177 0.04375
## Cumulative Proportion 0.29140 0.30601 0.31917 0.37892 0.43423 0.48601 0.52976
##                           CA5     CA6     CA7     CA8     CA9    CA10    CA11
## Eigenvalue            0.45865 0.44243 0.41654 0.40291 0.36557 0.33104 0.32385
## Proportion Explained  0.03849 0.03713 0.03496 0.03381 0.03068 0.02778 0.02718
## Cumulative Proportion 0.56825 0.60538 0.64034 0.67415 0.70483 0.73262 0.75980
##                          CA12    CA13    CA14    CA15    CA16    CA17    CA18
## Eigenvalue            0.28191 0.26436 0.25575 0.22694 0.21060 0.20656 0.19021
## Proportion Explained  0.02366 0.02219 0.02146 0.01905 0.01767 0.01734 0.01596
## Cumulative Proportion 0.78346 0.80564 0.82711 0.84615 0.86383 0.88117 0.89713
##                          CA19    CA20    CA21    CA22    CA23     CA24     CA25
## Eigenvalue            0.18272 0.16382 0.13811 0.12381 0.12069 0.108122 0.094558
## Proportion Explained  0.01534 0.01375 0.01159 0.01039 0.01013 0.009074 0.007936
## Cumulative Proportion 0.91246 0.92621 0.93780 0.94820 0.95832 0.967399 0.975335
##                           CA26    CA27     CA28    CA29     CA30
## Eigenvalue            0.083182 0.07125 0.064610 0.05063 0.024215
## Proportion Explained  0.006981 0.00598 0.005423 0.00425 0.002032
## Cumulative Proportion 0.982316 0.98830 0.993718 0.99797 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.6867 0.6152 0.5118 0.4420 0.3805 0.34212 0.27119
## Proportion Explained  0.1806 0.1618 0.1346 0.1162 0.1000 0.08996 0.07131
## Cumulative Proportion 0.1806 0.3423 0.4769 0.5931 0.6932 0.78314 0.85445
##                          CCA8    CCA9   CCA10
## Eigenvalue            0.22265 0.17403 0.15685
## Proportion Explained  0.05855 0.04576 0.04124
## Cumulative Proportion 0.91300 0.95876 1.00000
anova(Plant_CCA_Chem13)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O + Cu + TiO2 + P2O5, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model    10    3.8030 1.4064  0.001 ***
## Residual 30    8.1122                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4064, p value of 0.001

Plant_CCA_Chem14 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O +
           Cu + TiO2 + P2O5 + Mo, data = PlantChemistry)

plot(Plant_CCA_Chem14)  

summary(Plant_CCA_Chem14)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O +      Na2O + Cu + TiO2 + P2O5 + Mo, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     4.249     0.3566
## Unconstrained   7.666     0.6434
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.70550 0.62013 0.54603 0.46523 0.43933 0.36368 0.32570
## Proportion Explained  0.05921 0.05205 0.04583 0.03905 0.03687 0.03052 0.02734
## Cumulative Proportion 0.05921 0.11126 0.15708 0.19613 0.23300 0.26352 0.29086
##                          CCA8    CCA9   CCA10   CCA11     CA1     CA2     CA3
## Eigenvalue            0.27087 0.19735 0.16264 0.15299 0.66934 0.61738 0.58965
## Proportion Explained  0.02273 0.01656 0.01365 0.01284 0.05618 0.05181 0.04949
## Cumulative Proportion 0.31359 0.33015 0.34380 0.35664 0.41282 0.46463 0.51412
##                           CA4     CA5     CA6     CA7     CA8     CA9   CA10
## Eigenvalue            0.51142 0.45610 0.42517 0.40772 0.36571 0.36014 0.3241
## Proportion Explained  0.04292 0.03828 0.03568 0.03422 0.03069 0.03023 0.0272
## Cumulative Proportion 0.55704 0.59532 0.63100 0.66522 0.69591 0.72614 0.7533
##                          CA11    CA12   CA13    CA14    CA15    CA16    CA17
## Eigenvalue            0.28533 0.26889 0.2586 0.23679 0.22685 0.21039 0.19412
## Proportion Explained  0.02395 0.02257 0.0217 0.01987 0.01904 0.01766 0.01629
## Cumulative Proportion 0.77729 0.79985 0.8216 0.84143 0.86047 0.87813 0.89442
##                          CA18    CA19    CA20    CA21    CA22     CA23     CA24
## Eigenvalue            0.18672 0.16485 0.13879 0.13273 0.12190 0.110381 0.094619
## Proportion Explained  0.01567 0.01384 0.01165 0.01114 0.01023 0.009264 0.007941
## Cumulative Proportion 0.91009 0.92392 0.93557 0.94671 0.95694 0.966205 0.974147
##                           CA25     CA26     CA27     CA28     CA29
## Eigenvalue            0.083437 0.077854 0.067524 0.053670 0.025563
## Proportion Explained  0.007003 0.006534 0.005667 0.004504 0.002145
## Cumulative Proportion 0.981149 0.987683 0.993350 0.997855 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.7055 0.6201 0.5460 0.4652 0.4393 0.36368 0.32570
## Proportion Explained  0.1660 0.1459 0.1285 0.1095 0.1034 0.08558 0.07665
## Cumulative Proportion 0.1660 0.3120 0.4404 0.5499 0.6533 0.73890 0.81554
##                          CCA8    CCA9   CCA10 CCA11
## Eigenvalue            0.27087 0.19735 0.16264 0.153
## Proportion Explained  0.06374 0.04644 0.03827 0.036
## Cumulative Proportion 0.87929 0.92573 0.96400 1.000
anova(Plant_CCA_Chem14)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O + Cu + TiO2 + P2O5 + Mo, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model    11    4.2494 1.4614  0.001 ***
## Residual 29    7.6657                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4614, p value of 0.001

Plant_CCA_Chem15 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O +
                          Cu + TiO2 + P2O5 + Mo + Ni, data = PlantChemistry)

plot(Plant_CCA_Chem15) 

summary(Plant_CCA_Chem15)
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O +      Na2O + Cu + TiO2 + P2O5 + Mo + Ni, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     4.588     0.3851
## Unconstrained   7.327     0.6149
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.71183 0.64202 0.55363 0.47675 0.43955 0.40567 0.34900
## Proportion Explained  0.05974 0.05388 0.04646 0.04001 0.03689 0.03405 0.02929
## Cumulative Proportion 0.05974 0.11362 0.16009 0.20010 0.23699 0.27104 0.30033
##                          CCA8    CCA9   CCA10   CCA11   CCA12     CA1     CA2
## Eigenvalue            0.29763 0.24213 0.17098 0.15781 0.14146 0.66303 0.61714
## Proportion Explained  0.02498 0.02032 0.01435 0.01324 0.01187 0.05565 0.05179
## Cumulative Proportion 0.32531 0.34563 0.35998 0.37322 0.38509 0.44074 0.49254
##                           CA3     CA4     CA5     CA6     CA7     CA8     CA9
## Eigenvalue            0.51295 0.49344 0.44763 0.40784 0.40176 0.36303 0.34883
## Proportion Explained  0.04305 0.04141 0.03757 0.03423 0.03372 0.03047 0.02928
## Cumulative Proportion 0.53559 0.57700 0.61457 0.64880 0.68251 0.71298 0.74226
##                          CA10    CA11    CA12    CA13    CA14    CA15    CA16
## Eigenvalue            0.30969 0.26900 0.25913 0.23977 0.22776 0.21310 0.20171
## Proportion Explained  0.02599 0.02258 0.02175 0.02012 0.01911 0.01788 0.01693
## Cumulative Proportion 0.76825 0.79083 0.81257 0.83270 0.85181 0.86970 0.88663
##                          CA17    CA18    CA19    CA20    CA21     CA22     CA23
## Eigenvalue            0.19252 0.18672 0.16414 0.13843 0.12492 0.118184 0.109612
## Proportion Explained  0.01616 0.01567 0.01378 0.01162 0.01048 0.009919 0.009199
## Cumulative Proportion 0.90278 0.91845 0.93223 0.94385 0.95433 0.964252 0.973451
##                           CA24     CA25     CA26     CA27     CA28
## Eigenvalue            0.084553 0.082986 0.068923 0.053673 0.026200
## Proportion Explained  0.007096 0.006965 0.005784 0.004505 0.002199
## Cumulative Proportion 0.980547 0.987512 0.993296 0.997801 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.7118 0.6420 0.5536 0.4768 0.4396 0.40567 0.34900
## Proportion Explained  0.1551 0.1399 0.1207 0.1039 0.0958 0.08841 0.07606
## Cumulative Proportion 0.1551 0.2951 0.4157 0.5196 0.6154 0.70382 0.77988
##                          CCA8    CCA9   CCA10   CCA11   CCA12
## Eigenvalue            0.29763 0.24213 0.17098 0.15781 0.14146
## Proportion Explained  0.06486 0.05277 0.03726 0.03439 0.03083
## Cumulative Proportion 0.84474 0.89751 0.93478 0.96917 1.00000
anova(Plant_CCA_Chem15)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O + Cu + TiO2 + P2O5 + Mo + Ni, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model    12    4.5885 1.4613  0.001 ***
## Residual 28    7.3267                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4613, p value of 0.001

Plant_CCA_Chem16 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O +
              Cu + TiO2 + P2O5 + Mo + Ni + Pb, data = PlantChemistry)

plot(Plant_CCA_Chem16) 

summary(Plant_CCA_Chem16) 
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O +      Na2O + Cu + TiO2 + P2O5 + Mo + Ni + Pb, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     4.942     0.4147
## Unconstrained   6.973     0.5853
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5   CCA6    CCA7
## Eigenvalue            0.71191 0.64376 0.55547 0.50120 0.43960 0.4063 0.36058
## Proportion Explained  0.05975 0.05403 0.04662 0.04206 0.03689 0.0341 0.03026
## Cumulative Proportion 0.05975 0.11378 0.16040 0.20246 0.23935 0.2735 0.30372
##                          CCA8    CCA9   CCA10   CCA11   CCA12   CCA13     CA1
## Eigenvalue            0.34700 0.27796 0.23251 0.16913 0.15780 0.13855 0.64607
## Proportion Explained  0.02912 0.02333 0.01951 0.01419 0.01324 0.01163 0.05422
## Cumulative Proportion 0.33284 0.35617 0.37568 0.38988 0.40312 0.41475 0.46897
##                          CA2     CA3     CA4     CA5     CA6     CA7     CA8
## Eigenvalue            0.5839 0.51274 0.49224 0.44729 0.40226 0.38189 0.35106
## Proportion Explained  0.0490 0.04303 0.04131 0.03754 0.03376 0.03205 0.02946
## Cumulative Proportion 0.5180 0.56101 0.60232 0.63986 0.67362 0.70567 0.73513
##                           CA9   CA10    CA11    CA12    CA13    CA14    CA15
## Eigenvalue            0.31622 0.2872 0.26227 0.24085 0.22804 0.21311 0.20184
## Proportion Explained  0.02654 0.0241 0.02201 0.02021 0.01914 0.01789 0.01694
## Cumulative Proportion 0.76167 0.7858 0.80779 0.82800 0.84714 0.86502 0.88196
##                          CA16   CA17    CA18    CA19   CA20   CA21     CA22
## Eigenvalue            0.19710 0.1871 0.16910 0.14846 0.1370 0.1240 0.112020
## Proportion Explained  0.01654 0.0157 0.01419 0.01246 0.0115 0.0104 0.009401
## Cumulative Proportion 0.89851 0.9142 0.92840 0.94086 0.9524 0.9628 0.972166
##                           CA23    CA24     CA25     CA26     CA27
## Eigenvalue            0.092140 0.08341 0.073482 0.053835 0.028783
## Proportion Explained  0.007733 0.00700 0.006167 0.004518 0.002416
## Cumulative Proportion 0.979899 0.98690 0.993066 0.997584 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.7119 0.6438 0.5555 0.5012 0.43960 0.40629 0.36058
## Proportion Explained  0.1441 0.1303 0.1124 0.1014 0.08896 0.08222 0.07297
## Cumulative Proportion 0.1441 0.2743 0.3867 0.4882 0.57711 0.65933 0.73229
##                          CCA8    CCA9   CCA10   CCA11   CCA12   CCA13
## Eigenvalue            0.34700 0.27796 0.23251 0.16913 0.15780 0.13855
## Proportion Explained  0.07022 0.05625 0.04705 0.03423 0.03193 0.02804
## Cumulative Proportion 0.80251 0.85876 0.90581 0.94003 0.97196 1.00000
anova(Plant_CCA_Chem16) 
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O + Cu + TiO2 + P2O5 + Mo + Ni + Pb, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model    13    4.9418 1.4718  0.001 ***
## Residual 27    6.9734                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4718, p value of 0.001

Plant_CCA_Chem17 <- cca(PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O +
                     Cu + TiO2 + P2O5 + Mo + Ni + Sc, data = PlantChemistry)

plot(Plant_CCA_Chem17) 

summary(Plant_CCA_Chem17) 
## 
## Call:
## cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O +      Na2O + Cu + TiO2 + P2O5 + Mo + Ni + Sc, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     4.832     0.4055
## Unconstrained   7.083     0.5945
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2   CCA3    CCA4    CCA5    CCA6   CCA7
## Eigenvalue            0.72629 0.64265 0.5648 0.50155 0.44979 0.42552 0.3646
## Proportion Explained  0.06096 0.05394 0.0474 0.04209 0.03775 0.03571 0.0306
## Cumulative Proportion 0.06096 0.11489 0.1623 0.20438 0.24213 0.27785 0.3084
##                          CCA8    CCA9   CCA10   CCA11   CCA12    CCA13     CA1
## Eigenvalue            0.29879 0.25525 0.18369 0.16258 0.15477 0.101453 0.65116
## Proportion Explained  0.02508 0.02142 0.01542 0.01365 0.01299 0.008515 0.05465
## Cumulative Proportion 0.33353 0.35495 0.37036 0.38401 0.39700 0.405513 0.46016
##                           CA2     CA3     CA4     CA5     CA6     CA7    CA8
## Eigenvalue            0.61699 0.51059 0.46813 0.44695 0.40567 0.39524 0.3622
## Proportion Explained  0.05178 0.04285 0.03929 0.03751 0.03405 0.03317 0.0304
## Cumulative Proportion 0.51194 0.55480 0.59408 0.63160 0.66564 0.69881 0.7292
##                           CA9    CA10    CA11    CA12    CA13    CA14    CA15
## Eigenvalue            0.34689 0.29950 0.26731 0.25875 0.23912 0.22540 0.21099
## Proportion Explained  0.02911 0.02514 0.02243 0.02172 0.02007 0.01892 0.01771
## Cumulative Proportion 0.75833 0.78346 0.80590 0.82761 0.84768 0.86660 0.88431
##                          CA16    CA17   CA18    CA19    CA20     CA21     CA22
## Eigenvalue            0.19256 0.18814 0.1644 0.14277 0.12618 0.118604 0.110352
## Proportion Explained  0.01616 0.01579 0.0138 0.01198 0.01059 0.009954 0.009261
## Cumulative Proportion 0.90047 0.91626 0.9301 0.94204 0.95263 0.962581 0.971843
##                           CA23     CA24     CA25     CA26     CA27
## Eigenvalue            0.098136 0.083573 0.070802 0.054399 0.028590
## Proportion Explained  0.008236 0.007014 0.005942 0.004566 0.002399
## Cumulative Proportion 0.980079 0.987093 0.993035 0.997601 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.7263 0.6426 0.5648 0.5016 0.44979 0.42552 0.36463
## Proportion Explained  0.1503 0.1330 0.1169 0.1038 0.09309 0.08807 0.07547
## Cumulative Proportion 0.1503 0.2833 0.4002 0.5040 0.59710 0.68517 0.76064
##                          CCA8    CCA9   CCA10   CCA11   CCA12  CCA13
## Eigenvalue            0.29879 0.25525 0.18369 0.16258 0.15477 0.1015
## Proportion Explained  0.06184 0.05283 0.03802 0.03365 0.03203 0.0210
## Cumulative Proportion 0.82248 0.87531 0.91332 0.94697 0.97900 1.0000
anova(Plant_CCA_Chem17)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + Al2O3 + V + CaO + Co + K2O + Na2O + Cu + TiO2 + P2O5 + Mo + Ni + Sc, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model    13    4.8318 1.4167  0.001 ***
## Residual 27    7.0834                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4167, p value of 0.001

Plant_CCA_Chem17.1 <- cca(PlantSpecies ~ pH + P2O5 +SiO2 + Al2O3, data = PlantChemistry)

plot(Plant_CCA_Chem17.1) 

summary(Plant_CCA_Chem17.1) 
## 
## Call:
## cca(formula = PlantSpecies ~ pH + P2O5 + SiO2 + Al2O3, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           11.92     1.0000
## Constrained      1.88     0.1578
## Unconstrained   10.04     0.8422
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3   CCA4     CA1    CA2     CA3
## Eigenvalue            0.65252 0.48498 0.39111 0.3515 0.72539 0.7018 0.67461
## Proportion Explained  0.05476 0.04070 0.03282 0.0295 0.06088 0.0589 0.05662
## Cumulative Proportion 0.05476 0.09547 0.12829 0.1578 0.21867 0.2776 0.33418
##                           CA4     CA5     CA6     CA7     CA8    CA9    CA10
## Eigenvalue            0.60542 0.56604 0.53181 0.46156 0.45286 0.4194 0.40772
## Proportion Explained  0.05081 0.04751 0.04463 0.03874 0.03801 0.0352 0.03422
## Cumulative Proportion 0.38499 0.43250 0.47713 0.51587 0.55388 0.5891 0.62330
##                          CA11    CA12    CA13    CA14    CA15    CA16    CA17
## Eigenvalue            0.36319 0.33783 0.31977 0.30047 0.28576 0.27222 0.25484
## Proportion Explained  0.03048 0.02835 0.02684 0.02522 0.02398 0.02285 0.02139
## Cumulative Proportion 0.65378 0.68213 0.70897 0.73419 0.75817 0.78102 0.80240
##                          CA18    CA19   CA20    CA21   CA22    CA23    CA24
## Eigenvalue            0.23298 0.21587 0.2073 0.19815 0.1918 0.17379 0.16156
## Proportion Explained  0.01955 0.01812 0.0174 0.01663 0.0161 0.01459 0.01356
## Cumulative Proportion 0.82196 0.84007 0.8575 0.87410 0.8902 0.90478 0.91834
##                          CA25    CA26     CA27     CA28     CA29     CA30
## Eigenvalue            0.15308 0.12438 0.118993 0.113709 0.091497 0.084993
## Proportion Explained  0.01285 0.01044 0.009987 0.009543 0.007679 0.007133
## Cumulative Proportion 0.93119 0.94163 0.951615 0.961158 0.968837 0.975971
##                           CA31     CA32     CA33     CA34     CA35     CA36
## Eigenvalue            0.070946 0.061773 0.056059 0.049024 0.030681 0.017831
## Proportion Explained  0.005954 0.005184 0.004705 0.004114 0.002575 0.001497
## Cumulative Proportion 0.981925 0.987109 0.991814 0.995929 0.998503 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1  CCA2   CCA3   CCA4
## Eigenvalue            0.6525 0.485 0.3911 0.3515
## Proportion Explained  0.3471 0.258 0.2080 0.1869
## Cumulative Proportion 0.3471 0.605 0.8131 1.0000
anova(Plant_CCA_Chem17.1)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + P2O5 + SiO2 + Al2O3, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     4    1.8801 1.6861  0.001 ***
## Residual 36   10.0351                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.6861, p value of 0.001

Plant_CCA_Chem17.2 <- cca(PlantSpecies ~ pH + P2O5 +SiO2 + Al2O3 + 
                          V, data = PlantChemistry)

plot(Plant_CCA_Chem17.2) 

summary(Plant_CCA_Chem17.2) 
## 
## Call:
## cca(formula = PlantSpecies ~ pH + P2O5 + SiO2 + Al2O3 + V, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.142     0.1798
## Unconstrained   9.773     0.8202
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1    CCA2    CCA3    CCA4   CCA5     CA1     CA2
## Eigenvalue            0.6637 0.48605 0.39118 0.35188 0.2490 0.71987 0.70099
## Proportion Explained  0.0557 0.04079 0.03283 0.02953 0.0209 0.06042 0.05883
## Cumulative Proportion 0.0557 0.09650 0.12933 0.15886 0.1798 0.24017 0.29901
##                           CA3     CA4     CA5     CA6     CA7     CA8    CA9
## Eigenvalue            0.65646 0.57632 0.55174 0.52203 0.45888 0.44818 0.4194
## Proportion Explained  0.05509 0.04837 0.04631 0.04381 0.03851 0.03761 0.0352
## Cumulative Proportion 0.35410 0.40247 0.44877 0.49259 0.53110 0.56871 0.6039
##                          CA10    CA11   CA12    CA13    CA14    CA15    CA16
## Eigenvalue            0.40459 0.36137 0.3372 0.31843 0.29449 0.27827 0.27205
## Proportion Explained  0.03396 0.03033 0.0283 0.02672 0.02472 0.02335 0.02283
## Cumulative Proportion 0.63787 0.66819 0.6965 0.72322 0.74794 0.77129 0.79412
##                          CA17   CA18    CA19    CA20   CA21    CA22    CA23
## Eigenvalue            0.25189 0.2264 0.21232 0.20485 0.1918 0.17866 0.16642
## Proportion Explained  0.02114 0.0190 0.01782 0.01719 0.0161 0.01499 0.01397
## Cumulative Proportion 0.81526 0.8343 0.85209 0.86928 0.8854 0.90037 0.91434
##                          CA24   CA25    CA26     CA27    CA28     CA29     CA30
## Eigenvalue            0.15362 0.1466 0.12238 0.117509 0.09484 0.089906 0.071314
## Proportion Explained  0.01289 0.0123 0.01027 0.009862 0.00796 0.007546 0.005985
## Cumulative Proportion 0.92723 0.9395 0.94980 0.959663 0.96762 0.975168 0.981154
##                           CA31     CA32     CA33    CA34     CA35
## Eigenvalue            0.061799 0.056081 0.049759 0.03908 0.017835
## Proportion Explained  0.005187 0.004707 0.004176 0.00328 0.001497
## Cumulative Proportion 0.986340 0.991047 0.995223 0.99850 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5
## Eigenvalue            0.6637 0.4860 0.3912 0.3519 0.2490
## Proportion Explained  0.3099 0.2269 0.1826 0.1643 0.1163
## Cumulative Proportion 0.3099 0.5368 0.7194 0.8837 1.0000
anova(Plant_CCA_Chem17.2)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + P2O5 + SiO2 + Al2O3 + V, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     5    2.1418 1.5341  0.001 ***
## Residual 35    9.7733                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.5341, p value of 0.001

Plant_CCA_Chem17.3 <- cca(PlantSpecies ~ pH + P2O5 +SiO2 + Al2O3 + 
                            Co, data = PlantChemistry)

plot(Plant_CCA_Chem17.3) 

summary(Plant_CCA_Chem17.3) 
## 
## Call:
## cca(formula = PlantSpecies ~ pH + P2O5 + SiO2 + Al2O3 + Co, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     2.132     0.1789
## Unconstrained   9.783     0.8211
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3   CCA4    CCA5     CA1     CA2
## Eigenvalue            0.65751 0.48527 0.42155 0.3515 0.21640 0.72388 0.70172
## Proportion Explained  0.05518 0.04073 0.03538 0.0295 0.01816 0.06075 0.05889
## Cumulative Proportion 0.05518 0.09591 0.13129 0.1608 0.17895 0.23970 0.29860
##                           CA3     CA4     CA5     CA6     CA7     CA8     CA9
## Eigenvalue            0.66269 0.57993 0.56532 0.51101 0.46122 0.44630 0.41725
## Proportion Explained  0.05562 0.04867 0.04745 0.04289 0.03871 0.03746 0.03502
## Cumulative Proportion 0.35421 0.40288 0.45033 0.49322 0.53193 0.56938 0.60440
##                         CA10    CA11    CA12    CA13    CA14    CA15   CA16
## Eigenvalue            0.4076 0.36314 0.32041 0.31519 0.29653 0.27957 0.2634
## Proportion Explained  0.0342 0.03048 0.02689 0.02645 0.02489 0.02346 0.0221
## Cumulative Proportion 0.6386 0.66908 0.69597 0.72243 0.74731 0.77078 0.7929
##                          CA17    CA18   CA19    CA20   CA21    CA22    CA23
## Eigenvalue            0.25482 0.21596 0.2121 0.19815 0.1978 0.18700 0.17375
## Proportion Explained  0.02139 0.01812 0.0178 0.01663 0.0166 0.01569 0.01458
## Cumulative Proportion 0.81426 0.83239 0.8502 0.86682 0.8834 0.89912 0.91370
##                          CA24    CA25    CA26     CA27     CA28     CA29
## Eigenvalue            0.15382 0.13600 0.12104 0.115419 0.106435 0.086197
## Proportion Explained  0.01291 0.01141 0.01016 0.009687 0.008933 0.007234
## Cumulative Proportion 0.92661 0.93802 0.94818 0.957869 0.966802 0.974036
##                           CA30     CA31     CA32     CA33     CA34     CA35
## Eigenvalue            0.080520 0.068821 0.056060 0.052084 0.032675 0.019202
## Proportion Explained  0.006758 0.005776 0.004705 0.004371 0.002742 0.001612
## Cumulative Proportion 0.980794 0.986570 0.991275 0.995646 0.998388 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5
## Eigenvalue            0.6575 0.4853 0.4216 0.3515 0.2164
## Proportion Explained  0.3084 0.2276 0.1977 0.1648 0.1015
## Cumulative Proportion 0.3084 0.5360 0.7337 0.8985 1.0000
anova(Plant_CCA_Chem17.3)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + P2O5 + SiO2 + Al2O3 + Co, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     5    2.1322 1.5257  0.001 ***
## Residual 35    9.7830                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.5257, p value of 0.001

Plant_CCA_Chem17.4 <- cca(PlantSpecies ~ pH + P2O5 + Al2O3 + 
                            Co + V, data = PlantChemistry)

plot(Plant_CCA_Chem17.4) 

summary(Plant_CCA_Chem17.4) 
## 
## Call:
## cca(formula = PlantSpecies ~ pH + P2O5 + Al2O3 + Co + V, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     1.973     0.1656
## Unconstrained   9.942     0.8344
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2   CCA3    CCA4   CCA5     CA1     CA2
## Eigenvalue            0.64175 0.48592 0.3849 0.26070 0.2002 0.71571 0.70160
## Proportion Explained  0.05386 0.04078 0.0323 0.02188 0.0168 0.06007 0.05888
## Cumulative Proportion 0.05386 0.09464 0.1269 0.14882 0.1656 0.22569 0.28457
##                           CA3     CA4     CA5    CA6     CA7    CA8     CA9
## Eigenvalue            0.65684 0.57067 0.55604 0.5159 0.50650 0.4575 0.41689
## Proportion Explained  0.05513 0.04789 0.04667 0.0433 0.04251 0.0384 0.03499
## Cumulative Proportion 0.33970 0.38760 0.43426 0.4776 0.52007 0.5585 0.59346
##                          CA10    CA11    CA12    CA13    CA14    CA15    CA16
## Eigenvalue            0.40610 0.38445 0.36126 0.31604 0.29933 0.27681 0.26161
## Proportion Explained  0.03408 0.03227 0.03032 0.02652 0.02512 0.02323 0.02196
## Cumulative Proportion 0.62754 0.65981 0.69013 0.71665 0.74178 0.76501 0.78696
##                          CA17    CA18    CA19    CA20    CA21    CA22    CA23
## Eigenvalue            0.25637 0.24353 0.21221 0.20741 0.19673 0.18715 0.17804
## Proportion Explained  0.02152 0.02044 0.01781 0.01741 0.01651 0.01571 0.01494
## Cumulative Proportion 0.80848 0.82892 0.84673 0.86413 0.88065 0.89635 0.91129
##                          CA24    CA25    CA26     CA27     CA28     CA29
## Eigenvalue            0.15415 0.13994 0.13285 0.114326 0.110433 0.090925
## Proportion Explained  0.01294 0.01174 0.01115 0.009595 0.009268 0.007631
## Cumulative Proportion 0.92423 0.93598 0.94713 0.956721 0.965989 0.973621
##                           CA30     CA31     CA32     CA33     CA34     CA35
## Eigenvalue            0.081669 0.068771 0.055804 0.050092 0.039348 0.018632
## Proportion Explained  0.006854 0.005772 0.004683 0.004204 0.003302 0.001564
## Cumulative Proportion 0.980475 0.986246 0.990930 0.995134 0.998436 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5
## Eigenvalue            0.6417 0.4859 0.3849 0.2607 0.2002
## Proportion Explained  0.3252 0.2462 0.1950 0.1321 0.1014
## Cumulative Proportion 0.3252 0.5714 0.7665 0.8986 1.0000
anova(Plant_CCA_Chem17.4)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + P2O5 + Al2O3 + Co + V, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     5    1.9734 1.3895  0.001 ***
## Residual 35    9.9417                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.3895, p value of 0.003

Plant_CCA_Chem17.5 <- cca(PlantSpecies ~ pH + P2O5 + Al2O3 + 
                            Co + V + CaO + K2O + Mo, data = PlantChemistry)

plot(Plant_CCA_Chem17.5) 

summary(Plant_CCA_Chem17.5) 
## 
## Call:
## cca(formula = PlantSpecies ~ pH + P2O5 + Al2O3 + Co + V + CaO +      K2O + Mo, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915      1.000
## Constrained     3.241      0.272
## Unconstrained   8.674      0.728
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.69544 0.57931 0.48814 0.45499 0.35940 0.29098 0.21104
## Proportion Explained  0.05837 0.04862 0.04097 0.03819 0.03016 0.02442 0.01771
## Cumulative Proportion 0.05837 0.10699 0.14795 0.18614 0.21630 0.24072 0.25844
##                          CCA8     CA1     CA2     CA3    CA4     CA5     CA6
## Eigenvalue            0.16157 0.68459 0.67236 0.62800 0.5350 0.47006 0.46719
## Proportion Explained  0.01356 0.05746 0.05643 0.05271 0.0449 0.03945 0.03921
## Cumulative Proportion 0.27200 0.32945 0.38588 0.43859 0.4835 0.52293 0.56214
##                           CA7     CA8     CA9    CA10    CA11    CA12    CA13
## Eigenvalue            0.42912 0.40485 0.38308 0.36621 0.32985 0.32237 0.30240
## Proportion Explained  0.03601 0.03398 0.03215 0.03073 0.02768 0.02706 0.02538
## Cumulative Proportion 0.59816 0.63214 0.66429 0.69502 0.72271 0.74976 0.77514
##                          CA14   CA15    CA16    CA17    CA18    CA19    CA20
## Eigenvalue            0.26251 0.2526 0.22326 0.21264 0.19856 0.19107 0.18689
## Proportion Explained  0.02203 0.0212 0.01874 0.01785 0.01666 0.01604 0.01568
## Cumulative Proportion 0.79717 0.8184 0.83711 0.85496 0.87162 0.88766 0.90334
##                          CA21    CA22    CA23    CA24     CA25     CA26
## Eigenvalue            0.16465 0.15954 0.13505 0.11945 0.118224 0.097235
## Proportion Explained  0.01382 0.01339 0.01133 0.01002 0.009922 0.008161
## Cumulative Proportion 0.91716 0.93055 0.94189 0.95191 0.961833 0.969994
##                           CA27     CA28     CA29     CA30     CA31     CA32
## Eigenvalue            0.085243 0.075691 0.072575 0.056439 0.047289 0.020293
## Proportion Explained  0.007154 0.006352 0.006091 0.004737 0.003969 0.001703
## Cumulative Proportion 0.977148 0.983500 0.989591 0.994328 0.998297 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.6954 0.5793 0.4881 0.4550 0.3594 0.29098 0.21104
## Proportion Explained  0.2146 0.1788 0.1506 0.1404 0.1109 0.08978 0.06512
## Cumulative Proportion 0.2146 0.3933 0.5440 0.6843 0.7952 0.88503 0.95015
##                          CCA8
## Eigenvalue            0.16157
## Proportion Explained  0.04985
## Cumulative Proportion 1.00000
anova(Plant_CCA_Chem17.5)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + P2O5 + Al2O3 + Co + V + CaO + K2O + Mo, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     8    3.2409 1.4945  0.001 ***
## Residual 32    8.6743                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4945, p value of 0.001

Plant_CCA_Chem17.6 <- cca(PlantSpecies ~ pH + P2O5 + Al2O3 + 
                      Co + V + CaO + K2O + Mo + Ni, data = PlantChemistry)

plot(Plant_CCA_Chem17.6) 

summary(Plant_CCA_Chem17.6) 
## 
## Call:
## cca(formula = PlantSpecies ~ pH + P2O5 + Al2O3 + Co + V + CaO +      K2O + Mo + Ni, data = PlantChemistry) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          11.915     1.0000
## Constrained     3.582     0.3007
## Unconstrained   8.333     0.6993
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.70612 0.60199 0.50334 0.45538 0.39747 0.31494 0.23676
## Proportion Explained  0.05926 0.05052 0.04224 0.03822 0.03336 0.02643 0.01987
## Cumulative Proportion 0.05926 0.10979 0.15203 0.19025 0.22361 0.25004 0.26991
##                         CCA8    CCA9     CA1     CA2     CA3     CA4     CA5
## Eigenvalue            0.2109 0.15555 0.68332 0.64598 0.60008 0.51222 0.46926
## Proportion Explained  0.0177 0.01306 0.05735 0.05422 0.05036 0.04299 0.03938
## Cumulative Proportion 0.2876 0.30067 0.35801 0.41223 0.46259 0.50558 0.54496
##                           CA6     CA7     CA8     CA9    CA10    CA11    CA12
## Eigenvalue            0.45784 0.42703 0.39541 0.38274 0.36617 0.32328 0.30513
## Proportion Explained  0.03843 0.03584 0.03319 0.03212 0.03073 0.02713 0.02561
## Cumulative Proportion 0.58339 0.61923 0.65241 0.68454 0.71527 0.74240 0.76801
##                          CA13    CA14    CA15    CA16    CA17    CA18    CA19
## Eigenvalue            0.26272 0.25444 0.22374 0.21756 0.20596 0.19631 0.19021
## Proportion Explained  0.02205 0.02135 0.01878 0.01826 0.01729 0.01648 0.01596
## Cumulative Proportion 0.79006 0.81141 0.83019 0.84845 0.86573 0.88221 0.89817
##                          CA20    CA21   CA22    CA23     CA24     CA25     CA26
## Eigenvalue            0.16638 0.16138 0.1430 0.12437 0.118829 0.115489 0.095605
## Proportion Explained  0.01396 0.01354 0.0120 0.01044 0.009973 0.009693 0.008024
## Cumulative Proportion 0.91213 0.92568 0.9377 0.94812 0.958091 0.967784 0.975808
##                           CA27     CA28     CA29    CA30     CA31
## Eigenvalue            0.082864 0.075441 0.060130 0.04933 0.020485
## Proportion Explained  0.006954 0.006331 0.005047 0.00414 0.001719
## Cumulative Proportion 0.982762 0.989094 0.994140 0.99828 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.7061 0.6020 0.5033 0.4554 0.3975 0.31494 0.23676
## Proportion Explained  0.1971 0.1680 0.1405 0.1271 0.1109 0.08791 0.06609
## Cumulative Proportion 0.1971 0.3651 0.5056 0.6328 0.7437 0.83161 0.89770
##                          CCA8    CCA9
## Eigenvalue            0.21092 0.15555
## Proportion Explained  0.05888 0.04342
## Cumulative Proportion 0.95658 1.00000
anova(Plant_CCA_Chem17.6)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = PlantSpecies ~ pH + P2O5 + Al2O3 + Co + V + CaO + K2O + Mo + Ni, data = PlantChemistry)
##          Df ChiSquare      F Pr(>F)    
## Model     9    3.5825 1.4809  0.001 ***
## Residual 31    8.3327                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.4809, p value of 0.001

#Out of multiple CCAs with different combinations of different substrate variables, #the one with the highest F statistic is Plant_CCA_Chem17.1, with an F statistic of 1.6861. #However, for this CCA, the arrow for SiO2 is very short in comparison with that #of the other variables in the CCA. A CCA that may better represent the variety of #variables that significantly influence the plant species’ presence is Plant_CCA_Chem17.2, #which has a lower F statistic of 1.5341. (but the same p value of 0.001). From both a #visual standpoint as well as a statistical standpoint, Plant_CCA_Chem17.2 is the most #appropriate CCA for the substrate and plant data for all of the six study sites.

#Now to construct a more visually appropriate graph for Plant_CCA_Chem17.2.

options(max.print=1000000)

Plant_CCA_Chem17.2$CCA$v
##                                     CCA1        CCA2         CCA3        CCA4
## Agrostis.spp.               -0.833080122  0.77476402  0.400787415 -1.98063629
## Agrostis.canina              0.623736881 -0.46438794 -1.298282562 -3.15483736
## Alchemilla.mollis            0.178176796 -0.72191610 -1.028183836 -0.02297314
## Alopercus.pratensis          1.279951178  0.99613927  2.971890285 -0.16351709
## Angelica.sylvestris          0.031878731  0.13617742 -0.868565767 -0.86810661
## Anthoxanthum.odoratum       -1.640852883 -1.52703922  0.296935753 -0.63729365
## Anthyllis.vulneraria         0.783926509  0.48491353 -1.530503304 -1.12099453
## Aphanes.arvensis            -0.307099932  0.43874962 -1.545838694  0.33295947
## Arrhenatherum.elatius       -1.013895210 -0.75849547  0.053288382 -0.28876454
## Atrichum.undulatum          -1.388352612  0.67719956 -0.065136690  0.89702211
## Avenula.pratensis            1.279951178  0.99613927  2.971890285 -0.16351709
## Bellis.perennis              0.105177487 -0.67710212  0.429256459  0.40444994
## Betula.pubescens            -1.185831979 -2.53219279 -1.381739465 -0.16674097
## Blackstonia.perfoliata       1.769466831 -0.86940805 -2.242662836  0.69770099
## Brachythecium.albicans       0.634139460  0.07018656 -0.166147894  0.05204666
## Brachythecium.glareosum     -2.189892874  4.10955505  4.019324833  0.40997601
## Brachythecium.mildeanum     -1.160522998  1.57717917 -0.793189431  0.16805722
## Brachythecium.rutabulum     -0.350145061  0.96203288 -0.238898299  0.08385736
## Briza.media                  0.055797345  0.18123720 -3.958888181  1.61026416
## Bromus.hordeaceus            0.521438450  0.61384462 -0.609349053 -1.83188227
## Bryum.c.f..caespiticium     -1.185831979 -2.53219279 -1.381739465 -0.16674097
## Bryum.c.f..pallescens        0.764982845 -0.86393569  1.289728482  1.11391075
## Bryum.capillare             -1.531024245 -1.70040531  0.096179833 -1.78248657
## Bryum.spp.                   0.935104193  0.84117179  0.157205499 -1.54421157
## Calliergonella.cupsidata    -0.400059507  1.26420703 -0.145743890  0.36198794
## Campanula.rotundifolia       1.169154914  0.32549492 -1.718322281 -0.98642858
## Carex.distans                1.242383549  0.74328727  0.002730858 -3.31939345
## Carex.flacca                 1.400937262 -0.32904152 -1.474981116  0.22371309
## Carex.panicea                1.364728010  0.68839514 -0.505567398 -2.70701024
## Carlina.vulgaris             0.942571342 -0.42551407  1.406583994  1.28411027
## Centaurea.nigra             -0.288081831  1.32285850 -0.551787759  1.31912711
## Centaurium.erythraea         1.713598834 -0.78198126 -1.819484239  0.82181019
## Centaurium.littorale         1.125986364  0.22223000 -0.260824928 -0.77839848
## Centaurium.pulchellum        1.199355956  1.33989911 -0.213426394 -5.55733648
## Cerastium.fontanum          -0.320967668 -0.67316444 -0.385280919 -0.88151912
## Chamaenerion.angustifolium  -1.099102177  2.81210535 -0.466857190  1.97350650
## Cirriphyllum.piliferum      -1.185831979 -2.53219279 -1.381739465 -0.16674097
## Cirsium.arvense              0.111237543  0.24488928 -0.911944307 -1.55082169
## Cirsium.palustre            -1.722411147  3.55350518  2.096675395  1.08006050
## Crepis.capillaris           -1.975068305 -1.70529859  0.747900661 -0.82972107
## Cynosurus.cristatus          1.109363682 -0.20823030 -1.975595110  0.17623736
## Dactylis.glomerata          -1.036251975  1.05550070  1.554987482 -2.01205703
## Danthonia.decumbens         -1.431535800  1.11102212 -1.175216805  0.19509147
## Daucus.carrota               0.223408027 -0.11790409  0.019768529  0.07333142
## Dicranella.spp.              0.625261891 -1.22915209  1.505466433  1.63257330
## Dicranum.scoparium          -1.527751078 -0.19806281 -0.718763163  0.09218063
## Epilobium.montanum          -1.396800404  2.80643944  2.286363152 -0.38885228
## Equisetum.arvense            0.316897378 -0.44669613 -1.117460659 -0.28322111
## Equisteum.variegatum         1.169154914  0.32549492 -1.718322281 -0.98642858
## Erigeron.acer                0.958365521  0.23632282  3.751097218  2.47355761
## Euphrasia.agg                0.672042371 -0.37879503  0.283717102  1.05209292
## Festuca.ovina                0.818642114 -0.02297193  1.523853909  0.34059699
## Festuca.rubra                0.956935273  0.02390331  0.349686707  0.16212060
## Festuca.rubra.agg.          -1.531024245 -1.70040531  0.096179833 -1.78248657
## Filipendula.ulmaria         -1.718829290  3.25451740  3.077041554  0.04654305
## Fissidens.adianthoides      -1.185831979 -2.53219279 -1.381739465 -0.16674097
## Fissidens.dubius             0.046946624 -0.63470762  1.177790534  0.06796993
## Fissidens.exilis             0.625261891 -1.22915209  1.505466433  1.63257330
## Fragaria.vesca              -1.573825413 -1.61080505  0.072527183 -0.64634697
## Galium.aparine              -0.494671959  4.39546143  1.282530813  1.63868223
## Galium.arvense               0.623736881 -0.46438794 -1.298282562 -3.15483736
## Galium.saxatile              0.735901683 -0.34324138  1.652174409  1.80856910
## Galium.verum                 0.337942726  0.11415871 -2.297078854  0.94745631
## Geum.urbanum                -1.267581655  1.31842184  2.228051622 -3.13465442
## Glechoma.hederacea          -1.267581655  1.31842184  2.228051622 -3.13465442
## Helicotrichon.spp.           0.521438450  0.61384462 -0.609349053 -1.83188227
## Heracleum.sphondylium       -1.083558775  2.30584570 -0.647983117  1.39815864
## Hieracium.spp.              -0.148281678 -0.34123906 -0.038334084  0.55013364
## Holcus.spp.                  0.694655496  0.18637740  0.559062003  0.10260998
## Holcus.lanatus              -0.963422386 -1.04204723  0.164124055 -0.96376439
## Holcus.mollis               -0.511376028  1.10417216 -1.961705909  0.18543989
## Homalothecium.lutescens      0.767904594 -0.26445428  1.729804754  1.69256403
## Hylocomium.splendens        -1.460154411 -1.14584364 -0.500126392 -0.24160739
## Hypericum.perforatum        -0.722445056 -1.34517078  0.941873795 -0.13543294
## Hypnum.cupressiforme         0.399480782 -0.50804386 -0.398806987  0.42600312
## Hypnum.imponens             -1.145907655  1.99277136 -2.519719205  1.64586469
## Hypnum.jutlandicum          -1.641654725 -1.31881755  0.203743238 -0.36822861
## Hypochaeris.radicata         0.535466880  1.00305737  0.619525780 -1.56410663
## Kindbergia.praelonga        -0.983390075  1.71077787 -0.098089945 -0.45647388
## Lathyrus.pratensis           0.130793822  0.96569181 -1.388656511  0.70889377
## Leontodon.hispidus           0.385148562 -0.26113515  1.249934727  1.11788058
## Leontodon.saxatilis          0.697853140 -0.60652740  1.554900782  1.77483196
## Leucanthemum.vulgare        -0.268621258 -0.89206886  0.813737509  0.07539455
## Linum.catharticum            0.685726919 -0.27580862  1.770890757  0.82684832
## Lolium.perenne               0.578476817  0.57312437 -0.501934958 -1.64830936
## Lophocolea.semiteres        -1.185831979 -2.53219279 -1.381739465 -0.16674097
## Lotus.corniculatus           0.218125783 -0.56521043  0.013607226 -0.14511039
## Luzula.multiflora           -1.099102177  2.81210535 -0.466857190  1.97350650
## Lysimachia.maritima          1.197641504  1.27796640 -0.185530640 -5.37535804
## Medicago.lupulina            1.141730783  0.25056309 -1.308846185 -0.64671266
## Myosotis.arvensis            0.419584709  1.21775750  1.585051016  1.29470125
## Ononis.repens                1.442056047 -0.08231158 -1.018238804 -0.07657379
## Oxalis.acetosella           -1.267581655  1.31842184  2.228051622 -3.13465442
## Pastinaca.sativa             0.931446881  0.44199374  4.105016115  2.55933891
## Pentaglottis.sempervirens   -0.494671959  4.39546143  1.282530813  1.63868223
## Pillosella.officinarum       0.949684496 -0.72491251  0.456036323  1.15078433
## Plantago.coronopus           1.193081641  0.68244594  0.049398974 -3.00525442
## Plantago.lanceolata         -0.542313380 -0.73938235  0.551982366  0.24469166
## Pleurozium.schreberi        -1.721781072 -0.90127637 -0.025758130 -0.14408076
## Poa.annua                    1.217446783  0.44379435 -0.056941844 -1.73780802
## Poa.spp.                     0.521438450  0.61384462 -0.609349053 -1.83188227
## Polytrichum.commune         -1.145907655  1.99277136 -2.519719205  1.64586469
## Polytrichum.commune.agg.    -1.145907655  1.99277136 -2.519719205  1.64586469
## Polytrichum.formosum        -1.531024245 -1.70040531  0.096179833 -1.78248657
## Potentilla.reptans           1.370505144 -0.29633174 -1.852666677  0.15147582
## Prunella.vulgaris            0.338330990 -0.45193506  1.609435819  1.17986570
## Pseudoscleropidum.purum     -0.957661091 -1.23086522 -0.187505047 -0.14377789
## Pteridium.aquilinum         -1.690259976  2.93288216  2.360827035 -0.19905645
## Ranunculus.acris            -1.677603048 -1.45770623  0.336583809 -0.17946229
## Ranunculus.repens           -1.230805088  2.97342261  0.344083951  1.58194562
## Reseda.lutea                 0.931446881  0.44199374  4.105016115  2.55933891
## Rhinanthus.minor            -1.431535800  1.11102212 -1.175216805  0.19509147
## Rhizomnium.punctatum        -1.099102177  2.81210535 -0.466857190  1.97350650
## Rhytidadelphus.squarrosus   -0.895813673  0.54049376  0.324865348  0.58597339
## Rhytidadelphus.triquetris   -1.785526388 -1.56296838  0.477426317 -0.67499674
## Rubus.fruticosus            -1.938877651  2.44911809  2.669058758  0.26579677
## Sanguisorba.minor.spp.minor  0.498277132  0.09012796 -1.147650394  0.46720541
## Saniona.uncinata            -1.122504916  2.40243835 -1.493288197  1.80968559
## Sedum.anglicum               0.931446881  0.44199374  4.105016115  2.55933891
## Senecio.jacobaea             0.349807623 -0.05403574 -0.818766444 -0.92742770
## Senecio.vulgaris             0.697853140 -0.60652740  1.554900782  1.77483196
## Sonchus.arvensis            -1.113672498  2.19399669 -0.823393147  1.51847659
## Stachys.sylvatica            0.400956839 -0.59315202 -1.163233199 -1.58890525
## Stellaria.apetala            1.678860802 -0.41545942 -2.138558758  0.02579996
## Taraxacum.agg.               0.774485306 -0.22946489  1.799960996  1.81257379
## Thuidium.tamariscinum       -1.292163598  0.60662132 -0.562254392  0.72358486
## Thymus.polytrichus           1.191308621  0.15810838  0.586529511 -0.76269914
## Trichostomum.crispulum       1.079014407 -0.60623429  0.778397912  0.67614722
## Trifolium.campestre          0.576967129  0.20824021 -0.842771149 -0.11649275
## Trifolium.dubium             1.060657569 -0.69034756  1.172171557  1.21528484
## Trifolium.pratense          -0.007538585  0.55055435  1.641853586  1.28342778
## Trifolium.repens            -0.388377240  1.95447895 -0.368007265  0.82870769
## Trisetum.flavescens          1.695561874 -0.81802194 -2.127534158  0.71875366
## Tussilago.farfara            0.286557869 -0.36863234 -0.831103604 -0.20164877
## Urtica.diocia               -0.858133917  2.61939473  0.217499709  0.98558468
## Veronica.officinalis        -1.185831979 -2.53219279 -1.381739465 -0.16674097
## Vicia.sativa                -1.099102177  2.81210535 -0.466857190  1.97350650
## Viola.riviniana             -2.189892874  4.10955505  4.019324833  0.40997601
## Weissia.controversa         -1.185831979 -2.53219279 -1.381739465 -0.16674097
## Zygodon.stirtonii            0.459671361 -0.96891938  2.090277964  1.63877389
##                                    CCA5
## Agrostis.spp.                0.99520306
## Agrostis.canina             -0.26905251
## Alchemilla.mollis            1.73629747
## Alopercus.pratensis          6.22636864
## Angelica.sylvestris          1.10283630
## Anthoxanthum.odoratum       -0.05871122
## Anthyllis.vulneraria        -0.46190020
## Aphanes.arvensis             0.53458147
## Arrhenatherum.elatius       -0.23392101
## Atrichum.undulatum          -0.20861279
## Avenula.pratensis            6.22636864
## Bellis.perennis              0.45071929
## Betula.pubescens             0.77969182
## Blackstonia.perfoliata      -0.19041803
## Brachythecium.albicans      -0.33570227
## Brachythecium.glareosum     -0.89039348
## Brachythecium.mildeanum      0.53676567
## Brachythecium.rutabulum      0.18774468
## Briza.media                  0.22599456
## Bromus.hordeaceus           -0.50905023
## Bryum.c.f..caespiticium      0.77969182
## Bryum.c.f..pallescens        2.97769377
## Bryum.capillare             -0.16242496
## Bryum.spp.                  -0.86737598
## Calliergonella.cupsidata    -0.06555227
## Campanula.rotundifolia       0.29676532
## Carex.distans               -1.52928809
## Carex.flacca                -0.16523909
## Carex.panicea               -0.69966332
## Carlina.vulgaris             0.55496733
## Centaurea.nigra             -0.23691457
## Centaurium.erythraea        -0.37302350
## Centaurium.littorale        -1.00081643
## Centaurium.pulchellum       -1.57790389
## Cerastium.fontanum           0.25045868
## Chamaenerion.angustifolium   0.15220789
## Cirriphyllum.piliferum       0.77969182
## Cirsium.arvense              0.65953556
## Cirsium.palustre            -0.44356432
## Crepis.capillaris            0.01554101
## Cynosurus.cristatus          0.25075307
## Dactylis.glomerata           1.11036577
## Danthonia.decumbens          0.89617366
## Daucus.carrota              -1.16323337
## Dicranella.spp.             -1.38551017
## Dicranum.scoparium           0.02772461
## Epilobium.montanum          -0.61336395
## Equisetum.arvense            1.42736079
## Equisteum.variegatum         0.29676532
## Erigeron.acer               -2.78136591
## Euphrasia.agg               -0.27760197
## Festuca.ovina               -1.31487672
## Festuca.rubra               -1.14306259
## Festuca.rubra.agg.          -0.16242496
## Filipendula.ulmaria         -0.59511785
## Fissidens.adianthoides       0.77969182
## Fissidens.dubius            -0.99363999
## Fissidens.exilis            -1.38551017
## Fragaria.vesca               0.11877895
## Galium.aparine              -3.49900962
## Galium.arvense              -0.26905251
## Galium.saxatile             -2.33307568
## Galium.verum                 0.02497579
## Geum.urbanum                 1.88829689
## Glechoma.hederacea           1.88829689
## Helicotrichon.spp.          -0.50905023
## Heracleum.sphondylium        0.19566678
## Hieracium.spp.              -1.50073660
## Holcus.spp.                 -0.47045517
## Holcus.lanatus              -0.31041386
## Holcus.mollis                0.23766216
## Homalothecium.lutescens     -1.82957895
## Hylocomium.splendens         0.12462091
## Hypericum.perforatum        -0.78298360
## Hypnum.cupressiforme         0.50753234
## Hypnum.imponens              0.29761145
## Hypnum.jutlandicum          -0.41745852
## Hypochaeris.radicata        -1.06908413
## Kindbergia.praelonga         0.76698107
## Lathyrus.pratensis           0.31493430
## Leontodon.hispidus          -1.78000228
## Leontodon.saxatilis         -0.86627665
## Leucanthemum.vulgare        -0.87801413
## Linum.catharticum            0.29825790
## Lolium.perenne              -0.54473696
## Lophocolea.semiteres         0.77969182
## Lotus.corniculatus          -0.66798206
## Luzula.multiflora            0.15220789
## Lysimachia.maritima         -1.57743237
## Medicago.lupulina            0.07156511
## Myosotis.arvensis           -0.02313681
## Ononis.repens                1.13353806
## Oxalis.acetosella            1.88829689
## Pastinaca.sativa            -2.92950015
## Pentaglottis.sempervirens   -3.49900962
## Pillosella.officinarum      -0.58529408
## Plantago.coronopus          -1.73163462
## Plantago.lanceolata         -0.76772706
## Pleurozium.schreberi        -0.18081937
## Poa.annua                   -1.15530174
## Poa.spp.                    -0.50905023
## Polytrichum.commune          0.29761145
## Polytrichum.commune.agg.     0.29761145
## Polytrichum.formosum        -0.16242496
## Potentilla.reptans           0.13187266
## Prunella.vulgaris           -1.44964255
## Pseudoscleropidum.purum     -0.38523892
## Pteridium.aquilinum          0.16936197
## Ranunculus.acris            -0.56943347
## Ranunculus.repens           -0.06966448
## Reseda.lutea                -2.92950015
## Rhinanthus.minor             0.89617366
## Rhizomnium.punctatum         0.15220789
## Rhytidadelphus.squarrosus    0.41320259
## Rhytidadelphus.triquetris    0.06811933
## Rubus.fruticosus            -0.47287216
## Sanguisorba.minor.spp.minor -0.16609799
## Saniona.uncinata             0.22490967
## Sedum.anglicum              -2.92950015
## Senecio.jacobaea             0.61362362
## Senecio.vulgaris            -0.86627665
## Sonchus.arvensis             0.56993797
## Stachys.sylvatica            0.73362248
## Stellaria.apetala            0.18206487
## Taraxacum.agg.              -1.79125457
## Thuidium.tamariscinum        0.17821281
## Thymus.polytrichus           1.43292393
## Trichostomum.crispulum      -0.34595385
## Trifolium.campestre         -0.40965704
## Trifolium.dubium             3.58136646
## Trifolium.pratense          -1.65042817
## Trifolium.repens             0.02686566
## Trisetum.flavescens         -0.23985093
## Tussilago.farfara            1.01682289
## Urtica.diocia               -1.41796889
## Veronica.officinalis         0.77969182
## Vicia.sativa                 0.15220789
## Viola.riviniana             -0.89039348
## Weissia.controversa          0.77969182
## Zygodon.stirtonii           -1.88634940

#The “v values” show the positions of individual species on the graph, with the CCA1 value #representing the x axis and the CCA2 value representing the y axis, in the case of the #graph created in R.

#The "v values" show the positions of individual species on the graph, with the CCA1 value
#representing the x axis and the CCA2 value representing the y axis, in the case of the
#graph created in R.

plot(Plant_CCA_Chem17.2, choices = c(1,2), display = c("wa", "bp"), xlim = c(-6.5, 2.5), ylim = c(-4.5, 6.5))

#Increasing the xlim and ylim to give more room for writing on graph

points(x = 0.09178966, y = -1.264581673, pch = 15, col = "black")

#This point represents Agrostis canina

text('A. canina', x = 3.5, y = -1.75, cex = 0.88, pos = 2, col = "black")

#Adding text to this point.

points(x = -0.494671959, y = 4.39546143, pch = 15, col = "black")

#This point represents Galium aparine.

text('G. aparine', x = 3.7, y = 4.39546143, cex = 0.88, pos = 2, col = "black")

#Adding text to the point for Galium aparine.

points(x = -1.036251975, y = 1.05550070, pch = 15, col = "black")

#This point represents Dactylis glomerata.

text('D. glomerata', x = -1.036251975, y = 0.35, cex = 0.88, pos = 2, col = "black")

#Adding text to this point.

points(x = 0.634139460, y = 0.07018656, pch = 15, col = "black")

#This point represents Brachythecium albicans

text('B. albicans', x = 8, y = -1, cex = 0.88, pos = 2, col = "black")

#Adding text to this point

points(x = -1.267581655, y = 1.31842184, pch = 15, col = "black")

#This point represents Geum urbanum.

text('G. urbanum', x = -1.267581655, y = 1.31842184, cex = 0.88, pos = 2, col = "black")

#Adding text to this point.

points(x = -0.858133917, y = 2.61939473, pch = 15, col = "black")

#This point represents Urtica dioica.

text('U. dioica', x = -3, y = 3, cex = 0.88, pos = 2, col = "black")

#Adding text to this point.

####Barrow Data####

urlfile3  <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/BarrowPlantSpecies.csv'

BarrowPS <-read.csv(urlfile3)

urlfile4 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/BARROW_PLANT_CHEMISTRY_MG_KG.csv'

BarrowPC <-read.csv(urlfile4)
col_sums_Barrow     <- apply(X = BarrowPS, MARGIN = 2, FUN = sum);
rm_Barrow           <- which(is.na(col_sums) == TRUE);
BarrowPS <- BarrowPS[, -rm_Barrow];

print(PlantSpecies)
##    Agrostis.spp. Agrostis.canina Alchemilla.mollis Alopercus.pratensis
## 1              0               0                 0                   0
## 2              9               0                 0                   0
## 3              1               0                 0                   0
## 4              0               0                 0                   0
## 5              0               0                 0                   0
## 6              1               0                 0                   0
## 7              0               0                 0                   0
## 8              0               0                 0                   0
## 9              0               0                 0                   0
## 10            14               0                 0                   0
## 11             5               3                 0                   0
## 12             3               0                 1                   0
## 13            32               0                 0                   0
## 14            39               0                 0                   0
## 15             0               0                 0                   0
## 16             0               0                 0                   0
## 17             0               0                 0                   0
## 18             0               0                 0                   0
## 19             0               0                 0                   0
## 20             0               0                 0                   0
## 21             0               0                 0                  27
## 22             0               0                 0                   0
## 23             0               0                 0                   0
## 24             0               0                 0                   0
## 25             0               0                 0                   0
## 26             0               0                 0                   0
## 27             0               0                 0                   0
## 28             0               0                 0                   0
## 29             0               0                 0                   0
## 30             0               0                 0                   0
## 31             0               0                 0                   0
## 32             0               0                 0                   0
## 33             0               0                 0                   0
## 34             0               0                 0                   0
## 35             0               0                 0                   0
## 36             0               0                 0                   0
## 37             0               0                 0                   0
## 38             0               0                 0                   0
## 39             0               0                 0                   0
## 40             0               0                 0                   0
## 41             0               0                 0                   0
##    Angelica.sylvestris Anthoxanthum.odoratum Anthyllis.vulneraria
## 1                    0                    81                    0
## 2                    0                    18                    0
## 3                    0                     8                    0
## 4                    0                    82                    0
## 5                    0                    55                    0
## 6                    0                     0                    0
## 7                    0                     0                    0
## 8                    0                     0                    0
## 9                    0                     0                    0
## 10                   0                     0                    0
## 11                   0                     0                    0
## 12                   1                     0                    0
## 13                   1                     0                    0
## 14                   0                     0                    0
## 15                   0                     0                    0
## 16                   0                     0                    0
## 17                   0                     0                    0
## 18                   0                     0                    0
## 19                   0                     0                    0
## 20                   0                     0                    0
## 21                   0                     0                    0
## 22                   0                     0                    0
## 23                   0                     0                    0
## 24                   0                     0                    4
## 25                   0                     0                    0
## 26                   0                     0                  127
## 27                   0                     0                    0
## 28                   0                     0                   32
## 29                   0                     0                    0
## 30                   0                     0                    0
## 31                   0                     0                    0
## 32                   0                     0                    0
## 33                   0                     0                    0
## 34                   0                     0                    0
## 35                   0                     0                    0
## 36                   0                     0                   70
## 37                   0                     0                  189
## 38                   0                     7                    0
## 39                   0                     0                    0
## 40                   0                     0                    0
## 41                   0                     0                    0
##    Aphanes.arvensis Arrhenatherum.elatius Atrichum.undulatum Avenula.pratensis
## 1                 0                     0                  0                 0
## 2                 0                     0                  0                 0
## 3                 0                     0                  0                 0
## 4                 0                     2                  0                 0
## 5                 0                    42                 10                 0
## 6                 0                     0                  0                 0
## 7                 0                     0                  0                 0
## 8                 0                     3                 10                 0
## 9                 0                     1                  0                 0
## 10               11                     0                  0                 0
## 11                0                     0                  0                 0
## 12                0                     4                  0                 0
## 13                0                     0                  0                 0
## 14                0                     0                  0                 0
## 15                0                     0                  0                 0
## 16                0                     1                  0                 0
## 17                0                     0                  0                 0
## 18                0                     0                  0                 0
## 19                0                     0                  0                 0
## 20                0                     0                  0                 0
## 21                0                     0                  0                11
## 22                0                     0                  0                 0
## 23                0                     0                  0                 0
## 24                0                     0                  0                 0
## 25                0                     0                  0                 0
## 26                0                     0                  0                 0
## 27                0                     0                  0                 0
## 28                0                     0                  0                 0
## 29                0                     8                  0                 0
## 30                1                     0                  0                 0
## 31                5                     0                  0                 0
## 32                0                     0                  0                 0
## 33                0                     5                  0                 0
## 34                0                     0                  0                 0
## 35                0                     0                  0                 0
## 36                0                     0                  0                 0
## 37                0                     0                  0                 0
## 38                0                     0                  0                 0
## 39                0                     0                  0                 0
## 40                0                     0                  0                 0
## 41                0                     0                  0                 0
##    Bellis.perennis Betula.pubescens Blackstonia.perfoliata
## 1                1                0                      0
## 2                0                0                      0
## 3                8               12                      0
## 4               16                0                      0
## 5                0                0                      0
## 6                0                0                      0
## 7                0                0                      0
## 8                0                0                      0
## 9                0                0                      0
## 10               0                0                      0
## 11               0                0                      0
## 12               0                0                      0
## 13               0                0                      0
## 14               0                0                      0
## 15               0                0                      0
## 16               0                0                      0
## 17               0                0                      0
## 18              11                0                      0
## 19               0                0                      0
## 20               0                0                      0
## 21              10                0                      0
## 22               0                0                      0
## 23               0                0                      0
## 24               4                0                      0
## 25               6                0                      0
## 26               1                0                      0
## 27               0                0                      0
## 28               6                0                      0
## 29               0                0                      0
## 30               0                0                      0
## 31               2                0                      2
## 32               0                0                      0
## 33               0                0                      0
## 34               4                0                      0
## 35               0                0                      0
## 36               0                0                      0
## 37               1                0                      0
## 38               0                0                      0
## 39               0                0                      0
## 40               0                0                      0
## 41               0                0                      0
##    Brachythecium.albicans Brachythecium.glareosum Brachythecium.mildeanum
## 1                       0                       0                       0
## 2                       0                       0                       0
## 3                       0                       0                       0
## 4                       0                       0                       0
## 5                       0                       0                       0
## 6                       0                      10                      10
## 7                       0                       0                      80
## 8                       0                       0                       0
## 9                       0                       0                       0
## 10                      0                       0                     150
## 11                      0                       0                       0
## 12                      0                       0                       0
## 13                      0                       0                       0
## 14                      0                       0                       0
## 15                      0                       0                       0
## 16                      0                       0                       0
## 17                      0                       0                       0
## 18                      0                       0                       0
## 19                      0                       0                       0
## 20                      0                       0                       0
## 21                      0                       0                       0
## 22                      0                       0                       0
## 23                      0                       0                      20
## 24                      0                       0                       0
## 25                     30                       0                       0
## 26                      0                       0                       0
## 27                      0                       0                       0
## 28                      0                       0                       0
## 29                      0                       0                       0
## 30                      0                       0                       0
## 31                      0                       0                       0
## 32                      0                       0                       0
## 33                      0                       0                       0
## 34                      0                       0                       0
## 35                      0                       0                       0
## 36                      0                       0                       0
## 37                      0                       0                       0
## 38                      0                       0                       0
## 39                      0                       0                       0
## 40                      0                       0                       0
## 41                      0                       0                       0
##    Brachythecium.rutabulum Briza.media Bromus.hordeaceus
## 1                        0           0                 0
## 2                        0           0                 0
## 3                        0           0                 0
## 4                        0           0                 0
## 5                        0           0                 0
## 6                       10           0                 0
## 7                        0           0                 0
## 8                        0           0                 0
## 9                       10           0                 0
## 10                      10           0                 0
## 11                       0           0                 0
## 12                      10           0                 0
## 13                      10           0                 0
## 14                       0           0                 0
## 15                       0           0                 0
## 16                       0           0                 0
## 17                       0           0                 0
## 18                       0           0                 0
## 19                       0           0                 0
## 20                       0           0                 0
## 21                       0           0                 0
## 22                       0           0                 0
## 23                       0           0                 0
## 24                       0           0                 0
## 25                      30           0                 0
## 26                       0         138                 0
## 27                       0           9                 0
## 28                       0           8                 0
## 29                       0           0                 1
## 30                       0           0                 0
## 31                       0           0                 0
## 32                       0           0                 0
## 33                       0           0                 0
## 34                       0           0                 0
## 35                       0           0                 0
## 36                       0           0                 0
## 37                       0           0                 0
## 38                       0           0                 0
## 39                       0           0                 0
## 40                       0           0                 0
## 41                       0           0                 0
##    Bryum.c.f..caespiticium Bryum.c.f..pallescens Bryum.capillare Bryum.spp.
## 1                        0                     0               0          0
## 2                        0                     0              10          0
## 3                       10                    10               0          0
## 4                        0                     0               0          0
## 5                        0                     0               0          0
## 6                        0                     0               0          0
## 7                        0                     0               0          0
## 8                        0                     0               0         10
## 9                        0                     0               0          0
## 10                       0                     0               0          0
## 11                       0                     0               0          0
## 12                       0                     0               0          0
## 13                       0                     0               0          0
## 14                       0                     0               0          0
## 15                       0                     0               0          0
## 16                       0                    60               0          0
## 17                       0                     0               0          0
## 18                       0                     0               0          0
## 19                       0                     0               0         20
## 20                       0                     0               0          0
## 21                       0                     0               0          0
## 22                       0                    50               0          0
## 23                       0                     0               0          0
## 24                       0                     0               0          0
## 25                       0                     0               0          0
## 26                       0                     0               0          0
## 27                       0                     0               0          0
## 28                       0                     0               0          0
## 29                       0                     0               0          0
## 30                       0                     0               0          0
## 31                       0                     0               0          0
## 32                       0                     0               0          0
## 33                       0                     0               0          0
## 34                       0                     0               0          0
## 35                       0                     0               0          0
## 36                       0                     0               0          0
## 37                       0                     0               0         60
## 38                       0                     0               0          0
## 39                       0                     0               0          0
## 40                       0                     0               0          0
## 41                       0                     0               0          0
##    Calliergonella.cupsidata Campanula.rotundifolia Carex.distans Carex.flacca
## 1                         0                      0             0            0
## 2                         0                      0             0            0
## 3                        10                      0             0            0
## 4                        10                      0             0            0
## 5                        30                      0             0            0
## 6                        30                      0             0            0
## 7                       120                      0             0            0
## 8                       150                      0             0            1
## 9                        90                      0             0            0
## 10                        0                      0             0            9
## 11                        0                      0             0            0
## 12                       50                      0             0            0
## 13                      110                      0             0            0
## 14                        0                      0             0            0
## 15                        0                      0             0            0
## 16                        0                      0             0            0
## 17                        0                      0             0            0
## 18                        0                      0            23            0
## 19                      120                      0             0           24
## 20                        0                      0             0            0
## 21                       10                      0             0            0
## 22                        0                      0             0            0
## 23                        0                      0            52            0
## 24                        0                      0             0            0
## 25                       30                      0             0            0
## 26                       20                      0             0            0
## 27                      110                      0             0            0
## 28                        0                      0             0            0
## 29                        0                      0             0            0
## 30                       10                      0             0          120
## 31                        0                      0             0           40
## 32                        0                      0             0            0
## 33                        0                      0             0            0
## 34                        0                      0             0            0
## 35                        0                      0             0            0
## 36                        0                      0             0            0
## 37                        0                      0             0            0
## 38                        0                     42             0            0
## 39                        0                      0             0            3
## 40                        0                      0             0            0
## 41                        0                      0             0            2
##    Carex.panicea Carlina.vulgaris Centaurea.nigra Centaurium.erythraea
## 1              0                0               0                    0
## 2              0                0               0                    0
## 3              0                0               0                    0
## 4              0                0               0                    0
## 5              0                0               0                    0
## 6              0                0               0                    0
## 7              0                0               2                    0
## 8              0                0               0                    0
## 9              0                0               0                    0
## 10             0                0               0                    0
## 11             0                0               0                    0
## 12             0                0               0                    0
## 13             0                0               0                    0
## 14             0                0               0                    0
## 15             0                0               0                    0
## 16             0               11               0                    0
## 17             0                5               0                    0
## 18             0                4               0                    0
## 19             0                0               0                    0
## 20             0                0               0                    0
## 21             0                0               0                    0
## 22             0                3               0                    0
## 23             0                0               0                    0
## 24             0                0               0                    0
## 25             0                0               0                    0
## 26             0                0               0                    0
## 27             0                0               0                    0
## 28             0                0               0                    0
## 29             0                0               0                    0
## 30             0                0               0                    0
## 31             0                0               0                   14
## 32             0                2               0                    1
## 33             0                0               0                    0
## 34             0                5               0                    0
## 35             0                0               0                    0
## 36             0                0               0                    0
## 37             1                0               0                    0
## 38             0                3               0                    0
## 39             0                2               1                    0
## 40             0                1               0                    0
## 41             0                7               0                    0
##    Centaurium.littorale Centaurium.pulchellum Cerastium.fontanum
## 1                     0                     0                  0
## 2                     0                     0                  6
## 3                     0                     0                  0
## 4                     0                     0                  0
## 5                     0                     0                  0
## 6                     0                     0                  0
## 7                     0                     0                  0
## 8                     0                     0                  0
## 9                     0                     0                  0
## 10                    0                     0                  0
## 11                    0                     0                  0
## 12                    0                     0                  0
## 13                    0                     0                  0
## 14                    0                     0                  0
## 15                    0                     0                  0
## 16                    0                     0                  1
## 17                    0                     0                  0
## 18                    0                     0                  0
## 19                    0                     0                  0
## 20                    0                     0                  0
## 21                    0                     0                  0
## 22                    0                     0                  0
## 23                    0                     8                  0
## 24                    0                     0                  0
## 25                    0                     0                  0
## 26                    0                     0                  1
## 27                    0                     0                  2
## 28                    0                     0                  1
## 29                    0                     0                  0
## 30                    0                     0                  1
## 31                    0                     0                  0
## 32                    0                     0                  0
## 33                    0                     0                  0
## 34                    0                     0                  0
## 35                    0                     0                  0
## 36                    4                     0                  0
## 37                    0                     0                  0
## 38                    4                     0                  1
## 39                    5                     0                  0
## 40                    0                     0                  0
## 41                    1                     0                  0
##    Chamaenerion.angustifolium Cirriphyllum.piliferum Cirsium.arvense
## 1                           0                      0               0
## 2                           0                      0               0
## 3                           0                     10               0
## 4                           0                      0               0
## 5                           0                      0               0
## 6                           0                      0               0
## 7                           0                      0               0
## 8                           4                      0               0
## 9                           0                      0               0
## 10                          0                      0               0
## 11                          0                      0               3
## 12                          0                      0               4
## 13                          0                      0               8
## 14                          0                      0               0
## 15                          0                      0               0
## 16                          0                      0               0
## 17                          0                      0               0
## 18                          0                      0               0
## 19                          0                      0               0
## 20                          0                      0               0
## 21                          0                      0               0
## 22                          0                      0               0
## 23                          0                      0               0
## 24                          0                      0               0
## 25                          0                      0               0
## 26                          0                      0               0
## 27                          0                      0               0
## 28                          0                      0               0
## 29                          0                      0               0
## 30                          0                      0               0
## 31                          0                      0               0
## 32                          0                      0               0
## 33                          0                      0               0
## 34                          0                      0               0
## 35                          0                      0               0
## 36                          0                      0               0
## 37                          0                      0               0
## 38                          0                      0               0
## 39                          0                      0               0
## 40                          0                      0               0
## 41                          0                      0               0
##    Cirsium.palustre Crepis.capillaris Cynosurus.cristatus Dactylis.glomerata
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## 2                 0                 0                   0                  0
## 3                 0                 0                   0                  0
## 4                 0                 1                   0                  0
## 5                 0                 0                   0                  0
## 6                 4                 0                   0                  0
## 7                 0                 0                   0                  0
## 8                 3                 0                   0                  0
## 9                 0                 0                   0                  0
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## 15                0                 0                   0                  0
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## 37                0                 0                   0                  0
## 38                0                 0                   0                  0
## 39                0                 0                   0                  0
## 40                0                 0                   0                  0
## 41                0                 0                   0                 10
##    Danthonia.decumbens Daucus.carrota Dicranella.spp. Dicranum.scoparium
## 1                    0              0               0                 30
## 2                    0              0               0                 20
## 3                    0              0               0                  0
## 4                    0              0               0                 10
## 5                    0              0               0                 16
## 6                    0              0               0                  0
## 7                    0              0               0                  0
## 8                    0              0               0                  0
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## 10                   1              0               0                  0
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## 15                   0              0               0                  0
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## 17                   0              0               0                  0
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## 20                   0              0               0                  0
## 21                   0              0               0                  0
## 22                   0              0              50                  0
## 23                   0              0               0                  0
## 24                   0              0               0                  0
## 25                   0              0               0                  0
## 26                   0              0               0                  0
## 27                   0              0               0                  0
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## 29                   0              0               0                  0
## 30                   0              0               0                  0
## 31                   0              0               0                  0
## 32                   0              0               0                  0
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## 34                   0              0               0                  0
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## 37                   0              0               0                  0
## 38                   0              0               0                  0
## 39                   0              0               0                  0
## 40                   0              0               0                  0
## 41                   0              0               0                  0
##    Epilobium.montanum Equisetum.arvense Equisteum.variegatum Erigeron.acer
## 1                   0                 0                    0             0
## 2                   0                 0                    0             0
## 3                   0                 0                    0             0
## 4                   0                 0                    0             0
## 5                   0                 0                    0             0
## 6                   8                 0                    0             0
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## 8                   0                 0                    0             0
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## 37                  0                 0                    0             0
## 38                  0                10                   31             0
## 39                  0                 0                    0             0
## 40                  0                 0                    0             0
## 41                  0                 0                    0             0
##    Euphrasia.agg Festuca.ovina Festuca.rubra Festuca.rubra.agg.
## 1              3             0             0                  0
## 2              0             0             0                  5
## 3              6             0             0                  0
## 4              0             0             0                  0
## 5              1             0             0                  0
## 6              0             0             0                  0
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## 20             0            27             0                  0
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## 23             0            25             0                  0
## 24             0            66             0                  0
## 25             0             0            19                  0
## 26            14             0             1                  0
## 27             0             0            39                  0
## 28             0             2             2                  0
## 29             0             0            54                  0
## 30             0             0            42                  0
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## 34             4             0            44                  0
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## 36             0             0             0                  0
## 37             0             0             4                  0
## 38             0             0             2                  0
## 39            36             0            44                  0
## 40             0             0             0                  0
## 41            31             0            33                  0
##    Filipendula.ulmaria Fissidens.adianthoides Fissidens.dubius Fissidens.exilis
## 1                    0                      0                0                0
## 2                    0                      0                0                0
## 3                    0                     10               10                0
## 4                    0                      0                0                0
## 5                    0                      0                0                0
## 6                   27                      0                0                0
## 7                    0                      0                0                0
## 8                    0                      0                0                0
## 9                    0                      0                0                0
## 10                   0                      0                0                0
## 11                   3                      0                0                0
## 12                   3                      0                0                0
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## 14                   0                      0                0                0
## 15                   0                      0                0                0
## 16                   0                      0                0                0
## 17                   0                      0                0                0
## 18                   0                      0                0                0
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## 20                   0                      0                0                0
## 21                   0                      0                0                0
## 22                   0                      0                0               60
## 23                   0                      0                0                0
## 24                   0                      0                0                0
## 25                   0                      0                0                0
## 26                   0                      0                0                0
## 27                   0                      0                0                0
## 28                   0                      0                0                0
## 29                   0                      0                0                0
## 30                   0                      0                0                0
## 31                   0                      0                0                0
## 32                   0                      0                0                0
## 33                   0                      0                0                0
## 34                   0                      0                0                0
## 35                   0                      0                0                0
## 36                   0                      0                0                0
## 37                   0                      0                0                0
## 38                   0                      0                0                0
## 39                   0                      0                0                0
## 40                   0                      0                0                0
## 41                   0                      0                0                0
##    Fragaria.vesca Galium.aparine Galium.arvense Galium.saxatile Galium.verum
## 1              67              0              0               0            0
## 2              38              0              0               0            0
## 3              65              0              0               0            0
## 4             117              0              0               0            0
## 5              68              0              0               0            0
## 6               0              0              0               0            0
## 7               0              0              0               0            0
## 8               0              0              0               0            0
## 9               0              0              0               0            0
## 10              0              0              0               0            0
## 11              0              0              1               0            0
## 12              0              0              0               0            0
## 13              0              0              0               0            0
## 14             11              0              0               0            0
## 15              0             47              0               0            0
## 16              0              0              0               0            0
## 17              0              0              0               0            0
## 18              0              0              0               0            0
## 19              0              0              0               0            0
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## 21              0              0              0               0            0
## 22              0              0              0               0            0
## 23              0              0              0               0            0
## 24              0              0              0               0            0
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## 26              0              0              0               0           88
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## 38              0              0              0               0            0
## 39              0              0              0               0            0
## 40              0              0              0               0            0
## 41              0              0              0               0            0
##    Geum.urbanum Glechoma.hederacea Helicotrichon.spp. Heracleum.sphondylium
## 1             0                  0                  0                     0
## 2             0                  0                  0                     0
## 3             0                  0                  0                     0
## 4             0                  0                  0                     0
## 5             0                  0                  0                     0
## 6             0                  0                  0                     0
## 7             0                  0                  0                     8
## 8             0                  0                  0                     0
## 9             0                  0                  0                     0
## 10            0                  0                  0                     1
## 11            0                  0                  0                     0
## 12            0                  0                  0                     0
## 13            0                  0                  0                     0
## 14           48                  5                  0                     0
## 15            0                  0                  0                     1
## 16            0                  0                  0                     0
## 17            0                  0                  0                     0
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## 19            0                  0                  0                     0
## 20            0                  0                  0                     0
## 21            0                  0                  0                     0
## 22            0                  0                  0                     0
## 23            0                  0                  0                     0
## 24            0                  0                  0                     0
## 25            0                  0                  0                     0
## 26            0                  0                  0                     0
## 27            0                  0                  0                     0
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## 37            0                  0                  0                     0
## 38            0                  0                  0                     0
## 39            0                  0                  0                     0
## 40            0                  0                  0                     0
## 41            0                  0                  0                     0
##    Hieracium.spp. Holcus.spp. Holcus.lanatus Holcus.mollis
## 1               0           0             30             0
## 2               0           0             80             0
## 3               0           0              0             0
## 4               0           0             28             0
## 5               0           0             36             0
## 6               0           5              0             0
## 7               0          14              0             0
## 8               0          36              0             0
## 9               0           0              0           143
## 10              0           0              0             1
## 11              0           0              0            56
## 12              0           0              0            17
## 13              0           0              0             4
## 14              0           0              0             0
## 15              0           0              0             0
## 16              0          42              0             0
## 17              0           0              0             0
## 18              0          40              8             0
## 19              0          58              3             0
## 20              0          70              0             0
## 21              0          23              0             0
## 22              0           0              0             0
## 23              0          13              0             0
## 24              0           0              0             0
## 25              0          55              5             0
## 26              0           0              1             0
## 27              0          50             25             0
## 28              1           3              2             0
## 29              0         169              0             0
## 30              0          10              0             0
## 31              0          30              0             0
## 32              0           0              0             0
## 33              0          82              5            10
## 34              0           4              0             0
## 35              0          47              0             0
## 36              0           0              0             0
## 37              0           0              0             0
## 38              0           0             18             0
## 39              0          23              0             0
## 40              0          78              0             0
## 41              0          10              0             0
##    Homalothecium.lutescens Hylocomium.splendens Hypericum.perforatum
## 1                        0                   50                   11
## 2                        0                   80                   24
## 3                        0                  110                    2
## 4                        0                  160                    4
## 5                        0                   90                    1
## 6                        0                    0                    0
## 7                        0                    0                    0
## 8                        0                    1                    0
## 9                        0                   90                    0
## 10                       0                    0                    0
## 11                       0                    0                    0
## 12                       0                    0                    0
## 13                       0                    0                    0
## 14                       0                    0                    0
## 15                       0                    0                    0
## 16                       0                    0                    0
## 17                       0                    0                    0
## 18                       0                    0                    0
## 19                       0                    0                    0
## 20                     160                    0                    0
## 21                      10                    0                    0
## 22                       0                    0                    0
## 23                       0                    0                    0
## 24                       0                    0                    0
## 25                       0                    0                    0
## 26                       0                    0                    0
## 27                       0                    0                    0
## 28                       0                    0                    0
## 29                       0                    0                    0
## 30                       0                    0                    0
## 31                       0                    0                    0
## 32                       0                    0                    0
## 33                       0                    0                    0
## 34                       0                    0                   22
## 35                       0                    0                    0
## 36                       0                    0                    0
## 37                       0                    0                    0
## 38                       0                    0                    0
## 39                       0                    0                    0
## 40                       0                    0                    0
## 41                       0                    0                    0
##    Hypnum.cupressiforme Hypnum.imponens Hypnum.jutlandicum Hypochaeris.radicata
## 1                     0               0                  0                    0
## 2                    10               0                 20                    0
## 3                    60               0                  0                    0
## 4                    10               0                  0                    0
## 5                    20               0                120                    0
## 6                     0               0                  0                    0
## 7                     0               0                  0                    0
## 8                     0               0                  0                    0
## 9                    20              60                  0                    0
## 10                   50               0                 10                    0
## 11                    0               0                  0                    0
## 12                    0               0                  0                    0
## 13                    0               0                  0                    0
## 14                    0               0                  0                    0
## 15                    0               0                  0                    0
## 16                   60               0                  0                    0
## 17                  150               0                  0                    0
## 18                   60               0                  0                    0
## 19                    0               0                  0                    0
## 20                    0               0                  0                    0
## 21                    0               0                  0                    0
## 22                    0               0                  0                    0
## 23                    0               0                  0                    0
## 24                    0               0                  0                    0
## 25                    0               0                  0                    0
## 26                    0               0                  0                    0
## 27                    0               0                  0                    1
## 28                    0               0                  0                    0
## 29                    0               0                  0                    0
## 30                    0               0                  0                    0
## 31                    0               0                  0                    0
## 32                    0               0                  0                    0
## 33                    0               0                  0                    0
## 34                    0               0                  0                    0
## 35                    0               0                  0                    0
## 36                    0               0                  0                    0
## 37                    0               0                  0                    0
## 38                  160               0                  0                    0
## 39                    0               0                  0                    0
## 40                    0               0                  0                    0
## 41                    0               0                  0                    0
##    Kindbergia.praelonga Lathyrus.pratensis Leontodon.hispidus
## 1                     0                  0                  0
## 2                     0                  0                  0
## 3                     0                  0                  0
## 4                     0                  0                  0
## 5                     0                  0                  0
## 6                    10                  0                  0
## 7                    60                  0                  0
## 8                     0                 30                  0
## 9                    30                  0                  0
## 10                   10                 18                  0
## 11                    0                  0                  0
## 12                    0                  0                  0
## 13                   50                  0                  0
## 14                   50                  0                  0
## 15                    0                  0                  0
## 16                    0                  0                  0
## 17                    0                  0                  0
## 18                    0                  0                  0
## 19                    0                  0                  0
## 20                    0                  0                  0
## 21                    0                  0                  0
## 22                    0                  0                  0
## 23                    0                  0                  0
## 24                    0                  0                 18
## 25                    0                  0                  0
## 26                    0                  0                  0
## 27                    0                  0                  0
## 28                    0                  0                 30
## 29                    0                  0                  0
## 30                    0                 42                  0
## 31                    0                  0                  0
## 32                    0                  0                  0
## 33                    0                  0                  0
## 34                    0                  0                  0
## 35                    0                  0                  0
## 36                    0                  0                  0
## 37                    0                  0                  0
## 38                    0                  0                  0
## 39                    0                  0                 16
## 40                    0                  0                  2
## 41                    0                  0                 43
##    Leontodon.saxatilis Leucanthemum.vulgare Linum.catharticum Lolium.perenne
## 1                    0                   20                 0              0
## 2                    0                   15                 0              0
## 3                    0                    0                 0              0
## 4                    0                    7                 0              0
## 5                    0                    1                 0              0
## 6                    0                    0                 0              0
## 7                    0                    0                 0              0
## 8                    0                    0                 0              0
## 9                    0                    0                 0              0
## 10                   0                    0                 0              0
## 11                   0                    0                 0              0
## 12                   0                    0                 0              0
## 13                   0                    0                 0              0
## 14                   0                    0                 0              0
## 15                   0                    0                 0              0
## 16                   0                    0                 5              0
## 17                   0                    0                 0              0
## 18                   0                    0                 0              0
## 19                   0                    0                 0              0
## 20                   0                    0                 0              0
## 21                   0                    0                 0              0
## 22                   0                    0                 0              0
## 23                   0                    0                 0              0
## 24                   1                    0                 0              0
## 25                   0                   12                 0              0
## 26                   0                    0                 0              0
## 27                   0                    1                 0              0
## 28                   0                    3                 0              0
## 29                   0                    2                 0             85
## 30                   0                    0                 0              2
## 31                   0                    0                 0              0
## 32                   0                    2                 0              2
## 33                   0                    0                 0              5
## 34                   0                   24                 0              0
## 35                   0                    2                 0              0
## 36                   0                    0                 2              0
## 37                   0                    2                 0              0
## 38                   0                    1                 0              0
## 39                   0                    6                 1              0
## 40                   0                    0                 6              0
## 41                   0                    0                 6              0
##    Lophocolea.semiteres Lotus.corniculatus Luzula.multiflora
## 1                     0                 69                 0
## 2                     0                120                 0
## 3                    10                 92                 0
## 4                     0                  1                 0
## 5                     0                  0                 0
## 6                     0                  0                 0
## 7                     0                  0                 0
## 8                     0                  0                 1
## 9                     0                  0                 0
## 10                    0                  0                 0
## 11                    0                  0                 0
## 12                    0                  0                 0
## 13                    0                 12                 0
## 14                    0                  0                 0
## 15                    0                  0                 0
## 16                    0                  0                 0
## 17                    0                  0                 0
## 18                    0                220                 0
## 19                    0                 19                 0
## 20                    0                  0                 0
## 21                    0                  0                 0
## 22                    0                  0                 0
## 23                    0                  0                 0
## 24                    0                  0                 0
## 25                    0                 67                 0
## 26                    0                 18                 0
## 27                    0                 31                 0
## 28                    0                 12                 0
## 29                    0                140                 0
## 30                    0                  0                 0
## 31                    0                 14                 0
## 32                    0                  2                 0
## 33                    0                 98                 0
## 34                    0                 17                 0
## 35                    0                  0                 0
## 36                    0                  0                 0
## 37                    0                  0                 0
## 38                    0                  0                 0
## 39                    0                 57                 0
## 40                    0                  0                 0
## 41                    0                 20                 0
##    Lysimachia.maritima Medicago.lupulina Myosotis.arvensis Ononis.repens
## 1                    0                 0                 0             0
## 2                    0                 0                 0             0
## 3                    0                 0                 0             0
## 4                    0                 0                 0             0
## 5                    0                 0                 0             0
## 6                    0                 0                 0             0
## 7                    0                 0                 0             0
## 8                    0                 0                 2             0
## 9                    0                 0                 0             0
## 10                   0                 0                 0             2
## 11                   0                 0                 0             0
## 12                   0                 0                 0             0
## 13                   0                 0                 0             0
## 14                   0                 0                 0             0
## 15                   0                 0                 3             0
## 16                   0                 0                 0             0
## 17                   0                 0                 1             0
## 18                   0                 5                 0             0
## 19                   0                 0                 0             0
## 20                   0                 0                 6             2
## 21                   0                 0                 4            63
## 22                   0                 0                 0             0
## 23                  80                 0                 0             0
## 24                   0                 3                 0             0
## 25                   0                 3                 0             0
## 26                   0                 0                 0             0
## 27                   0                 0                 0             0
## 28                   0                 0                 0             0
## 29                   0                 0                 0             0
## 30                   0                 0                 0             0
## 31                   0                 0                 0           153
## 32                   0                 3                 0             0
## 33                   0                 0                 0             0
## 34                   0                 0                 0             0
## 35                   2                 0                 0             0
## 36                   0                 0                 0             5
## 37                   0                 0                 0             1
## 38                   0                91                 0           111
## 39                   0                 0                 0             2
## 40                   0                 0                 0             0
## 41                   0                 0                 0             0
##    Oxalis.acetosella Pastinaca.sativa Pentaglottis.sempervirens
## 1                  0                0                         0
## 2                  0                0                         0
## 3                  0                0                         0
## 4                  0                0                         0
## 5                  0                0                         0
## 6                  0                0                         0
## 7                  0                0                         0
## 8                  0                0                         0
## 9                  0                0                         0
## 10                 0                0                         0
## 11                 0                0                         0
## 12                 0                0                         0
## 13                 0                0                         0
## 14               113                0                         0
## 15                 0                0                         4
## 16                 0                0                         0
## 17                 0                0                         0
## 18                 0                0                         0
## 19                 0                0                         0
## 20                 0                0                         0
## 21                 0                0                         0
## 22                 0                0                         0
## 23                 0                0                         0
## 24                 0                0                         0
## 25                 0                0                         0
## 26                 0                0                         0
## 27                 0                0                         0
## 28                 0                0                         0
## 29                 0                0                         0
## 30                 0                0                         0
## 31                 0                0                         0
## 32                 0                1                         0
## 33                 0                0                         0
## 34                 0                0                         0
## 35                 0                0                         0
## 36                 0                0                         0
## 37                 0                0                         0
## 38                 0                0                         0
## 39                 0                0                         0
## 40                 0                0                         0
## 41                 0                0                         0
##    Pillosella.officinarum Plantago.coronopus Plantago.lanceolata
## 1                       0                  0                  13
## 2                       0                  0                   0
## 3                       0                  0                   0
## 4                       0                  0                  22
## 5                       0                  0                  36
## 6                       0                  0                   0
## 7                       0                  0                   0
## 8                       0                  0                   0
## 9                       0                  0                   0
## 10                      0                  0                   8
## 11                      0                  0                   0
## 12                      0                  0                   0
## 13                      0                  0                   0
## 14                      0                  0                   0
## 15                      0                  0                   0
## 16                     33                  0                   1
## 17                    286                  0                   0
## 18                      2                  0                   0
## 19                      0                  1                   0
## 20                     54                 19                   0
## 21                      0                  0                   1
## 22                      1                  0                   0
## 23                      0                114                   0
## 24                     22                  0                   0
## 25                      0                  0                   0
## 26                      0                  0                   0
## 27                      0                  0                   0
## 28                      4                  0                   3
## 29                      0                  0                   0
## 30                      0                  0                   1
## 31                      0                  0                   3
## 32                      3                  0                   0
## 33                      0                  0                   0
## 34                     14                  0                   3
## 35                      2                  0                   0
## 36                      0                  0                   0
## 37                      0                  0                   0
## 38                     91                  0                   5
## 39                     39                 50                  20
## 40                      0                  0                   0
## 41                      0                  0                  29
##    Pleurozium.schreberi Poa.annua Poa.spp. Polytrichum.commune
## 1                   110         0        0                   0
## 2                    10         0        0                   0
## 3                     0         0        0                   0
## 4                     0         0        0                   0
## 5                   120         0        0                   0
## 6                     0         0        0                   0
## 7                     0         0        0                   0
## 8                     0         0        0                   0
## 9                    60         0        0                  10
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## 37                    0        46        0                   0
## 38                    0         0        0                   0
## 39                    0        55        0                   0
## 40                    0         0        0                   0
## 41                    0         0        0                   0
##    Polytrichum.commune.agg. Polytrichum.formosum Potentilla.reptans
## 1                         0                    0                  0
## 2                         0                   40                  0
## 3                         0                    0                  0
## 4                         0                    0                  0
## 5                         0                    0                  0
## 6                         0                    0                  0
## 7                         0                    0                  0
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## 31                        0                    0                  1
## 32                        0                    0                  0
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## 36                        0                    0                  0
## 37                        0                    0                  0
## 38                        0                    0                  0
## 39                        0                    0                  0
## 40                        0                    0                  0
## 41                        0                    0                  0
##    Prunella.vulgaris Pseudoscleropidum.purum Pteridium.aquilinum
## 1                  1                      40                   0
## 2                  0                       0                   0
## 3                  2                     150                   0
## 4                  0                     150                   0
## 5                  0                      90                   0
## 6                  0                       0                   8
## 7                  0                       0                   4
## 8                  0                       0                   0
## 9                  0                      10                   0
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## 11                 0                       0                   0
## 12                 0                       0                   0
## 13                 0                       0                   0
## 14                 0                       0                   4
## 15                 0                       0                   0
## 16                 0                       0                   0
## 17                 0                       0                   0
## 18                 0                       0                   0
## 19                 0                       0                   0
## 20                 0                      30                   0
## 21                 0                       0                   0
## 22                 0                       0                   0
## 23                 0                      20                   0
## 24                 0                       0                   0
## 25                 0                       0                   0
## 26                 0                       0                   0
## 27                 0                       0                   0
## 28                 0                     160                   0
## 29                 0                       0                   0
## 30                 2                       0                   0
## 31                 0                       0                   0
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## 33                 0                       0                   0
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## 35                 0                       0                   0
## 36                 0                       0                   0
## 37                 0                       0                   0
## 38                 0                       0                   0
## 39                 0                       0                   0
## 40                 0                       0                   0
## 41                 2                       0                   0
##    Ranunculus.acris Ranunculus.repens Reseda.lutea Rhinanthus.minor
## 1                 0                 0            0                0
## 2                 0                 0            0                0
## 3                 0                 0            0                0
## 4                 0                 0            0                0
## 5                 2                 0            0                0
## 6                 0                 5            0                0
## 7                 0                 0            0                0
## 8                 0                23            0                0
## 9                 0                 0            0                0
## 10                0                 0            0                4
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## 14                0                 0            0                0
## 15                0                 0            0                0
## 16                0                 0            0                0
## 17                0                 0            0                0
## 18                0                 0            0                0
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## 21                0                 0            0                0
## 22                0                 0            0                0
## 23                0                 0            0                0
## 24                0                 0            0                0
## 25                0                 0            0                0
## 26                0                 0            0                0
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## 28                0                 0            0                0
## 29                0                 0            0                0
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## 37                0                 0            0                0
## 38                0                 0            0                0
## 39                0                 0            0                0
## 40                0                 0            0                0
## 41                0                 0            0                0
##    Rhizomnium.punctatum Rhytidadelphus.squarrosus Rhytidadelphus.triquetris
## 1                     0                       160                        20
## 2                     0                         0                         0
## 3                     0                        30                         0
## 4                     0                       150                        20
## 5                     0                        30                         0
## 6                     0                       130                         0
## 7                     0                       160                         0
## 8                     4                       110                         0
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## 20                    0                       140                         0
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## 36                    0                         0                         0
## 37                    0                         0                         0
## 38                    0                         0                         0
## 39                    0                         0                         0
## 40                    0                         0                         0
## 41                    0                         0                         0
##    Rubus.fruticosus Sanguisorba.minor.spp.minor Saniona.uncinata Sedum.anglicum
## 1                 0                           0                0              0
## 2                 0                           0                0              0
## 3                 1                           0                0              0
## 4                 0                           0                0              0
## 5                 0                           0                0              0
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## 9                 0                           0               10              0
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## 24                0                           0                0              0
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## 26                0                          10                0              0
## 27                0                           0                0              0
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## 30                0                           0                0              0
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## 33                0                           0                0              0
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## 38                0                           0                0              0
## 39                0                           0                0              0
## 40                0                           0                0              0
## 41                0                           0                0              0
##    Senecio.jacobaea Senecio.vulgaris Sonchus.arvensis Stachys.sylvatica
## 1                 0                0                0                 0
## 2                 0                0                0                 0
## 3                 0                0                0                 0
## 4                 0                0                0                 0
## 5                 0                0                0                 0
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## 38                0                0                0                 0
## 39                0                0                0                 0
## 40                0                0                0                 0
## 41                0                0                0                 0
##    Stellaria.apetala Taraxacum.agg. Thuidium.tamariscinum Thymus.polytrichus
## 1                  0              0                     0                  0
## 2                  0              0                     0                  0
## 3                  0              0                     0                  0
## 4                  0              0                    30                  0
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## 41                 0              1                     0                  0
##    Trichostomum.crispulum Trifolium.campestre Trifolium.dubium
## 1                       0                   0                0
## 2                       0                   0                0
## 3                       0                   0                0
## 4                       0                   0                0
## 5                       0                   0                0
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## 38                      0                   0                0
## 39                     70                   0                0
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## 41                      0                   0                0
##    Trifolium.pratense Trifolium.repens Trisetum.flavescens Tussilago.farfara
## 1                   0                0                   0                 0
## 2                   0                0                   0                 0
## 3                   0                0                   0                 0
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## 40                  0                0                   0                 0
## 41                 21                0                   0                 0
##    Urtica.diocia Veronica.officinalis Vicia.sativa Viola.riviniana
## 1              0                    0            0               0
## 2              0                    0            0               0
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##    Weissia.controversa Zygodon.stirtonii
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## 41                   0                 0

#Now to do some ANOSIM tests to assess any significant differences between plant species in #different chemical variables.

#anoBSiO2 <- anosim(BarrowPS, BarrowPC$SiO2, distance = “bray”, permutations = 9999)

#When this ANOSIM is run, the error message: “there should be replicates within groups” #comes up. This error message comes up for another substrate variables for the Barrow #data. From now on, only variables that were tested successfully will be included.

anoBK2O <- anosim(BarrowPS, BarrowPC$K2O, distance = "bray", permutations = 9999)

anoBK2O
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$K2O, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.3704 
##       Significance: 0.3281 
## 
## Permutation: free
## Number of permutations: 9999

#Not statistically significant, will mention statistically significant results when #they are generated.

anoBCr2O3 <- anosim(BarrowPS, BarrowPC$Cr2O3, distance = "bray", permutations = 9999)

anoBCr2O3
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$Cr2O3, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.009804 
##       Significance: 0.5134 
## 
## Permutation: free
## Number of permutations: 9999
anoBTiO2 <- anosim(BarrowPS, BarrowPC$TiO2, distance = "bray", permutations = 9999)

anoBTiO2
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$TiO2, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.01701 
##       Significance: 0.5226 
## 
## Permutation: free
## Number of permutations: 9999
anoBMnO <- anosim(BarrowPS, BarrowPC$MnO, distance = "bray", permutations = 9999)

anoBMnO
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$MnO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.2051 
##       Significance: 0.3197 
## 
## Permutation: free
## Number of permutations: 9999
anoBP2O5 <- anosim(BarrowPS, BarrowPC$P2O5, distance = "bray", permutations = 9999)

anoBP2O5
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$P2O5, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.6981 
##       Significance: 0.0429 
## 
## Permutation: free
## Number of permutations: 9999

#R statistic of 0.6981 and p value of 0.0456 for P2O5.

anoBSrO <- anosim(BarrowPS, BarrowPC$SrO, distance = "bray", permutations = 9999)

anoBSrO
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$SrO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1506 
##       Significance: 0.2044 
## 
## Permutation: free
## Number of permutations: 9999
anoBBaO <- anosim(BarrowPS, BarrowPC$BaO, distance = "bray", permutations = 9999)

anoBBaO
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$BaO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.3333 
##       Significance: 0.3464 
## 
## Permutation: free
## Number of permutations: 9999
anoBAg <- anosim(BarrowPS, BarrowPC$Ag, distance = "bray", permutations = 9999)

anoBAg
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$Ag, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.2128 
##       Significance: 0.1985 
## 
## Permutation: free
## Number of permutations: 9999
anoBAs <- anosim(BarrowPS, BarrowPC$As, distance = "bray", permutations = 9999)

anoBAs
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$As, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.2564 
##       Significance: 0.2192 
## 
## Permutation: free
## Number of permutations: 9999
anoBB <- anosim(BarrowPS, BarrowPC$B, distance = "bray", permutations = 9999)

anoBB
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$B, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.09158 
##       Significance: 0.3156 
## 
## Permutation: free
## Number of permutations: 9999
anoBCd <- anosim(BarrowPS, BarrowPC$Cd, distance = "bray", permutations = 9999)

anoBCd
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$Cd, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.01333 
##       Significance: 0.4498 
## 
## Permutation: free
## Number of permutations: 9999
anoBCo <- anosim(BarrowPS, BarrowPC$Co, distance = "bray", permutations = 9999)

anoBCo
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$Co, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:   0.5 
##       Significance: 0.0575 
## 
## Permutation: free
## Number of permutations: 9999

#R statistic of 0.5 and a close-to-significant p value of 0.0586 for Co.

anoBCu <- anosim(BarrowPS, BarrowPC$Cu, distance = "bray", permutations = 9999)

anoBCu
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$Cu, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.4444 
##       Significance: 0.7241 
## 
## Permutation: free
## Number of permutations: 9999
anoBNi <- anosim(BarrowPS, BarrowPC$Ni, distance = "bray", permutations = 9999)

anoBNi
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$Ni, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.434 
##       Significance: 0.1667 
## 
## Permutation: free
## Number of permutations: 9999
anoBS <- anosim(BarrowPS, BarrowPC$S, distance = "bray", permutations = 9999)

anoBS
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$S, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.4444 
##       Significance: 0.7254 
## 
## Permutation: free
## Number of permutations: 9999
anoBSb <- anosim(BarrowPS, BarrowPC$Sb, distance = "bray", permutations = 9999)

anoBSb
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$Sb, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.1795 
##       Significance: 0.8429 
## 
## Permutation: free
## Number of permutations: 9999
anoBSc <- anosim(BarrowPS, BarrowPC$Sc, distance = "bray", permutations = 9999)

anoBSc
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$Sc, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.07979 
##       Significance: 0.3496 
## 
## Permutation: free
## Number of permutations: 9999
anoBV <- anosim(BarrowPS, BarrowPC$V, distance = "bray", permutations = 9999)

anoBV
## 
## Call:
## anosim(x = BarrowPS, grouping = BarrowPC$V, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:     1 
##       Significance: 0.0182 
## 
## Permutation: free
## Number of permutations: 9999

#A high R statistic of 1, with a p value of 0.0186, for V.

#With two of the variables showing significant differences in different Barrow #samples, CCAs will be appropriate to demonstrate what is going on in the data.

BarrowCCA <-cca(BarrowPS, BarrowPC)
## 
## Some constraints or conditions were aliased because they were redundant. This
## can happen if terms are linearly dependent (collinear): 'MnO', 'P2O5', 'SrO',
## 'BaO', 'LOI', 'Ag', 'As', 'B', 'Be', 'Bi', 'Cd', 'Co', 'Cu', 'Ga', 'Hg', 'La',
## 'Li', 'Mo', 'Ni', 'Pb', 'S', 'Sb', 'Sc', 'Th', 'Tl', 'U', 'V', 'W', 'Zn',
## 'Akermanite', 'Albite', 'Aluminium.oxide.hydroxide', 'Anhydrite', 'Aragonite',
## 'Augite', 'Biotite', 'Birnessite', 'Calcite', 'Clinochlore', 'Cuspidine',
## 'Diaspore', 'Dickite', 'Gehlenite', 'Goethite', 'Haematite', 'Illite',
## 'Kaolinite', 'Langite', 'Linnaeite', 'Magnesioferrite', 'Melilite',
## 'Merwinite', 'Microcline', 'Mullite', 'Muscovite', 'Nitratine', 'Orthoclase',
## 'Orthopyroxene', 'Periclase', 'Pigeonite', 'Phengite', 'Pseudowollastonite',
## 'Quartz', 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component
print(BarrowCCA)
## Call: cca(X = BarrowPS, Y = BarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total           4.784      1.000     
## Constrained     4.784      1.000   10
## Unconstrained   0.000      0.000    0
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## Some constraints or conditions were aliased because they were redundant.
## This can happen if terms are linearly dependent (collinear): 'MnO', 'P2O5',
## 'SrO', 'BaO', 'LOI', 'Ag', 'As', 'B', 'Be', 'Bi', 'Cd', 'Co', 'Cu', 'Ga',
## 'Hg', 'La', 'Li', 'Mo', 'Ni', 'Pb', 'S', 'Sb', 'Sc', 'Th', 'Tl', 'U', 'V',
## 'W', 'Zn', 'Akermanite', 'Albite', 'Aluminium.oxide.hydroxide',
## 'Anhydrite', 'Aragonite', 'Augite', 'Biotite', 'Birnessite', 'Calcite',
## 'Clinochlore', 'Cuspidine', 'Diaspore', 'Dickite', 'Gehlenite', 'Goethite',
## 'Haematite', 'Illite', 'Kaolinite', 'Langite', 'Linnaeite',
## 'Magnesioferrite', 'Melilite', 'Merwinite', 'Microcline', 'Mullite',
## 'Muscovite', 'Nitratine', 'Orthoclase', 'Orthopyroxene', 'Periclase',
## 'Pigeonite', 'Phengite', 'Pseudowollastonite', 'Quartz', 'Staurolite',
## 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component.
## 
## 86 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6   CCA7   CCA8   CCA9  CCA10 
## 0.8172 0.7282 0.6488 0.5718 0.5651 0.4823 0.3271 0.2994 0.2659 0.0785
summary(BarrowCCA)
## 
## Call:
## cca(X = BarrowPS, Y = BarrowPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           4.784          1
## Constrained     4.784          1
## Unconstrained   0.000          0
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5   CCA6    CCA7    CCA8
## Eigenvalue            0.8172 0.7282 0.6488 0.5718 0.5651 0.4823 0.32715 0.29937
## Proportion Explained  0.1708 0.1522 0.1356 0.1195 0.1181 0.1008 0.06838 0.06257
## Cumulative Proportion 0.1708 0.3230 0.4586 0.5781 0.6962 0.7970 0.86542 0.92800
##                          CCA9   CCA10
## Eigenvalue            0.26594 0.07853
## Proportion Explained  0.05559 0.01641
## Cumulative Proportion 0.98359 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5   CCA6    CCA7    CCA8
## Eigenvalue            0.8172 0.7282 0.6488 0.5718 0.5651 0.4823 0.32715 0.29937
## Proportion Explained  0.1708 0.1522 0.1356 0.1195 0.1181 0.1008 0.06838 0.06257
## Cumulative Proportion 0.1708 0.3230 0.4586 0.5781 0.6962 0.7970 0.86542 0.92800
##                          CCA9   CCA10
## Eigenvalue            0.26594 0.07853
## Proportion Explained  0.05559 0.01641
## Cumulative Proportion 0.98359 1.00000
plot(BarrowCCA)

#This CCA uses all of the plant data and substrate data. As before, substrate samples will #be selected for CCAs that can be further examined using anova tests.

BarrowCCA1.1 <-cca(BarrowPS ~ pH_level + CaO + MgO + K2O + MgO + Al2O3 + Cr2O3, 
data = BarrowPC)

print(BarrowCCA1.1)
## Call: cca(formula = BarrowPS ~ pH_level + CaO + MgO + K2O + MgO + Al2O3 +
## Cr2O3, data = BarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          4.7843     1.0000     
## Constrained    3.3955     0.7097    6
## Unconstrained  1.3888     0.2903    4
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 86 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.8007 0.6694 0.6292 0.5458 0.4629 0.2875 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3    CA4 
## 0.5421 0.3504 0.2938 0.2025
summary(BarrowCCA1.1)
## 
## Call:
## cca(formula = BarrowPS ~ pH_level + CaO + MgO + K2O + MgO + Al2O3 +      Cr2O3, data = BarrowPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           4.784     1.0000
## Constrained     3.395     0.7097
## Unconstrained   1.389     0.2903
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4    CCA5   CCA6    CA1     CA2
## Eigenvalue            0.8007 0.6694 0.6292 0.5458 0.46287 0.2875 0.5421 0.35042
## Proportion Explained  0.1674 0.1399 0.1315 0.1141 0.09675 0.0601 0.1133 0.07324
## Cumulative Proportion 0.1674 0.3073 0.4388 0.5529 0.64961 0.7097 0.8230 0.89626
##                           CA3     CA4
## Eigenvalue            0.29381 0.20250
## Proportion Explained  0.06141 0.04233
## Cumulative Proportion 0.95767 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6
## Eigenvalue            0.8007 0.6694 0.6292 0.5458 0.4629 0.28751
## Proportion Explained  0.2358 0.1971 0.1853 0.1607 0.1363 0.08468
## Cumulative Proportion 0.2358 0.4330 0.6183 0.7790 0.9153 1.00000
plot(BarrowCCA1.1)

anova(BarrowCCA1.1)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = BarrowPS ~ pH_level + CaO + MgO + K2O + MgO + Al2O3 + Cr2O3, data = BarrowPC)
##          Df ChiSquare      F Pr(>F)    
## Model     6    3.3955 1.6299  0.001 ***
## Residual  4    1.3888                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.6299 and p value of 0.001.

BarrowCCA1.2 <-cca(BarrowPS ~ pH_level + CaO + K2O + Al2O3 + Pb + BaO + Calcite,
                   data = BarrowPC)

print(BarrowCCA1.2)
## Call: cca(formula = BarrowPS ~ pH_level + CaO + K2O + Al2O3 + Pb + BaO +
## Calcite, data = BarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          4.7843     1.0000     
## Constrained    3.8216     0.7988    7
## Unconstrained  0.9627     0.2012    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 86 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6   CCA7 
## 0.7990 0.7092 0.6201 0.5655 0.4759 0.3491 0.3027 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.4930 0.3464 0.1232
summary(BarrowCCA1.2)
## 
## Call:
## cca(formula = BarrowPS ~ pH_level + CaO + K2O + Al2O3 + Pb +      BaO + Calcite, data = BarrowPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          4.7843     1.0000
## Constrained    3.8216     0.7988
## Unconstrained  0.9627     0.2012
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                        CCA1   CCA2   CCA3   CCA4    CCA5    CCA6    CCA7    CA1
## Eigenvalue            0.799 0.7092 0.6201 0.5655 0.47594 0.34914 0.30269 0.4930
## Proportion Explained  0.167 0.1482 0.1296 0.1182 0.09948 0.07298 0.06327 0.1031
## Cumulative Proportion 0.167 0.3152 0.4449 0.5630 0.66253 0.73551 0.79877 0.9018
##                           CA2     CA3
## Eigenvalue            0.34644 0.12325
## Proportion Explained  0.07241 0.02576
## Cumulative Proportion 0.97424 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.7990 0.7092 0.6201 0.5655 0.4759 0.34914 0.30269
## Proportion Explained  0.2091 0.1856 0.1623 0.1480 0.1245 0.09136 0.07921
## Cumulative Proportion 0.2091 0.3947 0.5569 0.7049 0.8294 0.92079 1.00000
anova(BarrowCCA1.2)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = BarrowPS ~ pH_level + CaO + K2O + Al2O3 + Pb + BaO + Calcite, data = BarrowPC)
##          Df ChiSquare      F Pr(>F)   
## Model     7    3.8216 1.7012  0.002 **
## Residual  3    0.9627                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(BarrowCCA1.2)

#F statistic of 1.7012 and p value of 0.001

BarrowCCA1.3 <-cca(BarrowPS ~ pH_level + Cd + K2O + Al2O3 + Pb + BaO + Calcite,
                   data = BarrowPC)

print(BarrowCCA1.3)
## Call: cca(formula = BarrowPS ~ pH_level + Cd + K2O + Al2O3 + Pb + BaO +
## Calcite, data = BarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          4.7843     1.0000     
## Constrained    3.7693     0.7878    7
## Unconstrained  1.0150     0.2122    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 86 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6   CCA7 
## 0.8041 0.6865 0.6151 0.5653 0.4426 0.3398 0.3159 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.4643 0.4117 0.1391
summary(BarrowCCA1.3)
## 
## Call:
## cca(formula = BarrowPS ~ pH_level + Cd + K2O + Al2O3 + Pb + BaO +      Calcite, data = BarrowPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           4.784     1.0000
## Constrained     3.769     0.7878
## Unconstrained   1.015     0.2122
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4    CCA5    CCA6    CCA7
## Eigenvalue            0.8041 0.6865 0.6151 0.5653 0.44263 0.33975 0.31589
## Proportion Explained  0.1681 0.1435 0.1286 0.1182 0.09252 0.07101 0.06603
## Cumulative Proportion 0.1681 0.3116 0.4401 0.5583 0.65081 0.72182 0.78785
##                           CA1     CA2     CA3
## Eigenvalue            0.46428 0.41168 0.13905
## Proportion Explained  0.09704 0.08605 0.02906
## Cumulative Proportion 0.88489 0.97094 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.8041 0.6865 0.6151 0.5653 0.4426 0.33975 0.31589
## Proportion Explained  0.2133 0.1821 0.1632 0.1500 0.1174 0.09014 0.08381
## Cumulative Proportion 0.2133 0.3955 0.5587 0.7086 0.8261 0.91619 1.00000
anova(BarrowCCA1.3)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = BarrowPS ~ pH_level + Cd + K2O + Al2O3 + Pb + BaO + Calcite, data = BarrowPC)
##          Df ChiSquare      F Pr(>F)    
## Model     7    3.7693 1.5915  0.001 ***
## Residual  3    1.0150                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(BarrowCCA1.3)

#F statistic of 1.5915 and p value of 0.002

BarrowCCA1.4 <-cca(BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Calcite,
                   data = BarrowPC)

print(BarrowCCA1.4)
## Call: cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Calcite, data
## = BarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          4.7843     1.0000     
## Constrained    2.7935     0.5839    5
## Unconstrained  1.9908     0.4161    5
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 86 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5 
## 0.7867 0.6796 0.6052 0.3846 0.3373 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3    CA4    CA5 
## 0.6168 0.5222 0.4209 0.3203 0.1106
summary(BarrowCCA1.4)
## 
## Call:
## cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Calcite,      data = BarrowPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           4.784     1.0000
## Constrained     2.793     0.5839
## Unconstrained   1.991     0.4161
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4    CCA5    CA1    CA2     CA3
## Eigenvalue            0.7867 0.6796 0.6052 0.3846 0.33727 0.6168 0.5222 0.42092
## Proportion Explained  0.1644 0.1421 0.1265 0.0804 0.07049 0.1289 0.1092 0.08798
## Cumulative Proportion 0.1644 0.3065 0.4330 0.5134 0.58388 0.7128 0.8220 0.90994
##                           CA4     CA5
## Eigenvalue            0.32029 0.11059
## Proportion Explained  0.06695 0.02311
## Cumulative Proportion 0.97689 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5
## Eigenvalue            0.7867 0.6796 0.6052 0.3846 0.3373
## Proportion Explained  0.2816 0.2433 0.2166 0.1377 0.1207
## Cumulative Proportion 0.2816 0.5249 0.7416 0.8793 1.0000
anova(BarrowCCA1.4)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Calcite, data = BarrowPC)
##          Df ChiSquare      F Pr(>F)   
## Model     5    2.7935 1.4032  0.003 **
## Residual  5    1.9908                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(BarrowCCA1.4)

#F statistic of 1.4032 and p value of 0.002

BarrowCCA1.5 <-cca(BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni + Pb + Calcite,
                   data = BarrowPC)

print(BarrowCCA1.5)
## Call: cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni + Pb +
## Calcite, data = BarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          4.7843     1.0000     
## Constrained    3.8385     0.8023    7
## Unconstrained  0.9458     0.1977    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 86 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6   CCA7 
## 0.7987 0.7205 0.6123 0.5664 0.5006 0.3367 0.3033 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.4613 0.3326 0.1519
summary(BarrowCCA1.5)
## 
## Call:
## cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni +      Pb + Calcite, data = BarrowPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          4.7843     1.0000
## Constrained    3.8385     0.8023
## Unconstrained  0.9458     0.1977
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6   CCA7     CA1
## Eigenvalue            0.7987 0.7205 0.6123 0.5664 0.5006 0.33667 0.3033 0.46130
## Proportion Explained  0.1669 0.1506 0.1280 0.1184 0.1046 0.07037 0.0634 0.09642
## Cumulative Proportion 0.1669 0.3175 0.4455 0.5639 0.6685 0.73892 0.8023 0.89874
##                           CA2     CA3
## Eigenvalue            0.33262 0.15186
## Proportion Explained  0.06952 0.03174
## Cumulative Proportion 0.96826 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.7987 0.7205 0.6123 0.5664 0.5006 0.33667 0.30333
## Proportion Explained  0.2081 0.1877 0.1595 0.1476 0.1304 0.08771 0.07902
## Cumulative Proportion 0.2081 0.3958 0.5553 0.7028 0.8333 0.92098 1.00000
anova(BarrowCCA1.5)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni + Pb + Calcite, data = BarrowPC)
##          Df ChiSquare      F Pr(>F)    
## Model     7    3.8385 1.7394  0.001 ***
## Residual  3    0.9458                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(BarrowCCA1.5)

#F statistic of 1.7394 and p value of 0.001

BarrowCCA1.6 <-cca(BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni + Cd + Calcite,
                   data = BarrowPC)

print(BarrowCCA1.6)
## Call: cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni + Cd +
## Calcite, data = BarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          4.7843     1.0000     
## Constrained    3.8575     0.8063    7
## Unconstrained  0.9267     0.1937    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 86 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6   CCA7 
## 0.8032 0.7098 0.6100 0.5608 0.5214 0.3372 0.3151 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.4590 0.3245 0.1432
summary(BarrowCCA1.6)
## 
## Call:
## cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni +      Cd + Calcite, data = BarrowPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          4.7843     1.0000
## Constrained    3.8575     0.8063
## Unconstrained  0.9267     0.1937
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.8032 0.7098 0.6100 0.5608 0.5214 0.33717 0.31510
## Proportion Explained  0.1679 0.1484 0.1275 0.1172 0.1090 0.07047 0.06586
## Cumulative Proportion 0.1679 0.3163 0.4438 0.5610 0.6700 0.74043 0.80629
##                           CA1     CA2     CA3
## Eigenvalue            0.45903 0.32449 0.14324
## Proportion Explained  0.09594 0.06782 0.02994
## Cumulative Proportion 0.90224 0.97006 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5   CCA6    CCA7
## Eigenvalue            0.8032 0.7098 0.6100 0.5608 0.5214 0.3372 0.31510
## Proportion Explained  0.2082 0.1840 0.1581 0.1454 0.1352 0.0874 0.08168
## Cumulative Proportion 0.2082 0.3922 0.5504 0.6957 0.8309 0.9183 1.00000
anova(BarrowCCA1.6)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni + Cd + Calcite, data = BarrowPC)
##          Df ChiSquare      F Pr(>F)   
## Model     7    3.8575 1.7839  0.002 **
## Residual  3    0.9267                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(BarrowCCA1.6)

#F statistic of 1.7839 and p value of 0.001

BarrowCCA1.7 <-cca(BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni + As + Calcite,
                   data = BarrowPC)

print(BarrowCCA1.7)
## Call: cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni + As +
## Calcite, data = BarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          4.7843     1.0000     
## Constrained    3.7660     0.7872    7
## Unconstrained  1.0183     0.2128    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 86 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6   CCA7 
## 0.8130 0.7057 0.6142 0.5347 0.4617 0.3366 0.3001 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.4719 0.3936 0.1527
summary(BarrowCCA1.7)
## 
## Call:
## cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni +      As + Calcite, data = BarrowPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           4.784     1.0000
## Constrained     3.766     0.7872
## Unconstrained   1.018     0.2128
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.8130 0.7057 0.6142 0.5347 0.4617 0.33662 0.30013
## Proportion Explained  0.1699 0.1475 0.1284 0.1118 0.0965 0.07036 0.06273
## Cumulative Proportion 0.1699 0.3174 0.4458 0.5576 0.6541 0.72443 0.78716
##                           CA1     CA2     CA3
## Eigenvalue            0.47193 0.39363 0.15273
## Proportion Explained  0.09864 0.08228 0.03192
## Cumulative Proportion 0.88580 0.96808 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.8130 0.7057 0.6142 0.5347 0.4617 0.33662 0.30013
## Proportion Explained  0.2159 0.1874 0.1631 0.1420 0.1226 0.08938 0.07969
## Cumulative Proportion 0.2159 0.4033 0.5663 0.7083 0.8309 0.92031 1.00000
anova(BarrowCCA1.7)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Ni + As + Calcite, data = BarrowPC)
##          Df ChiSquare     F Pr(>F)   
## Model     7    3.7660 1.585  0.002 **
## Residual  3    1.0183                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(BarrowCCA1.7)

#F statistic of 1.585 and p value of 0.001

BarrowCCA1.8 <-cca(BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Pb + As + Calcite,
                   data = BarrowPC)

print(BarrowCCA1.8)
## Call: cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Pb + As +
## Calcite, data = BarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          4.7843     1.0000     
## Constrained    3.8046     0.7952    7
## Unconstrained  0.9797     0.2048    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 86 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6   CCA7 
## 0.7980 0.6957 0.6118 0.5705 0.4903 0.3365 0.3017 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.4735 0.3520 0.1542
summary(BarrowCCA1.8)
## 
## Call:
## cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Pb +      As + Calcite, data = BarrowPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          4.7843     1.0000
## Constrained    3.8046     0.7952
## Unconstrained  0.9797     0.2048
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6    CCA7
## Eigenvalue            0.7980 0.6957 0.6118 0.5705 0.4903 0.33654 0.30172
## Proportion Explained  0.1668 0.1454 0.1279 0.1193 0.1025 0.07034 0.06307
## Cumulative Proportion 0.1668 0.3122 0.4401 0.5593 0.6618 0.73217 0.79523
##                           CA1     CA2     CA3
## Eigenvalue            0.47352 0.35195 0.15420
## Proportion Explained  0.09897 0.07356 0.03223
## Cumulative Proportion 0.89421 0.96777 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6   CCA7
## Eigenvalue            0.7980 0.6957 0.6118 0.5705 0.4903 0.33654 0.3017
## Proportion Explained  0.2098 0.1829 0.1608 0.1500 0.1289 0.08846 0.0793
## Cumulative Proportion 0.2098 0.3926 0.5534 0.7034 0.8322 0.92070 1.0000
anova(BarrowCCA1.8)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = BarrowPS ~ pH_level + K2O + Al2O3 + BaO + Pb + As + Calcite, data = BarrowPC)
##          Df ChiSquare      F Pr(>F)   
## Model     7    3.8046 1.6644  0.002 **
## Residual  3    0.9797                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(BarrowCCA1.8)

#F statistic of 1.6644 and p value of 0.001

BarrowCCA2 <- cca(BarrowPS ~ Na2O + pH_level + MgO + CaO + Al2O3 + Cr2O3, data = BarrowPC)

print(BarrowCCA2)
## Call: cca(formula = BarrowPS ~ Na2O + pH_level + MgO + CaO + Al2O3 + Cr2O3,
## data = BarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          4.7843     1.0000     
## Constrained    3.3915     0.7089    6
## Unconstrained  1.3928     0.2911    4
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 86 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.8022 0.6645 0.6288 0.5407 0.4594 0.2958 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3    CA4 
## 0.5675 0.3797 0.3068 0.1388
summary(BarrowCCA2)
## 
## Call:
## cca(formula = BarrowPS ~ Na2O + pH_level + MgO + CaO + Al2O3 +      Cr2O3, data = BarrowPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           4.784     1.0000
## Constrained     3.392     0.7089
## Unconstrained   1.393     0.2911
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4    CCA5    CCA6    CA1
## Eigenvalue            0.8022 0.6645 0.6288 0.5407 0.45942 0.29580 0.5675
## Proportion Explained  0.1677 0.1389 0.1314 0.1130 0.09603 0.06183 0.1186
## Cumulative Proportion 0.1677 0.3066 0.4380 0.5510 0.64706 0.70889 0.8275
##                           CA2     CA3     CA4
## Eigenvalue            0.37966 0.30684 0.13880
## Proportion Explained  0.07935 0.06413 0.02901
## Cumulative Proportion 0.90685 0.97099 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4   CCA5    CCA6
## Eigenvalue            0.8022 0.6645 0.6288 0.5407 0.4594 0.29580
## Proportion Explained  0.2365 0.1959 0.1854 0.1594 0.1355 0.08722
## Cumulative Proportion 0.2365 0.4325 0.6179 0.7773 0.9128 1.00000
plot(BarrowCCA2)

anova(BarrowCCA2)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = BarrowPS ~ Na2O + pH_level + MgO + CaO + Al2O3 + Cr2O3, data = BarrowPC)
##          Df ChiSquare      F Pr(>F)   
## Model     6    3.3915 1.6234  0.002 **
## Residual  4    1.3928                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.6234 and a p value of 0.001

#After carrying out multiple CCAs with different substrate variables, the one with the #highest F statistic and lowest p value is BarrowCCA1.6, with an F statistic of 1.7839 and #a p value of 0.001. The plot for this CCA is also satisfying from a visual point of view.

#To better visualise the BarrowCCA1.6 graph…

BarrowCCA1.6$CCA$v
##                                    CCA1        CCA2        CCA3        CCA4
## Anthyllis.vulneraria        -1.31783160  0.35344535  1.72526151  0.10831579
## Aphanes.arvensis             1.47725932 -1.45761344  0.89570041 -1.02027936
## Arrhenatherum.elatius        0.41847103  0.92233498 -1.21985277 -0.58026244
## Bellis.perennis             -0.82748643 -0.77869917 -0.29202006 -0.10794327
## Blackstonia.perfoliata       1.50629701 -1.54369063  1.04515424 -1.85832964
## Brachythecium.albicans       0.10596200  0.52186038  0.38591936  0.29236224
## Brachythecium.rutabulum      0.10596200  0.52186038  0.38591936  0.29236224
## Briza.media                 -1.08445495  0.84019621  2.03456891  0.26570300
## Bromus.hordeaceus            0.43181039  1.01456410 -0.94551197 -0.92298231
## Calliergonella.cupsidata    -0.13149294  1.08372274  0.04481003  0.43849112
## Carex.flacca                 1.37562743 -1.15634329  0.37261199  1.91289664
## Carlina.vulgaris            -0.07277018  0.11542055 -1.64881538 -0.35202766
## Centaurium.erythraea         1.39223263 -1.43816970  0.79375160 -1.77550801
## Cerastium.fontanum          -0.44087789  0.23554575  0.25979022  0.60450856
## Cynosurus.cristatus          1.36994614 -1.13950210  0.34337102  2.07686300
## Daucus.carrota              -1.29452700 -0.84029216 -0.70822708 -0.66584380
## Erigeron.acer               -0.16892842  0.05979744 -2.43403419 -0.54447573
## Euphrasia.agg               -0.16861263  0.13758349  0.99812102 -0.37531258
## Festuca.ovina               -2.16781758 -2.37668105 -1.74960213  1.43259817
## Festuca.rubra                0.38636736  0.30260809 -0.76250886  0.12681728
## Galium.verum                -0.49157541  0.72140172  1.32036880  0.30472551
## Helicotrichon.spp.           0.43181039  1.01456410 -0.94551197 -0.92298231
## Hieracium.spp.              -2.14035453 -1.64782243 -0.23294158 -0.98281037
## Holcus.spp.                  0.38602690  0.68352800 -0.67238629 -0.39231100
## Holcus.lanatus              -0.17771215  1.06544204 -0.42965627  0.15467772
## Holcus.mollis                0.39712806  0.77476838 -1.65879807 -0.03191065
## Hypericum.perforatum        -0.02001079  0.14593942 -1.21798736 -0.24643668
## Hypochaeris.radicata        -0.15616075  1.45419652 -0.47304882  0.24807544
## Lathyrus.pratensis           1.33207090 -1.02722751  0.14843124  3.16997207
## Leontodon.hispidus          -2.15096525 -1.92942689 -0.81892407 -0.04958434
## Leontodon.saxatilis         -2.16864979 -2.39876768 -1.79556155  1.50579237
## Leucanthemum.vulgare        -0.12117400  0.19052215 -0.75262119 -0.18601055
## Lolium.perenne               0.43557796  0.93761258 -0.99805762 -0.78196931
## Lotus.corniculatus           0.19242291  0.69218956 -0.64193091 -0.35637040
## Medicago.lupulina           -0.75578548 -0.61259464 -1.37850920  0.39404984
## Ononis.repens                1.50629701 -1.54369063  1.04515424 -1.85832964
## Pastinaca.sativa            -0.20466866  0.03912337 -2.72588543 -0.61600510
## Pillosella.officinarum      -1.32943885 -1.33031760 -1.52706046  0.55576888
## Plantago.lanceolata         -0.06301341 -1.01639484 -0.10688928 -0.60927580
## Poa.spp.                     0.43181039  1.01456410 -0.94551197 -0.92298231
## Potentilla.reptans           1.26882247 -0.98148074  0.10252839  2.87344409
## Prunella.vulgaris            0.23439979 -0.26554831 -1.90465210  0.46570267
## Pseudoscleropidum.purum     -2.14035453 -1.64782243 -0.23294158 -0.98281037
## Ranunculus.repens           -0.15616075  1.45419652 -0.47304882  0.24807544
## Reseda.lutea                -0.20466866  0.03912337 -2.72588543 -0.61600510
## Sanguisorba.minor.spp.minor -0.16443489  0.61788885  0.82765566  0.30301405
## Sedum.anglicum              -0.20466866  0.03912337 -2.72588543 -0.61600510
## Senecio.jacobaea             0.43181039  1.01456410 -0.94551197 -0.92298231
## Senecio.vulgaris            -2.16864979 -2.39876768 -1.79556155  1.50579237
## Stellaria.apetala            1.33207090 -1.02722751  0.14843124  3.16997207
## Taraxacum.agg.              -0.48921717 -0.21700151 -1.49792538 -0.04552504
## Trifolium.campestre         -0.35166734  0.38932905  0.54369090  0.42056145
## Trifolium.pratense           0.10596200  0.52186038  0.38591936  0.29236224
## Trifolium.repens            -0.18807514  1.14975776  0.06840299  0.51800641
## Trisetum.flavescens          1.40668346 -1.53368733  0.98526977 -1.82786600
##                                    CCA5        CCA6        CCA7
## Anthyllis.vulneraria        -0.15909328 -0.01637360 -1.27877544
## Aphanes.arvensis            -0.37431626  0.16909897  0.21072447
## Arrhenatherum.elatius        0.82904525  0.99413159 -1.72571133
## Bellis.perennis             -0.15793714 -0.86917411  0.45913227
## Blackstonia.perfoliata      -0.66163215  0.23899293  0.35042576
## Brachythecium.albicans      -0.47222875  0.05360410  2.10858157
## Brachythecium.rutabulum     -0.47222875  0.05360410  2.10858157
## Briza.media                 -0.52367916  0.03357637 -1.32815327
## Bromus.hordeaceus            1.37679534  1.50471714 -1.31947802
## Calliergonella.cupsidata    -0.03004727  0.03917917  2.65329483
## Carex.flacca                 0.63128935 -0.07552989 -0.27823004
## Carlina.vulgaris            -1.99353884 -4.78080560 -0.92758623
## Centaurium.erythraea        -0.94561252  0.26269594  0.27963569
## Cerastium.fontanum           0.59815172 -0.15055271  1.21378877
## Cynosurus.cristatus          0.68750332 -0.08920479 -0.30556290
## Daucus.carrota               1.60133814 -0.43866171 -0.42644434
## Erigeron.acer               -4.12799862 -0.86200667 -0.76999796
## Euphrasia.agg               -1.00442047 -0.84266537 -1.08163765
## Festuca.ovina               -2.35603223  2.72840836 -0.04398466
## Festuca.rubra               -0.14203246 -0.72408045 -0.18213617
## Galium.verum                -0.58188337  0.06248474  0.12825326
## Helicotrichon.spp.           1.37679534  1.50471714 -1.31947802
## Hieracium.spp.               2.42568466 -0.74658992  0.54817580
## Holcus.spp.                  0.50513517  0.61932151 -0.25794795
## Holcus.lanatus               0.11867588  0.02481545  2.50811105
## Holcus.mollis               -0.04735490  0.17719472 -2.37568462
## Hypericum.perforatum        -0.82241932 -6.93094307 -1.01405059
## Hypochaeris.radicata         0.11971398  0.04817286  3.89299276
## Lathyrus.pratensis           1.06226318 -0.18037082 -0.48778197
## Leontodon.hispidus           0.57820313  0.59602305  0.31938653
## Leontodon.saxatilis         -2.50093275  2.83371134 -0.06192892
## Leucanthemum.vulgare        -0.57038921 -3.72028343  0.05548814
## Lolium.perenne               1.16034766  1.37888579 -1.34502627
## Lotus.corniculatus           0.35825771  0.28135716 -0.48811467
## Medicago.lupulina           -2.63149972  1.16061783  0.44507577
## Ononis.repens               -0.66163215  0.23899293  0.35042576
## Pastinaca.sativa            -4.92133766  0.59453807 -0.71142533
## Pillosella.officinarum      -1.66501547 -0.83475114 -0.36048180
## Plantago.lanceolata          0.38871628 -2.24959910 -0.08341291
## Poa.spp.                     1.37679534  1.50471714 -1.31947802
## Potentilla.reptans           0.92493167 -0.50741534 -0.49314020
## Prunella.vulgaris           -3.21173742  0.37313553 -0.64752723
## Pseudoscleropidum.purum      2.42568466 -0.74658992  0.54817580
## Ranunculus.repens            0.11971398  0.04817286  3.89299276
## Reseda.lutea                -4.92133766  0.59453807 -0.71142533
## Sanguisorba.minor.spp.minor -0.53231703  0.05911486  1.22539587
## Sedum.anglicum              -4.92133766  0.59453807 -0.71142533
## Senecio.jacobaea             1.37679534  1.50471714 -1.31947802
## Senecio.vulgaris            -2.50093275  2.83371134 -0.06192892
## Stellaria.apetala            1.06226318 -0.18037082 -0.48778197
## Taraxacum.agg.              -2.33525763 -2.57401785 -0.83317678
## Trifolium.campestre         -0.55190635  0.24853346  1.19448055
## Trifolium.pratense          -0.47222875  0.05360410  2.10858157
## Trifolium.repens             0.05274762  0.03346099  2.52589439
## Trisetum.flavescens         -0.62224440  0.21851101  0.34673599
## attr(,"na.action")
##              Agrostis.spp.            Agrostis.canina 
##                          1                          2 
##          Alchemilla.mollis        Alopercus.pratensis 
##                          3                          4 
##        Angelica.sylvestris      Anthoxanthum.odoratum 
##                          5                          6 
##         Atrichum.undulatum          Avenula.pratensis 
##                         10                         11 
##           Betula.pubescens    Brachythecium.glareosum 
##                         13                         16 
##    Brachythecium.mildeanum    Bryum.c.f..caespiticium 
##                         17                         21 
##      Bryum.c.f..pallescens            Bryum.capillare 
##                         22                         23 
##                 Bryum.spp.     Campanula.rotundifolia 
##                         24                         26 
##              Carex.distans              Carex.panicea 
##                         27                         29 
##            Centaurea.nigra       Centaurium.littorale 
##                         31                         33 
##      Centaurium.pulchellum Chamaenerion.angustifolium 
##                         34                         36 
##     Cirriphyllum.piliferum            Cirsium.arvense 
##                         37                         38 
##           Cirsium.palustre          Crepis.capillaris 
##                         39                         40 
##         Dactylis.glomerata        Danthonia.decumbens 
##                         42                         43 
##            Dicranella.spp.         Dicranum.scoparium 
##                         45                         46 
##         Epilobium.montanum          Equisetum.arvense 
##                         47                         48 
##       Equisteum.variegatum         Festuca.rubra.agg. 
##                         49                         54 
##        Filipendula.ulmaria     Fissidens.adianthoides 
##                         55                         56 
##           Fissidens.dubius           Fissidens.exilis 
##                         57                         58 
##             Fragaria.vesca             Galium.aparine 
##                         59                         60 
##             Galium.arvense            Galium.saxatile 
##                         61                         62 
##               Geum.urbanum         Glechoma.hederacea 
##                         64                         65 
##      Heracleum.sphondylium    Homalothecium.lutescens 
##                         67                         72 
##       Hylocomium.splendens       Hypnum.cupressiforme 
##                         73                         75 
##            Hypnum.imponens         Hypnum.jutlandicum 
##                         76                         77 
##       Kindbergia.praelonga          Linum.catharticum 
##                         79                         84 
##       Lophocolea.semiteres          Luzula.multiflora 
##                         86                         88 
##        Lysimachia.maritima          Myosotis.arvensis 
##                         89                         91 
##          Oxalis.acetosella  Pentaglottis.sempervirens 
##                         93                         95 
##         Plantago.coronopus       Pleurozium.schreberi 
##                         97                         99 
##                  Poa.annua        Polytrichum.commune 
##                        100                        102 
##   Polytrichum.commune.agg.       Polytrichum.formosum 
##                        103                        104 
##        Pteridium.aquilinum           Ranunculus.acris 
##                        108                        109 
##     Ranunculus.parviflorus           Rhinanthus.minor 
##                        110                        113 
##       Rhizomnium.punctatum  Rhytidadelphus.squarrosus 
##                        114                        115 
##  Rhytidadelphus.triquetris           Rubus.fruticosus 
##                        116                        117 
##           Saniona.uncinata           Sonchus.arvensis 
##                        119                        123 
##          Stachys.sylvatica      Thuidium.tamariscinum 
##                        124                        127 
##         Thymus.polytrichus     Trichostomum.crispulum 
##                        128                        129 
##           Trifolium.dubium          Tussilago.farfara 
##                        131                        135 
##              Urtica.diocia       Veronica.officinalis 
##                        136                        137 
##               Vicia.sativa            Viola.riviniana 
##                        138                        139 
##        Weissia.controversa          Zygodon.stirtonii 
##                        140                        141 
## attr(,"class")
## [1] "exclude"

#The “v values” show the positions of individual species on the graph, with the CCA1 value #representing the x axis and the CCA2 value representing the y axis, in the case of the #graph created in R.

plot(BarrowCCA1.6, choices = c(1,2), display = c("wa", "bp"), xlim = c(-4, 3),
     ylim = c(-3, 2))


#Increasing the xlim and ylim to give more room for writing on graph

points(x = -2.14035453, y = -1.64782243, pch = 15, col = "black")

#This point represents Pseudoscleropodium purum

text('P. purum', x = -2.14035453, y = -1.64782243, cex = 0.88, pos = 2, col = "black")

#Adding text for Pseudoscleropodium purum

points(x = -1.08445495, y = 0.84019621, pch = 15, col = "black")

#This point represents Briza media

text('Briza media', x = -1.08445495, y = 0.84019621, cex = 0.88, pos = 2, col = "black")

#Adding text for Briza media

points(x = -0.06301341, y = -1.01639484, pch = 15, col = "black")

#This point represents Plantago lanceolata

text('P. lanceolata', x = 1.1, y = -1.3, cex = 0.88, pos = 2, col = "black")

#Adding text for Plantago lanceolata

points(x = -2.16781758, y = -2.37668105, pch = 15, col = "black")

#This point represents Festuca ovina

text('F. ovina', x = -2.16781758, y = -2.37668105, cex = 0.88, pos = 2, col = "black")

#Adding text for Festuca ovina

points(x = 1.50629701, y = -1.54369063, pch = 15, col = "black")

#This point represents Blackstonia perfoliata

text('B. perfoliata', x = 3.5, y = -1.54369063, cex = 0.88, pos = 2, col = "black")

#Adding text for Blackstonia perfoliata

points(x = 0.43181039, y = 1.01456410, pch = 15, col = "black")

#This point represents Bromus hordeaceus

text('B. hordeaceus', x = 1.64, y = 1.01456410, pch = 15, col = "black")

#Adding text for Bromus hordeaceus

#Fallin Data#

urlfile5 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-for-six-study-sites-for-PhD/PhD-files/FallinPlantSpecies.csv'

FallinPS <- read.csv(urlfile5,  header = TRUE, colClasses = c("numeric"))

urlfile6 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/FALLIN_PLANT_CHEMISTRY_MG_KG.csv'

FallinPC <-read.csv(urlfile6, header = TRUE, colClasses = c("numeric"))

head(FallinPS)
##   Agrostis.spp. Agrostis.canina Alchemilla.mollis Alopercus.pratensis
## 1             0               0                 0                   0
## 2             9               0                 0                   0
## 3             1               0                 0                   0
## 4             0               0                 0                   0
## 5             0               0                 0                   0
##   Angelica.sylvestris Anthoxanthum.odoratum Anthyllis.vulneraria
## 1                   0                    81                    0
## 2                   0                    18                    0
## 3                   0                     8                    0
## 4                   0                    82                    0
## 5                   0                    55                    0
##   Aphanes.arvensis Arrhenatherum.elatius Atrichum.undulatum Avenula.pratensis
## 1                0                     0                  0                 0
## 2                0                     0                  0                 0
## 3                0                     0                  0                 0
## 4                0                     2                  0                 0
## 5                0                    42                 10                 0
##   Bellis.perennis Betula.pubescens Blackstonia.perfoliata
## 1               1                0                      0
## 2               0                0                      0
## 3               8               12                      0
## 4              16                0                      0
## 5               0                0                      0
##   Brachythecium.albicans Brachythecium.glareosum Brachythecium.mildeanum
## 1                      0                       0                       0
## 2                      0                       0                       0
## 3                      0                       0                       0
## 4                      0                       0                       0
## 5                      0                       0                       0
##   Brachythecium.rutabulum Briza.media Bromus.hordeaceus Bryum.c.f..caespiticium
## 1                       0           0                 0                       0
## 2                       0           0                 0                       0
## 3                       0           0                 0                      10
## 4                       0           0                 0                       0
## 5                       0           0                 0                       0
##   Bryum.c.f..pallescens Bryum.capillare Bryum.spp. Calliergonella.cupsidata
## 1                     0               0          0                        0
## 2                     0              10          0                        0
## 3                    10               0          0                       10
## 4                     0               0          0                       10
## 5                     0               0          0                       30
##   Calypogeia.arguta Campanula.rotundifolia Carex.distans Carex.flacca
## 1                 0                      0             0            0
## 2                20                      0             0            0
## 3                 0                      0             0            0
## 4                 0                      0             0            0
## 5                30                      0             0            0
##   Carex.panicea Carlina.vulgaris Centaurea.nigra Centaurium.erythraea
## 1             0                0               0                    0
## 2             0                0               0                    0
## 3             0                0               0                    0
## 4             0                0               0                    0
## 5             0                0               0                    0
##   Centaurium.littorale Centaurium.pulchellum Cerastium.fontanum
## 1                    0                     0                  0
## 2                    0                     0                  6
## 3                    0                     0                  0
## 4                    0                     0                  0
## 5                    0                     0                  0
##   Chamaenerion.angustifolium Cirriphyllum.piliferum Cirsium.arvense
## 1                          0                      0               0
## 2                          0                      0               0
## 3                          0                     10               0
## 4                          0                      0               0
## 5                          0                      0               0
##   Cirsium.palustre Crepis.capillaris Cynosurus.cristatus Dactylis.glomerata
## 1                0                 4                   0                  1
## 2                0                 0                   0                  0
## 3                0                 0                   0                  0
## 4                0                 1                   0                  0
## 5                0                 0                   0                  0
##   Dactylorhiza.fuchsii Danthonia.decumbens Daucus.carrota Dicranella.spp.
## 1                    0                   0              0               0
## 2                    0                   0              0               0
## 3                    0                   0              0               0
## 4                    0                   0              0               0
## 5                    0                   0              0               0
##   Dicranum.scoparium Epilobium.montanum Equisetum.arvense Equisteum.variegatum
## 1                 30                  0                 0                    0
## 2                 20                  0                 0                    0
## 3                  0                  0                 0                    0
## 4                 10                  0                 0                    0
## 5                 16                  0                 0                    0
##   Erigeron.acer Euphrasia.agg Festuca.ovina Festuca.rubra Festuca.rubra.agg.
## 1             0             3             0             0                  0
## 2             0             0             0             0                  5
## 3             0             6             0             0                  0
## 4             0             0             0             0                  0
## 5             0             1             0             0                  0
##   Filipendula.ulmaria Fissidens.adianthoides Fissidens.dubius Fissidens.exilis
## 1                   0                      0                0                0
## 2                   0                      0                0                0
## 3                   0                     10               10                0
## 4                   0                      0                0                0
## 5                   0                      0                0                0
##   Fragaria.vesca Galium.aparine Galium.arvense Galium.saxatile Galium.verum
## 1             67              0              0               0            0
## 2             38              0              0               0            0
## 3             65              0              0               0            0
## 4            117              0              0               0            0
## 5             68              0              0               0            0
##   Geum.urbanum Glechoma.hederacea Helicotrichon.spp. Heracleum.sphondylium
## 1            0                  0                  0                     0
## 2            0                  0                  0                     0
## 3            0                  0                  0                     0
## 4            0                  0                  0                     0
## 5            0                  0                  0                     0
##   Hieracium.spp. Holcus.spp. Holcus.lanatus Holcus.mollis
## 1              0           0             30             0
## 2              0           0             80             0
## 3              0           0              0             0
## 4              0           0             28             0
## 5              0           0             36             0
##   Homalothecium.lutescens Hylocomium.splendens Hypericum.perforatum
## 1                       0                   50                   11
## 2                       0                   80                   24
## 3                       0                  110                    2
## 4                       0                  160                    4
## 5                       0                   90                    1
##   Hypnum.cupressiforme Hypnum.imponens Hypnum.jutlandicum Hypochaeris.radicata
## 1                    0               0                  0                    0
## 2                   10               0                 20                    0
## 3                   60               0                  0                    0
## 4                   10               0                  0                    0
## 5                   20               0                120                    0
##   Kindbergia.praelonga Lathyrus.pratensis Leontodon.hispidus
## 1                    0                  0                  0
## 2                    0                  0                  0
## 3                    0                  0                  0
## 4                    0                  0                  0
## 5                    0                  0                  0
##   Leontodon.saxatilis Leucanthemum.vulgare Linum.catharticum Lolium.perenne
## 1                   0                   20                 0              0
## 2                   0                   15                 0              0
## 3                   0                    0                 0              0
## 4                   0                    7                 0              0
## 5                   0                    1                 0              0
##   Lophocolea.semiteres Lotus.corniculatus Luzula.multiflora Lysimachia.maritima
## 1                    0                 69                 0                   0
## 2                    0                120                 0                   0
## 3                   10                 92                 0                   0
## 4                    0                  1                 0                   0
## 5                    0                  0                 0                   0
##   Medicago.lupulina Myosotis.arvensis Ononis.repens Oxalis.acetosella
## 1                 0                 0             0                 0
## 2                 0                 0             0                 0
## 3                 0                 0             0                 0
## 4                 0                 0             0                 0
## 5                 0                 0             0                 0
##   Pastinaca.sativa Pentaglottis.sempervirens Pillosella.officinarum
## 1                0                         0                      0
## 2                0                         0                      0
## 3                0                         0                      0
## 4                0                         0                      0
## 5                0                         0                      0
##   Plantago.coronopus Plantago.lanceolata Pleurozium.schreberi Poa.annua
## 1                  0                  13                  110         0
## 2                  0                   0                   10         0
## 3                  0                   0                    0         0
## 4                  0                  22                    0         0
## 5                  0                  36                  120         0
##   Poa.spp. Polytrichum.commune Polytrichum.commune.agg. Polytrichum.formosum
## 1        0                   0                        0                    0
## 2        0                   0                        0                   40
## 3        0                   0                        0                    0
## 4        0                   0                        0                    0
## 5        0                   0                        0                    0
##   Potentilla.reptans Prunella.vulgaris Pseudoscleropidum.purum
## 1                  0                 1                      40
## 2                  0                 0                       0
## 3                  0                 2                     150
## 4                  0                 0                     150
## 5                  0                 0                      90
##   Pteridium.aquilinum Ranunculus.acris Ranunculus.parviflorus Ranunculus.repens
## 1                   0                0                      0                 0
## 2                   0                0                      0                 0
## 3                   0                0                      0                 0
## 4                   0                0                      0                 0
## 5                   0                2                      0                 0
##   Reseda.lutea Rhinanthus.minor Rhizomnium.punctatum Rhytidadelphus.squarrosus
## 1            0                0                    0                       160
## 2            0                0                    0                         0
## 3            0                0                    0                        30
## 4            0                0                    0                       150
## 5            0                0                    0                        30
##   Rhytidadelphus.triquetris Rubus.fruticosus Sanguisorba.minor.spp.minor
## 1                        20                0                           0
## 2                         0                0                           0
## 3                         0                1                           0
## 4                        20                0                           0
## 5                         0                0                           0
##   Saniona.uncinata Sedum.anglicum Senecio.jacobaea Senecio.vulgaris
## 1                0              0                0                0
## 2                0              0                0                0
## 3                0              0                0                0
## 4                0              0                0                0
## 5                0              0                0                0
##   Sonchus.arvensis Stachys.sylvatica Stellaria.apetala Taraxacum.agg.
## 1                0                 0                 0              0
## 2                0                 0                 0              0
## 3                0                 0                 0              0
## 4                0                 0                 0              0
## 5                0                 0                 0              0
##   Thuidium.tamariscinum Thymus.polytrichus Trichostomum.crispulum
## 1                     0                  0                      0
## 2                     0                  0                      0
## 3                     0                  0                      0
## 4                    30                  0                      0
## 5                     0                  0                      0
##   Trifolium.campestre Trifolium.dubium Trifolium.pratense Trifolium.repens
## 1                   0                0                  0                0
## 2                   0                0                  0                0
## 3                   0                0                  0                0
## 4                   0                0                  0                0
## 5                   0                0                  0                0
##   Trisetum.flavescens Tussilago.farfara Urtica.diocia Veronica.officinalis
## 1                   0                 0             0                    0
## 2                   0                 0             0                    0
## 3                   0                 0             0                    2
## 4                   0                 0             0                    0
## 5                   0                 0             0                    0
##   Vicia.sativa Viola.riviniana Weissia.controversa Zygodon.stirtonii
## 1            0               0                   0                 0
## 2            0               0                   0                 0
## 3            0               0                  20                 0
## 4            0               0                   0                 0
## 5            0               0                   0                 0
head(FallinPC)
##   pH_level     SiO2    Al2O3    Fe2O3      CaO      MgO     Na2O      K2O
## 1    6.070 179027.6 88649.43 18534.78 4431.083 4522.769 667.6712 15274.72
## 2    6.403 226705.9 83621.55 34901.33 2429.949 3377.001 519.2998 18097.22
## 3    7.073 201464.5 93941.94 28116.91 4002.268 4703.680 741.8569 16685.97
## 4    6.620 189311.1 84680.05 38468.40 3716.392 4341.858 593.4855 15191.70
## 5    6.633 173418.4 85738.56 18115.12 4145.206 4281.555 667.6712 15772.81
##      Cr2O3     TiO2       MnO      P2O5       SrO      BaO  LOI   Ag As  B  Be
## 1 82.10429 4015.597  387.2287 1099.8580 169.11891 358.2605 37.9 0.15  8 10 1.4
## 2 75.26227 5454.020 1006.7947  999.8709  84.55946 447.8257 24.5 0.15  5  5 1.1
## 3 88.94632 4614.940  929.3490 1199.8451  84.55946 358.2605 30.4 0.15  3  5 1.4
## 4 82.10429 4375.203  697.0117 1499.8063  84.55946 358.2605 32.4 0.15  8 10 1.4
## 5 75.26227 3955.663  387.2287 1399.8192 169.11891 358.2605 39.5 0.20  5 10 1.6
##    Bi   Cd Co Cu Ga  Hg La Li  Mo Ni Pb   S  Sb Sc Th Tl U  V W Zn Akermanite
## 1 1.5 0.25 20 51  5 0.5 10 10 1.0 29 42 800 1.5  2 10  5 5 11 5 57          0
## 2 1.5 0.25 28 44  5 0.5 20  5 1.0 31 50 800 1.5  3 10  5 5  8 5 53          0
## 3 1.5 0.25 23 48  5 0.5 10 10 0.5 32 51 600 1.5  3 10  5 5 15 5 44          0
## 4 1.5 0.25 24 44  5 0.5 10 10 1.0 35 45 900 1.5  4 10  5 5 18 5 61          0
## 5 1.5 0.25 31 65  5 0.5 10 10 1.0 35 69 800 1.5  2 10  5 5 10 5 54          0
##   Albite Aluminium.oxide.hydroxide Anhydrite Aragonite Biotite Birnessite
## 1      0                         0         0         0       1          0
## 2      0                         0         0         0       0          0
## 3      0                         0         0         0       0          1
## 4      0                         0         0         0       0          0
## 5      0                         0         0         0       0          0
##   Calcite Clinochlore Cuspidine Diaspore Dickite Gehlenite Goethite Haematite
## 1       0           0         0        0       0         0        0         0
## 2       0           0         0        0       0         0        0         0
## 3       0           0         0        0       0         0        0         0
## 4       0           0         0        0       0         0        0         0
## 5       0           1         0        0       1         0        0         1
##   Illite Kaolinite Langite Linnaeite Magnesioferrite Melilite Merwinite
## 1      0         0       0         0               0        0         0
## 2      0         1       0         0               0        0         0
## 3      0         0       0         0               0        0         0
## 4      0         0       1         0               0        0         0
## 5      0         0       0         0               0        0         0
##   Microcline Mullite Muscovite Orthoclase Orthopyroxene Periclase Phengite
## 1          0       0         1          0             0         0        0
## 2          0       0         0          0             0         0        1
## 3          0       0         1          0             0         0        0
## 4          0       0         1          0             0         0        0
## 5          0       0         1          0             0         0        0
##   Pseudowollastonite Quartz Staurolite Valentinite
## 1                  0      1          0           0
## 2                  0      1          0           0
## 3                  0      1          0           0
## 4                  0      1          0           0
## 5                  0      1          0           0
sapply(FallinPS, class)
##               Agrostis.spp.             Agrostis.canina 
##                   "numeric"                   "numeric" 
##           Alchemilla.mollis         Alopercus.pratensis 
##                   "numeric"                   "numeric" 
##         Angelica.sylvestris       Anthoxanthum.odoratum 
##                   "numeric"                   "numeric" 
##        Anthyllis.vulneraria            Aphanes.arvensis 
##                   "numeric"                   "numeric" 
##       Arrhenatherum.elatius          Atrichum.undulatum 
##                   "numeric"                   "numeric" 
##           Avenula.pratensis             Bellis.perennis 
##                   "numeric"                   "numeric" 
##            Betula.pubescens      Blackstonia.perfoliata 
##                   "numeric"                   "numeric" 
##      Brachythecium.albicans     Brachythecium.glareosum 
##                   "numeric"                   "numeric" 
##     Brachythecium.mildeanum     Brachythecium.rutabulum 
##                   "numeric"                   "numeric" 
##                 Briza.media           Bromus.hordeaceus 
##                   "numeric"                   "numeric" 
##     Bryum.c.f..caespiticium       Bryum.c.f..pallescens 
##                   "numeric"                   "numeric" 
##             Bryum.capillare                  Bryum.spp. 
##                   "numeric"                   "numeric" 
##    Calliergonella.cupsidata           Calypogeia.arguta 
##                   "numeric"                   "numeric" 
##      Campanula.rotundifolia               Carex.distans 
##                   "numeric"                   "numeric" 
##                Carex.flacca               Carex.panicea 
##                   "numeric"                   "numeric" 
##            Carlina.vulgaris             Centaurea.nigra 
##                   "numeric"                   "numeric" 
##        Centaurium.erythraea        Centaurium.littorale 
##                   "numeric"                   "numeric" 
##       Centaurium.pulchellum          Cerastium.fontanum 
##                   "numeric"                   "numeric" 
##  Chamaenerion.angustifolium      Cirriphyllum.piliferum 
##                   "numeric"                   "numeric" 
##             Cirsium.arvense            Cirsium.palustre 
##                   "numeric"                   "numeric" 
##           Crepis.capillaris         Cynosurus.cristatus 
##                   "numeric"                   "numeric" 
##          Dactylis.glomerata        Dactylorhiza.fuchsii 
##                   "numeric"                   "numeric" 
##         Danthonia.decumbens              Daucus.carrota 
##                   "numeric"                   "numeric" 
##             Dicranella.spp.          Dicranum.scoparium 
##                   "numeric"                   "numeric" 
##          Epilobium.montanum           Equisetum.arvense 
##                   "numeric"                   "numeric" 
##        Equisteum.variegatum               Erigeron.acer 
##                   "numeric"                   "numeric" 
##               Euphrasia.agg               Festuca.ovina 
##                   "numeric"                   "numeric" 
##               Festuca.rubra          Festuca.rubra.agg. 
##                   "numeric"                   "numeric" 
##         Filipendula.ulmaria      Fissidens.adianthoides 
##                   "numeric"                   "numeric" 
##            Fissidens.dubius            Fissidens.exilis 
##                   "numeric"                   "numeric" 
##              Fragaria.vesca              Galium.aparine 
##                   "numeric"                   "numeric" 
##              Galium.arvense             Galium.saxatile 
##                   "numeric"                   "numeric" 
##                Galium.verum                Geum.urbanum 
##                   "numeric"                   "numeric" 
##          Glechoma.hederacea          Helicotrichon.spp. 
##                   "numeric"                   "numeric" 
##       Heracleum.sphondylium              Hieracium.spp. 
##                   "numeric"                   "numeric" 
##                 Holcus.spp.              Holcus.lanatus 
##                   "numeric"                   "numeric" 
##               Holcus.mollis     Homalothecium.lutescens 
##                   "numeric"                   "numeric" 
##        Hylocomium.splendens        Hypericum.perforatum 
##                   "numeric"                   "numeric" 
##        Hypnum.cupressiforme             Hypnum.imponens 
##                   "numeric"                   "numeric" 
##          Hypnum.jutlandicum        Hypochaeris.radicata 
##                   "numeric"                   "numeric" 
##        Kindbergia.praelonga          Lathyrus.pratensis 
##                   "numeric"                   "numeric" 
##          Leontodon.hispidus         Leontodon.saxatilis 
##                   "numeric"                   "numeric" 
##        Leucanthemum.vulgare           Linum.catharticum 
##                   "numeric"                   "numeric" 
##              Lolium.perenne        Lophocolea.semiteres 
##                   "numeric"                   "numeric" 
##          Lotus.corniculatus           Luzula.multiflora 
##                   "numeric"                   "numeric" 
##         Lysimachia.maritima           Medicago.lupulina 
##                   "numeric"                   "numeric" 
##           Myosotis.arvensis               Ononis.repens 
##                   "numeric"                   "numeric" 
##           Oxalis.acetosella            Pastinaca.sativa 
##                   "numeric"                   "numeric" 
##   Pentaglottis.sempervirens      Pillosella.officinarum 
##                   "numeric"                   "numeric" 
##          Plantago.coronopus         Plantago.lanceolata 
##                   "numeric"                   "numeric" 
##        Pleurozium.schreberi                   Poa.annua 
##                   "numeric"                   "numeric" 
##                    Poa.spp.         Polytrichum.commune 
##                   "numeric"                   "numeric" 
##    Polytrichum.commune.agg.        Polytrichum.formosum 
##                   "numeric"                   "numeric" 
##          Potentilla.reptans           Prunella.vulgaris 
##                   "numeric"                   "numeric" 
##     Pseudoscleropidum.purum         Pteridium.aquilinum 
##                   "numeric"                   "numeric" 
##            Ranunculus.acris      Ranunculus.parviflorus 
##                   "numeric"                   "numeric" 
##           Ranunculus.repens                Reseda.lutea 
##                   "numeric"                   "numeric" 
##            Rhinanthus.minor        Rhizomnium.punctatum 
##                   "numeric"                   "numeric" 
##   Rhytidadelphus.squarrosus   Rhytidadelphus.triquetris 
##                   "numeric"                   "numeric" 
##            Rubus.fruticosus Sanguisorba.minor.spp.minor 
##                   "numeric"                   "numeric" 
##            Saniona.uncinata              Sedum.anglicum 
##                   "numeric"                   "numeric" 
##            Senecio.jacobaea            Senecio.vulgaris 
##                   "numeric"                   "numeric" 
##            Sonchus.arvensis           Stachys.sylvatica 
##                   "numeric"                   "numeric" 
##           Stellaria.apetala              Taraxacum.agg. 
##                   "numeric"                   "numeric" 
##       Thuidium.tamariscinum          Thymus.polytrichus 
##                   "numeric"                   "numeric" 
##      Trichostomum.crispulum         Trifolium.campestre 
##                   "numeric"                   "numeric" 
##            Trifolium.dubium          Trifolium.pratense 
##                   "numeric"                   "numeric" 
##            Trifolium.repens         Trisetum.flavescens 
##                   "numeric"                   "numeric" 
##           Tussilago.farfara               Urtica.diocia 
##                   "numeric"                   "numeric" 
##        Veronica.officinalis                Vicia.sativa 
##                   "numeric"                   "numeric" 
##             Viola.riviniana         Weissia.controversa 
##                   "numeric"                   "numeric" 
##           Zygodon.stirtonii 
##                   "numeric"
sapply(FallinPC, class)
##                  pH_level                      SiO2                     Al2O3 
##                 "numeric"                 "numeric"                 "numeric" 
##                     Fe2O3                       CaO                       MgO 
##                 "numeric"                 "numeric"                 "numeric" 
##                      Na2O                       K2O                     Cr2O3 
##                 "numeric"                 "numeric"                 "numeric" 
##                      TiO2                       MnO                      P2O5 
##                 "numeric"                 "numeric"                 "numeric" 
##                       SrO                       BaO                       LOI 
##                 "numeric"                 "numeric"                 "numeric" 
##                        Ag                        As                         B 
##                 "numeric"                 "numeric"                 "numeric" 
##                        Be                        Bi                        Cd 
##                 "numeric"                 "numeric"                 "numeric" 
##                        Co                        Cu                        Ga 
##                 "numeric"                 "numeric"                 "numeric" 
##                        Hg                        La                        Li 
##                 "numeric"                 "numeric"                 "numeric" 
##                        Mo                        Ni                        Pb 
##                 "numeric"                 "numeric"                 "numeric" 
##                         S                        Sb                        Sc 
##                 "numeric"                 "numeric"                 "numeric" 
##                        Th                        Tl                         U 
##                 "numeric"                 "numeric"                 "numeric" 
##                         V                         W                        Zn 
##                 "numeric"                 "numeric"                 "numeric" 
##                Akermanite                    Albite Aluminium.oxide.hydroxide 
##                 "numeric"                 "numeric"                 "numeric" 
##                 Anhydrite                 Aragonite                   Biotite 
##                 "numeric"                 "numeric"                 "numeric" 
##                Birnessite                   Calcite               Clinochlore 
##                 "numeric"                 "numeric"                 "numeric" 
##                 Cuspidine                  Diaspore                   Dickite 
##                 "numeric"                 "numeric"                 "numeric" 
##                 Gehlenite                  Goethite                 Haematite 
##                 "numeric"                 "numeric"                 "numeric" 
##                    Illite                 Kaolinite                   Langite 
##                 "numeric"                 "numeric"                 "numeric" 
##                 Linnaeite           Magnesioferrite                  Melilite 
##                 "numeric"                 "numeric"                 "numeric" 
##                 Merwinite                Microcline                   Mullite 
##                 "numeric"                 "numeric"                 "numeric" 
##                 Muscovite                Orthoclase             Orthopyroxene 
##                 "numeric"                 "numeric"                 "numeric" 
##                 Periclase                  Phengite        Pseudowollastonite 
##                 "numeric"                 "numeric"                 "numeric" 
##                    Quartz                Staurolite               Valentinite 
##                 "numeric"                 "numeric"                 "numeric"
rowSums(FallinPS)
## [1] 711 525 639 820 798

#Time to do the ANOSIM tests for the Fallin data

#anoFSiO2 <- anosim(FallinPS, FallinPC$SiO2, distance = “bray”, permutations = 9999)

#When this ANOSIM is run, the error message: “there should be replicates within groups” #comes up. This error message came up for other substrate variables for the #data. From now on, only variables that were tested successfully will be included.

anoFNa2O <- anosim(FallinPS, FallinPC$Na2O, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoFNa2O
## 
## Call:
## anosim(x = FallinPS, grouping = FallinPC$Na2O, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.7778 
##       Significance: 0.2 
## 
## Permutation: free
## Number of permutations: 119
anoFCr2O3 <- anosim(FallinPS, FallinPC$Cr2O3, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoFCr2O3
## 
## Call:
## anosim(x = FallinPS, grouping = FallinPC$Cr2O3, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.125 
##       Significance: 0.46667 
## 
## Permutation: free
## Number of permutations: 119
anoFSrO <- anosim(FallinPS, FallinPC$SrO, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoFSrO
## 
## Call:
## anosim(x = FallinPS, grouping = FallinPC$SrO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.08333 
##       Significance: 0.7 
## 
## Permutation: free
## Number of permutations: 119
anoFBaO <- anosim(FallinPS, FallinPC$BaO, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoFBaO
## 
## Call:
## anosim(x = FallinPS, grouping = FallinPC$BaO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.9167 
##       Significance: 0.2 
## 
## Permutation: free
## Number of permutations: 119
anoFAs <- anosim(FallinPS, FallinPC$As, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoFAs
## 
## Call:
## anosim(x = FallinPS, grouping = FallinPC$As, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.125 
##       Significance: 0.46667 
## 
## Permutation: free
## Number of permutations: 119
anoFBe <- anosim(FallinPS, FallinPC$Be, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoFBe
## 
## Call:
## anosim(x = FallinPS, grouping = FallinPC$Be, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.5238 
##       Significance: 0.2 
## 
## Permutation: free
## Number of permutations: 119
anoFCu <- anosim(FallinPS, FallinPC$Cu, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoFCu
## 
## Call:
## anosim(x = FallinPS, grouping = FallinPC$Cu, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:    -1 
##       Significance: 1 
## 
## Permutation: free
## Number of permutations: 119
anoFNi <- anosim(FallinPS, FallinPC$Ni, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoFNi
## 
## Call:
## anosim(x = FallinPS, grouping = FallinPC$Ni, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.3333 
##       Significance: 0.4 
## 
## Permutation: free
## Number of permutations: 119
anoFS <- anosim(FallinPS, FallinPC$S, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoFS
## 
## Call:
## anosim(x = FallinPS, grouping = FallinPC$S, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.04762 
##       Significance: 0.6 
## 
## Permutation: free
## Number of permutations: 119
anoFSc <- anosim(FallinPS, FallinPC$Sc, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoFSc
## 
## Call:
## anosim(x = FallinPS, grouping = FallinPC$Sc, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.125 
##       Significance: 0.46667 
## 
## Permutation: free
## Number of permutations: 119

#None of the ANOSIM tests led to stastistically significant results. Because of this, #CCAs might not be entirely appropriate to represent the data visually. #Both CCA and NMDS analyses will be utilised to visualise the plant data.

FallinNMDS <- metaMDS(FallinPS, noshare = TRUE, autotransform = FALSE, trymax = 500)
## Run 0 stress 0.08152132 
## Run 1 stress 0.0839104 
## Run 2 stress 0.02952015 
## ... New best solution
## ... Procrustes: rmse 0.2122265  max resid 0.3062251 
## Run 3 stress 0.0839104 
## Run 4 stress 0.0927171 
## Run 5 stress 0.02952015 
## ... New best solution
## ... Procrustes: rmse 5.981661e-07  max resid 1.00664e-06 
## ... Similar to previous best
## Run 6 stress 0.05541858 
## Run 7 stress 0.0554184 
## Run 8 stress 0.0839104 
## Run 9 stress 0.09271713 
## Run 10 stress 0.05541844 
## Run 11 stress 0.02952015 
## ... Procrustes: rmse 6.57376e-07  max resid 1.103654e-06 
## ... Similar to previous best
## Run 12 stress 0.09271721 
## Run 13 stress 0.09271712 
## Run 14 stress 0.02952015 
## ... Procrustes: rmse 5.085642e-07  max resid 7.735351e-07 
## ... Similar to previous best
## Run 15 stress 0.09271712 
## Run 16 stress 0.02952015 
## ... Procrustes: rmse 3.73838e-07  max resid 5.479893e-07 
## ... Similar to previous best
## Run 17 stress 0.09271715 
## Run 18 stress 0.05541853 
## Run 19 stress 0.09271712 
## Run 20 stress 0.09271717 
## *** Best solution repeated 4 times
plot(FallinNMDS)

FallinNMDS
## 
## Call:
## metaMDS(comm = FallinPS, trymax = 500, autotransform = FALSE,      noshare = TRUE) 
## 
## global Multidimensional Scaling using monoMDS
## 
## Data:     FallinPS 
## Distance: bray 
## 
## Dimensions: 2 
## Stress:     0.02952015 
## Stress type 1, weak ties
## Best solution was repeated 4 times in 20 tries
## The best solution was from try 5 (random start)
## Scaling: centring, PC rotation, halfchange scaling 
## Species: expanded scores based on 'FallinPS'
#This simple NMDS shows communities represented as circles and species represented as 
#red crosses.

plot(FallinNMDS, "sites")   # Produces distance 

plot(FallinNMDS, "species", xlim = c(-0.5, 0.5), ylim = c(-1.5, 1.0))
orditorp(FallinNMDS, "species")

#We are only seeing some of the Fallin species in the graph produced by the function
#"orditorp", but this still gives an idea of how different species are differently and/or
#similarly distributed in different communities on Fallin Bing.

#CCA analyses for Fallin data... It might be easier to visualise what is going on
#using an appropriate CCA, especially with substrate variables being taken into account
#in the CCA.

#CCA analyses for Fallin data…#

FallinCCA <- cca(FallinPS ~ pH_level + SiO2 + Al2O3 + Fe2O3 + CaO + MgO + MgO + Na2O + 
K2O + Cr2O3 + TiO2 + MnO + P2O5 + SrO + BaO + Ag + As + B + Be + Bi + Cd + Co + Cu + 
Ga + Hg + La + Li + Mo + Ni + Pb + S + Sb + Sc + Th + Tl + U + V + W + Zn + Akermanite + 
Albite + Aluminium.oxide.hydroxide + Anhydrite + Aragonite + Biotite + Birnessite + 
Calcite + Clinochlore + Cuspidine + Diaspore + Dickite + Gehlenite + Goethite + Haematite +
Illite + Kaolinite + Langite + Linnaeite + Magnesioferrite + Melilite + Merwinite + 
Microcline + Mullite + Muscovite + Orthoclase + Orthopyroxene + Periclase + Phengite + 
Pseudowollastonite + Quartz + Staurolite + Valentinite, data = FallinPC)
## 
## Some constraints or conditions were aliased because they were redundant. This
## can happen if terms are linearly dependent (collinear): 'CaO', 'MgO', 'Na2O',
## 'K2O', 'Cr2O3', 'TiO2', 'MnO', 'P2O5', 'SrO', 'BaO', 'Ag', 'As', 'B', 'Be',
## 'Bi', 'Cd', 'Co', 'Cu', 'Ga', 'Hg', 'La', 'Li', 'Mo', 'Ni', 'Pb', 'S', 'Sb',
## 'Sc', 'Th', 'Tl', 'U', 'V', 'W', 'Zn', 'Akermanite', 'Albite',
## 'Aluminium.oxide.hydroxide', 'Anhydrite', 'Aragonite', 'Biotite', 'Birnessite',
## 'Calcite', 'Clinochlore', 'Cuspidine', 'Diaspore', 'Dickite', 'Gehlenite',
## 'Goethite', 'Haematite', 'Illite', 'Kaolinite', 'Langite', 'Linnaeite',
## 'Magnesioferrite', 'Melilite', 'Merwinite', 'Microcline', 'Mullite',
## 'Muscovite', 'Orthoclase', 'Orthopyroxene', 'Periclase', 'Phengite',
## 'Pseudowollastonite', 'Quartz', 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component
print(FallinCCA)
## Call: cca(formula = FallinPS ~ pH_level + SiO2 + Al2O3 + Fe2O3 + CaO + MgO
## + MgO + Na2O + K2O + Cr2O3 + TiO2 + MnO + P2O5 + SrO + BaO + Ag + As + B +
## Be + Bi + Cd + Co + Cu + Ga + Hg + La + Li + Mo + Ni + Pb + S + Sb + Sc +
## Th + Tl + U + V + W + Zn + Akermanite + Albite + Aluminium.oxide.hydroxide
## + Anhydrite + Aragonite + Biotite + Birnessite + Calcite + Clinochlore +
## Cuspidine + Diaspore + Dickite + Gehlenite + Goethite + Haematite + Illite
## + Kaolinite + Langite + Linnaeite + Magnesioferrite + Melilite + Merwinite
## + Microcline + Mullite + Muscovite + Orthoclase + Orthopyroxene + Periclase
## + Phengite + Pseudowollastonite + Quartz + Staurolite + Valentinite, data =
## FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.9405     1.0000    4
## Unconstrained  0.0000     0.0000    0
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## Some constraints or conditions were aliased because they were redundant.
## This can happen if terms are linearly dependent (collinear): 'CaO', 'MgO',
## 'Na2O', 'K2O', 'Cr2O3', 'TiO2', 'MnO', 'P2O5', 'SrO', 'BaO', 'Ag', 'As',
## 'B', 'Be', 'Bi', 'Cd', 'Co', 'Cu', 'Ga', 'Hg', 'La', 'Li', 'Mo', 'Ni',
## 'Pb', 'S', 'Sb', 'Sc', 'Th', 'Tl', 'U', 'V', 'W', 'Zn', 'Akermanite',
## 'Albite', 'Aluminium.oxide.hydroxide', 'Anhydrite', 'Aragonite', 'Biotite',
## 'Birnessite', 'Calcite', 'Clinochlore', 'Cuspidine', 'Diaspore', 'Dickite',
## 'Gehlenite', 'Goethite', 'Haematite', 'Illite', 'Kaolinite', 'Langite',
## 'Linnaeite', 'Magnesioferrite', 'Melilite', 'Merwinite', 'Microcline',
## 'Mullite', 'Muscovite', 'Orthoclase', 'Orthopyroxene', 'Periclase',
## 'Phengite', 'Pseudowollastonite', 'Quartz', 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component.
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3    CCA4 
## 0.31034 0.30762 0.22427 0.09823
plot(FallinCCA)

FallinCCA2 <- cca(FallinPS ~ pH_level + SiO2 + Al2O3 +
                    Fe2O3,
                  data= FallinPC)
## 
## The model is overfitted with no unconstrained (residual) component
print(FallinCCA2)
## Call: cca(formula = FallinPS ~ pH_level + SiO2 + Al2O3 + Fe2O3, data =
## FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.9405     1.0000    4
## Unconstrained  0.0000     0.0000    0
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## The model is overfitted with no unconstrained (residual) component.
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3    CCA4 
## 0.31034 0.30762 0.22427 0.09823
plot(FallinCCA2)

FallinCCA3 <- cca(FallinPS ~ pH_level + SiO2 + Al2O3,
                  data= FallinPC)

print(FallinCCA3)
## Call: cca(formula = FallinPS ~ pH_level + SiO2 + Al2O3, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.6991     0.7434    3
## Unconstrained  0.2413     0.2566    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30817 0.27501 0.11594 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.24134
plot(FallinCCA3)

anova(FallinCCA3)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ pH_level + SiO2 + Al2O3, data = FallinPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   0.69912 0.9656  0.475
## Residual  1   0.24134

#F statistic of 0.9656, p value of 0.475

FallinCCA4 <- cca(FallinPS ~ pH_level + SiO2 + CaO, data= FallinPC)

print(FallinCCA4)
## Call: cca(formula = FallinPS ~ pH_level + SiO2 + CaO, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7223     0.7680    3
## Unconstrained  0.2182     0.2320    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30843 0.28080 0.13306 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.21817
plot(FallinCCA4)

anova(FallinCCA4)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ pH_level + SiO2 + CaO, data = FallinPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   0.72228 1.1035  0.325
## Residual  1   0.21817

#F statistic of 1.1035, p value of 0.3333

FallinCCA5 <- cca(FallinPS ~ pH_level + SiO2 + MgO, data= FallinPC)

print(FallinCCA5)
## Call: cca(formula = FallinPS ~ pH_level + SiO2 + MgO, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7721     0.8210    3
## Unconstrained  0.1684     0.1790    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30942 0.29229 0.17036 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.16838
plot(FallinCCA5)

anova(FallinCCA5)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ pH_level + SiO2 + MgO, data = FallinPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   0.77208 1.5285 0.1833
## Residual  1   0.16838

#F statistic of 1.5285, p value of 0.2

FallinCCA6 <- cca(FallinPS ~ Al2O3 + SiO2 + MgO, data= FallinPC)

print(FallinCCA6)
## Call: cca(formula = FallinPS ~ Al2O3 + SiO2 + MgO, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7483     0.7957    3
## Unconstrained  0.1922     0.2043    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30947 0.30456 0.13426 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.19216
plot(FallinCCA6)

anova(FallinCCA6)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ Al2O3 + SiO2 + MgO, data = FallinPC)
##          Df ChiSquare     F Pr(>F)
## Model     3   0.74830 1.298 0.2083
## Residual  1   0.19216

#F statistic of 1.298, p value of 0.2

FallinCCA7 <- cca(FallinPS ~ Na2O + Al2O3 + MgO, data= FallinPC)

print(FallinCCA7)
## Call: cca(formula = FallinPS ~ Na2O + Al2O3 + MgO, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7680     0.8166    3
## Unconstrained  0.1724     0.1834    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30764 0.28205 0.17832 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.17244
plot(FallinCCA7)

anova(FallinCCA7)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ Na2O + Al2O3 + MgO, data = FallinPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   0.76801 1.4846  0.175
## Residual  1   0.17244

#F statistic of 1.4846, p value of 0.1583

FallinCCA8 <- cca(FallinPS ~ K2O + Pb + MgO,
                  data= FallinPC)

print(FallinCCA8)
## Call: cca(formula = FallinPS ~ K2O + Pb + MgO, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7869     0.8367    3
## Unconstrained  0.1536     0.1633    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30772 0.25876 0.22042 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.15356
plot(FallinCCA8)

anova(FallinCCA8)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ K2O + Pb + MgO, data = FallinPC)
##          Df ChiSquare      F  Pr(>F)  
## Model     3   0.78690 1.7081 0.08333 .
## Residual  1   0.15356                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.7081, p value of 0.08333

FallinCCA9 <- cca(FallinPS ~ K2O + Cr2O3 + MgO, data= FallinPC)

print(FallinCCA9)
## Call: cca(formula = FallinPS ~ K2O + Cr2O3 + MgO, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7896     0.8396    3
## Unconstrained  0.1508     0.1604    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30880 0.29062 0.19022 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.15082
plot(FallinCCA9)

anova(FallinCCA9)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ K2O + Cr2O3 + MgO, data = FallinPC)
##          Df ChiSquare      F Pr(>F)  
## Model     3   0.78964 1.7452  0.075 .
## Residual  1   0.15082                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.7452, p value of 0.09167

FallinCCA10 <- cca(FallinPS ~ K2O + Cu + MgO, data= FallinPC)

print(FallinCCA10)
## Call: cca(formula = FallinPS ~ K2O + Cu + MgO, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7908     0.8408    3
## Unconstrained  0.1497     0.1592    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30866 0.28930 0.19280 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.14969
plot(FallinCCA10)

anova(FallinCCA10)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ K2O + Cu + MgO, data = FallinPC)
##          Df ChiSquare      F  Pr(>F)  
## Model     3   0.79076 1.7608 0.06667 .
## Residual  1   0.14969                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.7608, p value of 0.075

FallinCCA10.1 <- cca(FallinPS ~ K2O + Cu + Zn,
                   data= FallinPC)

print(FallinCCA10.1)
## Call: cca(formula = FallinPS ~ K2O + Cu + Zn, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7953     0.8456    3
## Unconstrained  0.1452     0.1544    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30877 0.29116 0.19532 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.1452
plot(FallinCCA10.1)

anova(FallinCCA10.1)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ K2O + Cu + Zn, data = FallinPC)
##          Df ChiSquare      F  Pr(>F)  
## Model     3   0.79525 1.8256 0.06667 .
## Residual  1   0.14520                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.8256, p value of 0.06667

FallinCCA11 <- cca(FallinPS ~ K2O + Pb + MgO, data= FallinPC)

print(FallinCCA11)
## Call: cca(formula = FallinPS ~ K2O + Pb + MgO, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7869     0.8367    3
## Unconstrained  0.1536     0.1633    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30772 0.25876 0.22042 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.15356
plot(FallinCCA11)

anova(FallinCCA11)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ K2O + Pb + MgO, data = FallinPC)
##          Df ChiSquare      F  Pr(>F)  
## Model     3   0.78690 1.7081 0.08333 .
## Residual  1   0.15356                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.7081, p value of 0.08333

FallinCCA12 <- cca(FallinPS ~ K2O + SrO + MgO, data= FallinPC)

print(FallinCCA12)
## Call: cca(formula = FallinPS ~ K2O + SrO + MgO, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7402     0.7871    3
## Unconstrained  0.2003     0.2129    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.31012 0.29597 0.13411 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.20026
plot(FallinCCA12)

anova(FallinCCA12)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ K2O + SrO + MgO, data = FallinPC)
##          Df ChiSquare     F Pr(>F)
## Model     3   0.74019 1.232 0.1917
## Residual  1   0.20026

#F statistic of 1.232, p value of 0.2167

FallinCCA13 <- cca(FallinPS ~ K2O + Zn + MgO, data= FallinPC)

print(FallinCCA13)
## Call: cca(formula = FallinPS ~ K2O + Zn + MgO, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7931     0.8433    3
## Unconstrained  0.1474     0.1567    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30828 0.28394 0.20084 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.14739
plot(FallinCCA13)

anova(FallinCCA13)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ K2O + Zn + MgO, data = FallinPC)
##          Df ChiSquare      F  Pr(>F)  
## Model     3   0.79306 1.7935 0.08333 .
## Residual  1   0.14739                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.7935, p value of 0.08333

FallinCCA14 <- cca(FallinPS ~ K2O + Dickite + MgO, data= FallinPC)

print(FallinCCA14)
## Call: cca(formula = FallinPS ~ K2O + Dickite + MgO, data = FallinPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          0.9405     1.0000     
## Constrained    0.7921     0.8423    3
## Unconstrained  0.1483     0.1577    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##    CCA1    CCA2    CCA3 
## 0.30789 0.27171 0.21250 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.14835
plot(FallinCCA14)

anova(FallinCCA14)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = FallinPS ~ K2O + Dickite + MgO, data = FallinPC)
##          Df ChiSquare      F  Pr(>F)  
## Model     3   0.79211 1.7798 0.09167 .
## Residual  1   0.14835                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.7798, p value of 0.08333

#Due to the fact that, though several combinations of data were tried, none of the CCAs #generated for the Fallin data generated significant values in the relevant ANOVA tests. #This would indicate that the NMDS generated previously better represents the data and the #differences between both communities and species.

###Addiewell###

urlfile7 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/AddiewellPlantSpecies.csv'

AddiewellPS <- read.csv(urlfile7,  header = TRUE, colClasses = c("numeric"))

urlfile8 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/ADDIEWELL_PLANT_CHEMISTRY_MG_KG.csv'

AddiewellPC <-read.csv(urlfile8, header = TRUE, 
                    colClasses = c("numeric"))

head(AddiewellPS)
##   Agrostis.spp. Agrostis.canina Alchemilla.mollis Alopercus.pratensis
## 1             1               0                 0                   0
## 2             0               0                 0                   0
## 3             0               0                 0                   0
## 4             0               0                 0                   0
## 5            14               0                 0                   0
##   Angelica.sylvestris Anthoxanthum.odoratum Anthyllis.vulneraria
## 1                   0                     0                    0
## 2                   0                     0                    0
## 3                   0                     0                    0
## 4                   0                     0                    0
## 5                   0                     0                    0
##   Aphanes.arvensis Arrhenatherum.elatius Atrichum.undulatum Avenula.pratensis
## 1                0                     0                  0                 0
## 2                0                     0                  0                 0
## 3                0                     3                 10                 0
## 4                0                     1                  0                 0
## 5               11                     0                  0                 0
##   Bellis.perennis Betula.pubescens Blackstonia.perfoliata
## 1               0                0                      0
## 2               0                0                      0
## 3               0                0                      0
## 4               0                0                      0
## 5               0                0                      0
##   Brachythecium.albicans Brachythecium.glareosum Brachythecium.mildeanum
## 1                      0                      10                      10
## 2                      0                       0                      80
## 3                      0                       0                       0
## 4                      0                       0                       0
## 5                      0                       0                     150
##   Brachythecium.rutabulum Briza.media Bromus.hordeaceus Bryum.c.f..caespiticium
## 1                      10           0                 0                       0
## 2                       0           0                 0                       0
## 3                       0           0                 0                       0
## 4                      10           0                 0                       0
## 5                      10           0                 0                       0
##   Bryum.c.f..pallescens Bryum.capillare Bryum.spp. Calliergonella.cupsidata
## 1                     0               0          0                       30
## 2                     0               0          0                      120
## 3                     0               0         10                      150
## 4                     0               0          0                       90
## 5                     0               0          0                        0
##   Calypogeia.arguta Campanula.rotundifolia Carex.distans Carex.flacca
## 1               130                      0             0            0
## 2                80                      0             0            0
## 3                30                      0             0            1
## 4               110                      0             0            0
## 5                10                      0             0            9
##   Carex.panicea Carlina.vulgaris Centaurea.nigra Centaurium.erythraea
## 1             0                0               0                    0
## 2             0                0               2                    0
## 3             0                0               0                    0
## 4             0                0               0                    0
## 5             0                0               0                    0
##   Centaurium.littorale Centaurium.pulchellum Cerastium.fontanum
## 1                    0                     0                  0
## 2                    0                     0                  0
## 3                    0                     0                  0
## 4                    0                     0                  0
## 5                    0                     0                  0
##   Chamaenerion.angustifolium Cirriphyllum.piliferum Cirsium.arvense
## 1                          0                      0               0
## 2                          0                      0               0
## 3                          4                      0               0
## 4                          0                      0               0
## 5                          0                      0               0
##   Cirsium.palustre Crepis.capillaris Cynosurus.cristatus Dactylis.glomerata
## 1                4                 0                   0                  0
## 2                0                 0                   0                  0
## 3                3                 0                   0                  0
## 4                0                 0                   0                  0
## 5                0                 0                  16                 12
##   Dactylorhiza.fuchsii Danthonia.decumbens Daucus.carrota Dicranella.spp.
## 1                    0                   0              0               0
## 2                    0                   0              0               0
## 3                   22                   0              0               0
## 4                    0                   0              0               0
## 5                    1                   1              0               0
##   Dicranum.scoparium Epilobium.montanum Equisetum.arvense Equisteum.variegatum
## 1                  0                  8                 0                    0
## 2                  0                  1                 0                    0
## 3                  0                  0                 0                    0
## 4                 50                  0                 0                    0
## 5                  0                  0                 0                    0
##   Erigeron.acer Euphrasia.agg Festuca.ovina Festuca.rubra Festuca.rubra.agg.
## 1             0             0             0             0                  0
## 2             0             0             0             0                  0
## 3             0             0             0             0                  0
## 4             0             0             0             0                  0
## 5             0             0             0             0                  0
##   Filipendula.ulmaria Fissidens.adianthoides Fissidens.dubius Fissidens.exilis
## 1                  27                      0                0                0
## 2                   0                      0                0                0
## 3                   0                      0                0                0
## 4                   0                      0                0                0
## 5                   0                      0                0                0
##   Fragaria.vesca Galium.aparine Galium.arvense Galium.saxatile Galium.verum
## 1              0              0              0               0            0
## 2              0              0              0               0            0
## 3              0              0              0               0            0
## 4              0              0              0               0            0
## 5              0              0              0               0            0
##   Geum.urbanum Glechoma.hederacea Helicotrichon.spp. Heracleum.sphondylium
## 1            0                  0                  0                     0
## 2            0                  0                  0                     8
## 3            0                  0                  0                     0
## 4            0                  0                  0                     0
## 5            0                  0                  0                     1
##   Hieracium.spp. Holcus.spp. Holcus.lanatus Holcus.mollis
## 1              0           5              0             0
## 2              0          14              0             0
## 3              0          36              0             0
## 4              0           0              0           143
## 5              0           0              0             1
##   Homalothecium.lutescens Hylocomium.splendens Hypericum.perforatum
## 1                       0                    0                    0
## 2                       0                    0                    0
## 3                       0                    1                    0
## 4                       0                   90                    0
## 5                       0                    0                    0
##   Hypnum.cupressiforme Hypnum.imponens Hypnum.jutlandicum Hypochaeris.radicata
## 1                    0               0                  0                    0
## 2                    0               0                  0                    0
## 3                    0               0                  0                    0
## 4                   20              60                  0                    0
## 5                   50               0                 10                    0
##   Kindbergia.praelonga Lathyrus.pratensis Leontodon.hispidus
## 1                   10                  0                  0
## 2                   60                  0                  0
## 3                    0                 30                  0
## 4                   30                  0                  0
## 5                   10                 18                  0
##   Leontodon.saxatilis Leucanthemum.vulgare Linum.catharticum Lolium.perenne
## 1                   0                    0                 0              0
## 2                   0                    0                 0              0
## 3                   0                    0                 0              0
## 4                   0                    0                 0              0
## 5                   0                    0                 0              0
##   Lophocolea.semiteres Lotus.corniculatus Luzula.multiflora Lysimachia.maritima
## 1                    0                  0                 0                   0
## 2                    0                  0                 0                   0
## 3                    0                  0                 1                   0
## 4                    0                  0                 0                   0
## 5                    0                  0                 0                   0
##   Medicago.lupulina Myosotis.arvensis Ononis.repens Oxalis.acetosella
## 1                 0                 0             0                 0
## 2                 0                 0             0                 0
## 3                 0                 2             0                 0
## 4                 0                 0             0                 0
## 5                 0                 0             2                 0
##   Pastinaca.sativa Pentaglottis.sempervirens Pillosella.officinarum
## 1                0                         0                      0
## 2                0                         0                      0
## 3                0                         0                      0
## 4                0                         0                      0
## 5                0                         0                      0
##   Plantago.coronopus Plantago.lanceolata Pleurozium.schreberi Poa.annua
## 1                  0                   0                    0         0
## 2                  0                   0                    0         0
## 3                  0                   0                    0         0
## 4                  0                   0                   60         0
## 5                  0                   8                    0         0
##   Poa.spp. Polytrichum.commune Polytrichum.commune.agg. Polytrichum.formosum
## 1        0                   0                        0                    0
## 2        0                   0                        0                    0
## 3        0                   0                        0                    0
## 4        0                  10                       10                    0
## 5        0                   0                        0                    0
##   Potentilla.reptans Prunella.vulgaris Pseudoscleropidum.purum
## 1                  0                 0                       0
## 2                  0                 0                       0
## 3                  0                 0                       0
## 4                  0                 0                      10
## 5                  4                 0                       0
##   Pteridium.aquilinum Ranunculus.acris Ranunculus.parviflorus Ranunculus.repens
## 1                   8                0                      0                 5
## 2                   4                0                      0                 0
## 3                   0                0                      0                23
## 4                   0                0                      0                 0
## 5                   0                0                      0                 0
##   Reseda.lutea Rhinanthus.minor Rhizomnium.punctatum Rhytidadelphus.squarrosus
## 1            0                0                    0                       130
## 2            0                0                    0                       160
## 3            0                0                    4                       110
## 4            0                0                    0                       110
## 5            0                4                    0                         0
##   Rhytidadelphus.triquetris Rubus.fruticosus Sanguisorba.minor.spp.minor
## 1                         0                3                           0
## 2                         0                0                           0
## 3                         0                0                           0
## 4                         0                0                           0
## 5                         0                0                           0
##   Saniona.uncinata Sedum.anglicum Senecio.jacobaea Senecio.vulgaris
## 1                0              0                0                0
## 2                0              0                0                0
## 3               10              0                0                0
## 4               10              0                0                0
## 5                0              0                0                0
##   Sonchus.arvensis Stachys.sylvatica Stellaria.apetala Taraxacum.agg.
## 1                0                 0                 0              0
## 2                3                 0                 0              1
## 3                0                 0                 0              0
## 4                0                 0                 0              0
## 5                0                 0                 0              0
##   Thuidium.tamariscinum Thymus.polytrichus Trichostomum.crispulum
## 1                     0                  0                      0
## 2                     0                  0                      0
## 3                    20                  0                      0
## 4                    10                  0                      0
## 5                     0                  0                      0
##   Trifolium.campestre Trifolium.dubium Trifolium.pratense Trifolium.repens
## 1                   0                0                  0                0
## 2                   0                0                  0                0
## 3                   0                0                  5               35
## 4                   0                0                  0                0
## 5                   0                0                  1                0
##   Trisetum.flavescens Tussilago.farfara Urtica.diocia Veronica.officinalis
## 1                   0                 0             1                    0
## 2                   0                 0             0                    0
## 3                   1                 0             0                    0
## 4                   0                 0             0                    0
## 5                   0                 0            52                    0
##   Vicia.sativa Viola.riviniana Weissia.controversa Zygodon.stirtonii
## 1            0              28                   0                 0
## 2            0               0                   0                 0
## 3          110               0                   0                 0
## 4            0               0                   0                 0
## 5            0               0                   0                 0
head(AddiewellPC)
##   pH_level     SiO2    Al2O3    Fe2O3      CaO      MgO     Na2O       K2O
## 1    5.046 118728.5 53983.53 39237.77 5503.119 3859.430 1557.899  6724.197
## 2    6.175 164069.7 76476.67 49799.10 8790.696 6512.788 2151.385 11290.010
## 3    6.227 148176.9 72507.30 50778.29 8218.944 5970.055 2151.385 10210.818
## 4    5.989 182299.6 86797.06 51407.77 7861.598 7357.038 3115.799 13282.364
## 5    5.717 198659.8 84415.43 54555.19 6146.341 5427.323 2967.428 11622.069
##       Cr2O3     TiO2      MnO     P2O5       SrO      BaO  LOI   Ag As  B  Be
## 1  82.10429 3236.452 1084.240 3899.496  84.55946 268.6954 54.8 0.20 26 10 1.5
## 2  95.78834 4495.072 1006.795 4199.458  84.55946 358.2605 37.7 0.30 24 10 1.7
## 3  88.94632 4375.203 1084.240 4499.419  84.55946 358.2605 41.5 0.20 24 10 1.8
## 4  95.78834 5274.217 1161.686 4699.393 169.11891 358.2605 31.9 0.15 60 10 1.5
## 5 102.63036 6353.035  619.566 3599.535 169.11891 447.8257 28.6 0.15 20 10 1.3
##    Bi   Cd Co Cr Cu  Ga Hg La Li Mo  Ni   Pb   S Sb Sc Th Ti Tl U   V     W
## 1 1.5 0.90 20 87 10 0.5 20 10  4 52 148 1600 3.0  3 10  5  5 55 5 221 0.001
## 2 1.5 0.70 22 56 10 0.5 30 20  3 63  92 1500 1.5  6 10  5  5 57 5 154 0.001
## 3 1.5 0.80 23 59 10 0.5 30 20  4 62 103 1700 1.5  5 10  5  5 59 5 180 0.001
## 4 1.5 0.80 22 54 10 1.0 30 40  3 61  36 1400 1.5  7 10  5  5 53 5  98 0.001
## 5 1.5 0.25 14 41 10 0.5 20 20  2 43  65 3500 1.5  5 10  5  5 48 5  84 0.001
##       Zn Akermanite Albite Aluminium.oxide.hydroxide Anhydrite Aragonite
## 1 0.0221          0      0                         0         0         0
## 2 0.0154          0      0                         0         0         0
## 3 0.0180          0      0                         0         0         0
## 4 0.0098          0      0                         0         0         0
## 5 0.0084          0      0                         0         0         0
##   Biotite Birnessite Calcite Clinochlore Cuspidine Diaspore Dickite Gehlenite
## 1       0          0       0           0         0        0       0         0
## 2       0          0       0           0         0        0       0         0
## 3       0          0       0           0         0        0       0         0
## 4       0          0       0           0         0        0       0         0
## 5       0          0       0           0         0        0       1         0
##   Goethite Haematite Illite Kaolinite Langite Linnaeite Magnesioferrite
## 1        0         0      0         0       0         0               0
## 2        0         0      0         0       0         0               1
## 3        0         0      0         0       0         0               0
## 4        0         0      1         0       0         0               0
## 5        0         1      0         0       0         0               0
##   Melilite Merwinite Microcline Mullite Muscovite Orthoclase Orthopyroxene
## 1        0         0          0       0         1          0             0
## 2        0         0          0       0         1          0             0
## 3        0         0          0       0         1          0             0
## 4        0         0          0       0         0          0             0
## 5        0         0          0       0         1          0             0
##   Periclase Phengite Pseudowollastonite Quartz Staurolite Valentinite
## 1         0        0                  0      1          0           0
## 2         0        0                  0      1          0           0
## 3         0        0                  0      1          0           0
## 4         0        0                  0      1          0           0
## 5         0        0                  0      0          0           0

#Now to run some ANOSIMS…

#anoASiO2 <- anosim(AddiewellPS, AddiewellPC$SiO2, distance = “bray”, permutations = 9999)

#When this ANOSIM is run, the error message: “there should be replicates within groups” #comes up. This error message came up for other substrate variables for the #data. From now on, only variables that were tested successfully will be included.

anoANa2O <- anosim(AddiewellPS, AddiewellPC$Na2O, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoANa2O
## 
## Call:
## anosim(x = AddiewellPS, grouping = AddiewellPC$Na2O, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.7778 
##       Significance: 0.2 
## 
## Permutation: free
## Number of permutations: 119

#High R statistic, but with a non-significant p value of 0.2

anoACr2O3 <- anosim(AddiewellPS, AddiewellPC$Cr2O3, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoACr2O3
## 
## Call:
## anosim(x = AddiewellPS, grouping = AddiewellPC$Cr2O3, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.5556 
##       Significance: 0.3 
## 
## Permutation: free
## Number of permutations: 119
anoAMnO <- anosim(AddiewellPS, AddiewellPC$MnO, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoAMnO
## 
## Call:
## anosim(x = AddiewellPS, grouping = AddiewellPC$MnO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1111 
##       Significance: 0.5 
## 
## Permutation: free
## Number of permutations: 119
anoASrO <- anosim(AddiewellPS, AddiewellPC$SrO, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoASrO
## 
## Call:
## anosim(x = AddiewellPS, grouping = AddiewellPC$SrO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.4167 
##       Significance: 0.1 
## 
## Permutation: free
## Number of permutations: 119
anoABaO <- anosim(AddiewellPS, AddiewellPC$BaO, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoABaO
## 
## Call:
## anosim(x = AddiewellPS, grouping = AddiewellPC$BaO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.5238 
##       Significance: 0.3 
## 
## Permutation: free
## Number of permutations: 119
anoAAg <- anosim(AddiewellPS, AddiewellPC$Ag, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoAAg
## 
## Call:
## anosim(x = AddiewellPS, grouping = AddiewellPC$Ag, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.375 
##       Significance: 1 
## 
## Permutation: free
## Number of permutations: 119
anoAAs <- anosim(AddiewellPS, AddiewellPC$As, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoAAs
## 
## Call:
## anosim(x = AddiewellPS, grouping = AddiewellPC$As, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.7778 
##       Significance: 0.2 
## 
## Permutation: free
## Number of permutations: 119
anoABe <- anosim(AddiewellPS, AddiewellPC$Be, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoABe
## 
## Call:
## anosim(x = AddiewellPS, grouping = AddiewellPC$Be, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.3333 
##       Significance: 0.4 
## 
## Permutation: free
## Number of permutations: 119
anoACd <- anosim(AddiewellPS, AddiewellPC$Cd, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoACd
## 
## Call:
## anosim(x = AddiewellPS, grouping = AddiewellPC$Cd, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.1111 
##       Significance: 0.6 
## 
## Permutation: free
## Number of permutations: 119
anoACo <- anosim(AddiewellPS, AddiewellPC$Co, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoACo
## 
## Call:
## anosim(x = AddiewellPS, grouping = AddiewellPC$Co, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.5556 
##       Significance: 0.3 
## 
## Permutation: free
## Number of permutations: 119
anoASb <- anosim(AddiewellPS, AddiewellPC$Sb, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoASb
## 
## Call:
## anosim(x = AddiewellPS, grouping = AddiewellPC$Sb, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:    -1 
##       Significance: 1 
## 
## Permutation: free
## Number of permutations: 119

#None of the ANOSIM tests led to stastistically significant results. Because of this, #CCAs might not be entirely appropriate to represent the data visually. #NMDS analyses will be utilised instead to visualise the plant data.

AddiewellNMDS <- metaMDS(AddiewellPS, noshare = TRUE, autotransform = FALSE, trymax = 500)
## Run 0 stress 4.555731e-05 
## Run 1 stress 0 
## ... New best solution
## ... Procrustes: rmse 0.1394386  max resid 0.199908 
## Run 2 stress 5.334061e-05 
## ... Procrustes: rmse 0.02781573  max resid 0.03736889 
## Run 3 stress 0 
## ... Procrustes: rmse 0.04312613  max resid 0.06217065 
## Run 4 stress 9.628981e-05 
## ... Procrustes: rmse 0.2605213  max resid 0.4116508 
## Run 5 stress 6.607449e-05 
## ... Procrustes: rmse 0.1559432  max resid 0.239096 
## Run 6 stress 8.004008e-05 
## ... Procrustes: rmse 0.2101967  max resid 0.3296899 
## Run 7 stress 4.756845e-05 
## ... Procrustes: rmse 0.1958024  max resid 0.3024243 
## Run 8 stress 9.927506e-05 
## ... Procrustes: rmse 0.2967313  max resid 0.4221668 
## Run 9 stress 5.733367e-05 
## ... Procrustes: rmse 0.2906466  max resid 0.4051213 
## Run 10 stress 0.000124645 
## ... Procrustes: rmse 0.2940408  max resid 0.4214675 
## Run 11 stress 5.512373e-05 
## ... Procrustes: rmse 0.1825714  max resid 0.2816075 
## Run 12 stress 9.789625e-05 
## ... Procrustes: rmse 0.09300779  max resid 0.1378204 
## Run 13 stress 3.864466e-05 
## ... Procrustes: rmse 0.1534289  max resid 0.2375754 
## Run 14 stress 8.745128e-05 
## ... Procrustes: rmse 0.1625155  max resid 0.2342181 
## Run 15 stress 8.064009e-05 
## ... Procrustes: rmse 0.1579679  max resid 0.2466169 
## Run 16 stress 5.418653e-05 
## ... Procrustes: rmse 0.2443975  max resid 0.3972858 
## Run 17 stress 9.876665e-05 
## ... Procrustes: rmse 0.09985639  max resid 0.1617047 
## Run 18 stress 0 
## ... Procrustes: rmse 0.03220173  max resid 0.05169976 
## Run 19 stress 5.4069e-05 
## ... Procrustes: rmse 0.071993  max resid 0.1164186 
## Run 20 stress 7.830082e-05 
## ... Procrustes: rmse 0.1491511  max resid 0.2014685 
## Run 21 stress 8.71607e-05 
## ... Procrustes: rmse 0.2158104  max resid 0.3236803 
## Run 22 stress 9.508762e-05 
## ... Procrustes: rmse 0.2658905  max resid 0.4200486 
## Run 23 stress 9.586218e-05 
## ... Procrustes: rmse 0.2237021  max resid 0.2843755 
## Run 24 stress 9.103485e-05 
## ... Procrustes: rmse 0.2559357  max resid 0.4206671 
## Run 25 stress 5.734731e-05 
## ... Procrustes: rmse 0.08941837  max resid 0.1293258 
## Run 26 stress 0.0001934982 
## ... Procrustes: rmse 0.126113  max resid 0.190014 
## Run 27 stress 9.427861e-05 
## ... Procrustes: rmse 0.215611  max resid 0.3046192 
## Run 28 stress 0 
## ... Procrustes: rmse 0.03576356  max resid 0.05520864 
## Run 29 stress 9.439427e-05 
## ... Procrustes: rmse 0.2384413  max resid 0.3885948 
## Run 30 stress 9.735806e-05 
## ... Procrustes: rmse 0.1686201  max resid 0.2577146 
## Run 31 stress 9.744262e-05 
## ... Procrustes: rmse 0.2644396  max resid 0.4327375 
## Run 32 stress 9.633098e-05 
## ... Procrustes: rmse 0.2314866  max resid 0.2818013 
## Run 33 stress 9.727373e-05 
## ... Procrustes: rmse 0.2134852  max resid 0.2977612 
## Run 34 stress 4.412856e-05 
## ... Procrustes: rmse 0.2273248  max resid 0.3568848 
## Run 35 stress 9.809342e-05 
## ... Procrustes: rmse 0.2027214  max resid 0.267987 
## Run 36 stress 7.944163e-05 
## ... Procrustes: rmse 0.1283586  max resid 0.1841102 
## Run 37 stress 9.901716e-05 
## ... Procrustes: rmse 0.2267937  max resid 0.2856523 
## Run 38 stress 9.595322e-05 
## ... Procrustes: rmse 0.2679173  max resid 0.39266 
## Run 39 stress 4.921681e-05 
## ... Procrustes: rmse 0.1130304  max resid 0.1610114 
## Run 40 stress 9.877517e-05 
## ... Procrustes: rmse 0.08107369  max resid 0.1168006 
## Run 41 stress 6.06864e-05 
## ... Procrustes: rmse 0.1638209  max resid 0.2049504 
## Run 42 stress 8.624905e-05 
## ... Procrustes: rmse 0.2705442  max resid 0.4358683 
## Run 43 stress 9.928364e-05 
## ... Procrustes: rmse 0.2084866  max resid 0.320789 
## Run 44 stress 9.994884e-05 
## ... Procrustes: rmse 0.0566009  max resid 0.08906317 
## Run 45 stress 8.971732e-05 
## ... Procrustes: rmse 0.2078997  max resid 0.3324217 
## Run 46 stress 5.983457e-05 
## ... Procrustes: rmse 0.01697042  max resid 0.02855343 
## Run 47 stress 9.795553e-05 
## ... Procrustes: rmse 0.2258254  max resid 0.3624661 
## Run 48 stress 9.077041e-05 
## ... Procrustes: rmse 0.2326288  max resid 0.2817835 
## Run 49 stress 1.780997e-06 
## ... Procrustes: rmse 0.03455924  max resid 0.03951522 
## Run 50 stress 0.0005588758 
## Run 51 stress 9.743025e-05 
## ... Procrustes: rmse 0.2264446  max resid 0.2909201 
## Run 52 stress 8.984606e-05 
## ... Procrustes: rmse 0.2154693  max resid 0.3195796 
## Run 53 stress 0 
## ... Procrustes: rmse 0.03001268  max resid 0.04955042 
## Run 54 stress 8.846187e-05 
## ... Procrustes: rmse 0.2264834  max resid 0.2863919 
## Run 55 stress 5.686017e-05 
## ... Procrustes: rmse 0.2350458  max resid 0.3027396 
## Run 56 stress 7.96967e-05 
## ... Procrustes: rmse 0.2246847  max resid 0.345365 
## Run 57 stress 9.415498e-05 
## ... Procrustes: rmse 0.03078587  max resid 0.04816126 
## Run 58 stress 7.103488e-05 
## ... Procrustes: rmse 0.1161369  max resid 0.155063 
## Run 59 stress 9.926696e-05 
## ... Procrustes: rmse 0.1503476  max resid 0.2378199 
## Run 60 stress 8.939536e-05 
## ... Procrustes: rmse 0.2087667  max resid 0.2660027 
## Run 61 stress 9.92562e-05 
## ... Procrustes: rmse 0.2238046  max resid 0.2892603 
## Run 62 stress 9.477649e-05 
## ... Procrustes: rmse 0.1514453  max resid 0.2479281 
## Run 63 stress 8.586595e-05 
## ... Procrustes: rmse 0.2478378  max resid 0.4151296 
## Run 64 stress 9.982107e-05 
## ... Procrustes: rmse 0.2756214  max resid 0.4354381 
## Run 65 stress 3.969653e-05 
## ... Procrustes: rmse 0.03531637  max resid 0.05149841 
## Run 66 stress 8.336222e-05 
## ... Procrustes: rmse 0.2213674  max resid 0.2918831 
## Run 67 stress 8.244809e-05 
## ... Procrustes: rmse 0.08956448  max resid 0.1226475 
## Run 68 stress 3.776605e-05 
## ... Procrustes: rmse 0.205024  max resid 0.2685254 
## Run 69 stress 9.813386e-05 
## ... Procrustes: rmse 0.2670257  max resid 0.4438814 
## Run 70 stress 9.325933e-05 
## ... Procrustes: rmse 0.06159678  max resid 0.08251229 
## Run 71 stress 8.241086e-05 
## ... Procrustes: rmse 0.2430191  max resid 0.3833474 
## Run 72 stress 8.13581e-05 
## ... Procrustes: rmse 0.2269246  max resid 0.2827465 
## Run 73 stress 7.201479e-05 
## ... Procrustes: rmse 0.2410271  max resid 0.2864472 
## Run 74 stress 9.866711e-05 
## ... Procrustes: rmse 0.2189354  max resid 0.2967141 
## Run 75 stress 8.080119e-05 
## ... Procrustes: rmse 0.1979584  max resid 0.3282312 
## Run 76 stress 8.540973e-05 
## ... Procrustes: rmse 0.2147006  max resid 0.3086361 
## Run 77 stress 7.576413e-05 
## ... Procrustes: rmse 0.1894706  max resid 0.2937232 
## Run 78 stress 2.676033e-05 
## ... Procrustes: rmse 0.2222876  max resid 0.3568479 
## Run 79 stress 9.820088e-05 
## ... Procrustes: rmse 0.2756163  max resid 0.4354511 
## Run 80 stress 3.737498e-05 
## ... Procrustes: rmse 0.2350954  max resid 0.3338334 
## Run 81 stress 5.170606e-05 
## ... Procrustes: rmse 0.03348428  max resid 0.05290226 
## Run 82 stress 0.0001615429 
## ... Procrustes: rmse 0.1172044  max resid 0.1755751 
## Run 83 stress 9.629054e-05 
## ... Procrustes: rmse 0.227002  max resid 0.2856541 
## Run 84 stress 5.749932e-06 
## ... Procrustes: rmse 0.01607455  max resid 0.02001607 
## Run 85 stress 0 
## ... Procrustes: rmse 0.1161329  max resid 0.1733693 
## Run 86 stress 8.757929e-05 
## ... Procrustes: rmse 0.2230758  max resid 0.2922253 
## Run 87 stress 9.889862e-05 
## ... Procrustes: rmse 0.04534924  max resid 0.06498945 
## Run 88 stress 9.911963e-05 
## ... Procrustes: rmse 0.2574684  max resid 0.3733342 
## Run 89 stress 0.0002175778 
## ... Procrustes: rmse 0.09485009  max resid 0.1413596 
## Run 90 stress 9.63271e-05 
## ... Procrustes: rmse 0.2226154  max resid 0.2899366 
## Run 91 stress 9.589235e-05 
## ... Procrustes: rmse 0.2326569  max resid 0.2985666 
## Run 92 stress 9.851625e-05 
## ... Procrustes: rmse 0.2234867  max resid 0.3562357 
## Run 93 stress 9.673675e-05 
## ... Procrustes: rmse 0.2338646  max resid 0.2790294 
## Run 94 stress 6.004884e-05 
## ... Procrustes: rmse 0.2493266  max resid 0.4028386 
## Run 95 stress 9.987296e-05 
## ... Procrustes: rmse 0.07106277  max resid 0.1133562 
## Run 96 stress 6.78939e-05 
## ... Procrustes: rmse 0.02605334  max resid 0.04261392 
## Run 97 stress 9.995533e-05 
## ... Procrustes: rmse 0.220866  max resid 0.2685383 
## Run 98 stress 9.438229e-05 
## ... Procrustes: rmse 0.2204371  max resid 0.3366578 
## Run 99 stress 6.421406e-05 
## ... Procrustes: rmse 0.270726  max resid 0.4310821 
## Run 100 stress 2.696124e-05 
## ... Procrustes: rmse 0.01978326  max resid 0.02632141 
## Run 101 stress 9.227456e-05 
## ... Procrustes: rmse 0.2450924  max resid 0.379314 
## Run 102 stress 7.940942e-05 
## ... Procrustes: rmse 0.2149571  max resid 0.3092425 
## Run 103 stress 9.793945e-05 
## ... Procrustes: rmse 0.2335197  max resid 0.2812273 
## Run 104 stress 9.912932e-05 
## ... Procrustes: rmse 0.2911421  max resid 0.4217707 
## Run 105 stress 0 
## ... Procrustes: rmse 0.01593162  max resid 0.02528953 
## Run 106 stress 9.491467e-05 
## ... Procrustes: rmse 0.2023571  max resid 0.2677698 
## Run 107 stress 9.64597e-05 
## ... Procrustes: rmse 0.1095906  max resid 0.1617171 
## Run 108 stress 9.860447e-05 
## ... Procrustes: rmse 0.2067299  max resid 0.3165291 
## Run 109 stress 7.262788e-05 
## ... Procrustes: rmse 0.2196147  max resid 0.3513147 
## Run 110 stress 9.388294e-05 
## ... Procrustes: rmse 0.2678891  max resid 0.4331526 
## Run 111 stress 2.990623e-05 
## ... Procrustes: rmse 0.2381909  max resid 0.3748571 
## Run 112 stress 5.576394e-05 
## ... Procrustes: rmse 0.1678861  max resid 0.2518949 
## Run 113 stress 7.738752e-05 
## ... Procrustes: rmse 0.061483  max resid 0.08766965 
## Run 114 stress 9.755985e-05 
## ... Procrustes: rmse 0.2684587  max resid 0.4011294 
## Run 115 stress 8.465723e-05 
## ... Procrustes: rmse 0.1883264  max resid 0.2836363 
## Run 116 stress 2.015106e-05 
## ... Procrustes: rmse 0.03172841  max resid 0.05339025 
## Run 117 stress 9.880862e-05 
## ... Procrustes: rmse 0.2183645  max resid 0.2963482 
## Run 118 stress 9.466567e-05 
## ... Procrustes: rmse 0.1163633  max resid 0.1875544 
## Run 119 stress 9.212682e-05 
## ... Procrustes: rmse 0.07853849  max resid 0.1127383 
## Run 120 stress 9.526069e-05 
## ... Procrustes: rmse 0.2162678  max resid 0.2771077 
## Run 121 stress 5.073535e-05 
## ... Procrustes: rmse 0.3219801  max resid 0.4370961 
## Run 122 stress 5.543104e-05 
## ... Procrustes: rmse 0.1655598  max resid 0.2557364 
## Run 123 stress 5.541805e-05 
## ... Procrustes: rmse 0.2651334  max resid 0.4364372 
## Run 124 stress 8.917724e-05 
## ... Procrustes: rmse 0.2206187  max resid 0.293042 
## Run 125 stress 0 
## ... Procrustes: rmse 0.03103839  max resid 0.0517568 
## Run 126 stress 9.868087e-05 
## ... Procrustes: rmse 0.2703791  max resid 0.4052905 
## Run 127 stress 5.151571e-05 
## ... Procrustes: rmse 0.1887136  max resid 0.2840723 
## Run 128 stress 8.627828e-05 
## ... Procrustes: rmse 0.1431563  max resid 0.2168914 
## Run 129 stress 0.0002353894 
## ... Procrustes: rmse 0.2944349  max resid 0.4295659 
## Run 130 stress 8.382393e-05 
## ... Procrustes: rmse 0.08444356  max resid 0.1199069 
## Run 131 stress 8.487414e-05 
## ... Procrustes: rmse 0.179345  max resid 0.2665164 
## Run 132 stress 3.585677e-05 
## ... Procrustes: rmse 0.05596548  max resid 0.08449081 
## Run 133 stress 9.237112e-05 
## ... Procrustes: rmse 0.2624736  max resid 0.4458163 
## Run 134 stress 0.0001379646 
## ... Procrustes: rmse 0.3057661  max resid 0.4220396 
## Run 135 stress 9.818747e-05 
## ... Procrustes: rmse 0.2197128  max resid 0.2827065 
## Run 136 stress 9.728388e-05 
## ... Procrustes: rmse 0.2192869  max resid 0.3025434 
## Run 137 stress 9.990504e-05 
## ... Procrustes: rmse 0.2284228  max resid 0.3121845 
## Run 138 stress 8.692552e-05 
## ... Procrustes: rmse 0.1677465  max resid 0.2654495 
## Run 139 stress 9.447367e-05 
## ... Procrustes: rmse 0.2398571  max resid 0.3775603 
## Run 140 stress 0.0007236415 
## Run 141 stress 5.352662e-05 
## ... Procrustes: rmse 0.1590046  max resid 0.2094758 
## Run 142 stress 9.315055e-05 
## ... Procrustes: rmse 0.2179084  max resid 0.3322182 
## Run 143 stress 8.729033e-05 
## ... Procrustes: rmse 0.2323969  max resid 0.2800636 
## Run 144 stress 0 
## ... Procrustes: rmse 0.03920591  max resid 0.05540056 
## Run 145 stress 9.84576e-05 
## ... Procrustes: rmse 0.06416471  max resid 0.09333506 
## Run 146 stress 0.0003089019 
## ... Procrustes: rmse 0.03591237  max resid 0.05331922 
## Run 147 stress 7.372445e-05 
## ... Procrustes: rmse 0.2015201  max resid 0.3255738 
## Run 148 stress 9.167227e-05 
## ... Procrustes: rmse 0.2213787  max resid 0.2911152 
## Run 149 stress 0.0001172193 
## ... Procrustes: rmse 0.1904607  max resid 0.2965131 
## Run 150 stress 2.092111e-05 
## ... Procrustes: rmse 0.156601  max resid 0.2213505 
## Run 151 stress 2.627147e-05 
## ... Procrustes: rmse 0.05892797  max resid 0.09179957 
## Run 152 stress 0 
## ... Procrustes: rmse 0.02953372  max resid 0.03743263 
## Run 153 stress 7.444393e-05 
## ... Procrustes: rmse 0.2154414  max resid 0.3218797 
## Run 154 stress 9.958915e-05 
## ... Procrustes: rmse 0.09608842  max resid 0.1408996 
## Run 155 stress 6.737471e-05 
## ... Procrustes: rmse 0.1827998  max resid 0.2925356 
## Run 156 stress 0 
## ... Procrustes: rmse 0.02089313  max resid 0.03376175 
## Run 157 stress 9.818532e-05 
## ... Procrustes: rmse 0.03711718  max resid 0.06151738 
## Run 158 stress 8.107503e-05 
## ... Procrustes: rmse 0.2079819  max resid 0.2522333 
## Run 159 stress 4.978986e-05 
## ... Procrustes: rmse 0.1860952  max resid 0.2802297 
## Run 160 stress 9.400989e-05 
## ... Procrustes: rmse 0.2148671  max resid 0.3139049 
## Run 161 stress 8.800288e-05 
## ... Procrustes: rmse 0.2512408  max resid 0.3960858 
## Run 162 stress 9.935937e-05 
## ... Procrustes: rmse 0.2718659  max resid 0.4057625 
## Run 163 stress 9.343577e-05 
## ... Procrustes: rmse 0.2304909  max resid 0.2823695 
## Run 164 stress 9.586156e-05 
## ... Procrustes: rmse 0.2328287  max resid 0.2801917 
## Run 165 stress 8.374148e-05 
## ... Procrustes: rmse 0.07612721  max resid 0.1045267 
## Run 166 stress 0 
## ... Procrustes: rmse 0.03836524  max resid 0.05510684 
## Run 167 stress 9.395692e-05 
## ... Procrustes: rmse 0.2227071  max resid 0.3586932 
## Run 168 stress 8.837876e-05 
## ... Procrustes: rmse 0.119388  max resid 0.1808288 
## Run 169 stress 8.496701e-05 
## ... Procrustes: rmse 0.2262469  max resid 0.3505862 
## Run 170 stress 3.788856e-05 
## ... Procrustes: rmse 0.236963  max resid 0.2784925 
## Run 171 stress 5.755605e-05 
## ... Procrustes: rmse 0.1472538  max resid 0.2227193 
## Run 172 stress 9.215724e-05 
## ... Procrustes: rmse 0.2387749  max resid 0.2821092 
## Run 173 stress 6.67605e-05 
## ... Procrustes: rmse 0.02693745  max resid 0.04535003 
## Run 174 stress 9.607199e-05 
## ... Procrustes: rmse 0.2570506  max resid 0.3913349 
## Run 175 stress 8.499008e-05 
## ... Procrustes: rmse 0.1861608  max resid 0.305338 
## Run 176 stress 9.665384e-05 
## ... Procrustes: rmse 0.2156676  max resid 0.3061237 
## Run 177 stress 9.799095e-05 
## ... Procrustes: rmse 0.2283665  max resid 0.3765548 
## Run 178 stress 9.307685e-05 
## ... Procrustes: rmse 0.2126754  max resid 0.2945302 
## Run 179 stress 7.569902e-05 
## ... Procrustes: rmse 0.2267289  max resid 0.2857681 
## Run 180 stress 9.366532e-05 
## ... Procrustes: rmse 0.2211097  max resid 0.3024885 
## Run 181 stress 3.479911e-05 
## ... Procrustes: rmse 0.0729068  max resid 0.1033163 
## Run 182 stress 8.897008e-05 
## ... Procrustes: rmse 0.0928177  max resid 0.1463303 
## Run 183 stress 9.447818e-05 
## ... Procrustes: rmse 0.2308205  max resid 0.2853456 
## Run 184 stress 5.813384e-05 
## ... Procrustes: rmse 0.130485  max resid 0.1615704 
## Run 185 stress 1.574195e-05 
## ... Procrustes: rmse 0.1756863  max resid 0.2883974 
## Run 186 stress 6.113626e-05 
## ... Procrustes: rmse 0.150811  max resid 0.1997707 
## Run 187 stress 0.0001718735 
## ... Procrustes: rmse 0.3115801  max resid 0.4331315 
## Run 188 stress 9.89834e-05 
## ... Procrustes: rmse 0.07655785  max resid 0.124899 
## Run 189 stress 9.536423e-05 
## ... Procrustes: rmse 0.2673298  max resid 0.383448 
## Run 190 stress 9.465914e-05 
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## ... Procrustes: rmse 0.2380415  max resid 0.3894336 
## Run 416 stress 5.25995e-05 
## ... Procrustes: rmse 0.2323588  max resid 0.3195136 
## Run 417 stress 8.816897e-05 
## ... Procrustes: rmse 0.2216945  max resid 0.2930355 
## Run 418 stress 9.497403e-05 
## ... Procrustes: rmse 0.2188269  max resid 0.3327576 
## Run 419 stress 9.046932e-05 
## ... Procrustes: rmse 0.1078563  max resid 0.1741128 
## Run 420 stress 8.632903e-05 
## ... Procrustes: rmse 0.2208885  max resid 0.3261937 
## Run 421 stress 9.950429e-05 
## ... Procrustes: rmse 0.1995912  max resid 0.3042185 
## Run 422 stress 6.122063e-05 
## ... Procrustes: rmse 0.2528445  max resid 0.4354527 
## Run 423 stress 9.455573e-05 
## ... Procrustes: rmse 0.2213979  max resid 0.3212053 
## Run 424 stress 9.792788e-05 
## ... Procrustes: rmse 0.2571578  max resid 0.432684 
## Run 425 stress 0 
## ... Procrustes: rmse 0.04548339  max resid 0.06628296 
## Run 426 stress 9.854064e-05 
## ... Procrustes: rmse 0.2554386  max resid 0.4247143 
## Run 427 stress 0 
## ... Procrustes: rmse 0.08494806  max resid 0.1216343 
## Run 428 stress 9.623568e-05 
## ... Procrustes: rmse 0.2702595  max resid 0.4392824 
## Run 429 stress 9.376665e-05 
## ... Procrustes: rmse 0.245473  max resid 0.373825 
## Run 430 stress 8.206008e-05 
## ... Procrustes: rmse 0.2252953  max resid 0.2872246 
## Run 431 stress 9.735089e-05 
## ... Procrustes: rmse 0.14694  max resid 0.23872 
## Run 432 stress 4.99489e-05 
## ... Procrustes: rmse 0.1565731  max resid 0.2130734 
## Run 433 stress 7.928159e-05 
## ... Procrustes: rmse 0.1641939  max resid 0.2265678 
## Run 434 stress 8.092843e-05 
## ... Procrustes: rmse 0.244528  max resid 0.3855202 
## Run 435 stress 9.662347e-05 
## ... Procrustes: rmse 0.217878  max resid 0.2973681 
## Run 436 stress 9.549408e-05 
## ... Procrustes: rmse 0.2561546  max resid 0.4326797 
## Run 437 stress 9.759213e-05 
## ... Procrustes: rmse 0.2339005  max resid 0.2799411 
## Run 438 stress 6.48888e-05 
## ... Procrustes: rmse 0.1468361  max resid 0.2199348 
## Run 439 stress 6.59974e-05 
## ... Procrustes: rmse 0.1462041  max resid 0.2032058 
## Run 440 stress 9.498861e-05 
## ... Procrustes: rmse 0.04138316  max resid 0.05472961 
## Run 441 stress 0 
## ... Procrustes: rmse 0.06942347  max resid 0.09792683 
## Run 442 stress 9.837632e-05 
## ... Procrustes: rmse 0.2533589  max resid 0.3817529 
## Run 443 stress 5.085659e-05 
## ... Procrustes: rmse 0.02867107  max resid 0.04585516 
## Run 444 stress 9.933902e-05 
## ... Procrustes: rmse 0.2137123  max resid 0.3005852 
## Run 445 stress 5.104407e-05 
## ... Procrustes: rmse 0.1580489  max resid 0.2145353 
## Run 446 stress 9.648709e-05 
## ... Procrustes: rmse 0.0742925  max resid 0.1025462 
## Run 447 stress 0.0002590302 
## ... Procrustes: rmse 0.2959958  max resid 0.4262425 
## Run 448 stress 9.02819e-05 
## ... Procrustes: rmse 0.209556  max resid 0.3392181 
## Run 449 stress 9.462175e-05 
## ... Procrustes: rmse 0.2238921  max resid 0.2892609 
## Run 450 stress 7.729072e-05 
## ... Procrustes: rmse 0.2225207  max resid 0.3216539 
## Run 451 stress 9.056759e-05 
## ... Procrustes: rmse 0.08121007  max resid 0.1162538 
## Run 452 stress 9.726661e-05 
## ... Procrustes: rmse 0.09480156  max resid 0.1474081 
## Run 453 stress 9.975859e-05 
## ... Procrustes: rmse 0.2790455  max resid 0.4377186 
## Run 454 stress 8.399496e-05 
## ... Procrustes: rmse 0.2516333  max resid 0.3856527 
## Run 455 stress 4.515116e-05 
## ... Procrustes: rmse 0.2284668  max resid 0.33025 
## Run 456 stress 8.857325e-05 
## ... Procrustes: rmse 0.2134521  max resid 0.2759809 
## Run 457 stress 9.590961e-05 
## ... Procrustes: rmse 0.2332462  max resid 0.2801812 
## Run 458 stress 3.674049e-05 
## ... Procrustes: rmse 0.1936236  max resid 0.2879405 
## Run 459 stress 9.909255e-05 
## ... Procrustes: rmse 0.2249898  max resid 0.2790781 
## Run 460 stress 8.60942e-05 
## ... Procrustes: rmse 0.04451893  max resid 0.07172618 
## Run 461 stress 9.746941e-05 
## ... Procrustes: rmse 0.2255474  max resid 0.339368 
## Run 462 stress 9.31125e-05 
## ... Procrustes: rmse 0.2238536  max resid 0.3013185 
## Run 463 stress 8.519307e-05 
## ... Procrustes: rmse 0.108933  max resid 0.1638492 
## Run 464 stress 8.660003e-05 
## ... Procrustes: rmse 0.2205404  max resid 0.3453623 
## Run 465 stress 8.991698e-05 
## ... Procrustes: rmse 0.2521634  max resid 0.3659159 
## Run 466 stress 2.675409e-05 
## ... Procrustes: rmse 0.04872326  max resid 0.06920561 
## Run 467 stress 5.36961e-05 
## ... Procrustes: rmse 0.06088975  max resid 0.08629013 
## Run 468 stress 9.664431e-05 
## ... Procrustes: rmse 0.2211369  max resid 0.3355072 
## Run 469 stress 2.853497e-05 
## ... Procrustes: rmse 0.2107122  max resid 0.3492797 
## Run 470 stress 0.0001896754 
## ... Procrustes: rmse 0.1423791  max resid 0.2166194 
## Run 471 stress 8.64418e-05 
## ... Procrustes: rmse 0.2503737  max resid 0.3987527 
## Run 472 stress 0.0001244962 
## ... Procrustes: rmse 0.310245  max resid 0.4368616 
## Run 473 stress 9.298615e-05 
## ... Procrustes: rmse 0.2756289  max resid 0.4354629 
## Run 474 stress 9.361769e-05 
## ... Procrustes: rmse 0.2415814  max resid 0.4125999 
## Run 475 stress 9.687431e-05 
## ... Procrustes: rmse 0.1162057  max resid 0.1753214 
## Run 476 stress 9.863084e-05 
## ... Procrustes: rmse 0.2222163  max resid 0.3068564 
## Run 477 stress 8.159918e-05 
## ... Procrustes: rmse 0.2033148  max resid 0.3094495 
## Run 478 stress 0 
## ... Procrustes: rmse 0.02300545  max resid 0.03135208 
## Run 479 stress 9.358367e-05 
## ... Procrustes: rmse 0.221202  max resid 0.2799728 
## Run 480 stress 9.442935e-05 
## ... Procrustes: rmse 0.2149894  max resid 0.2705135 
## Run 481 stress 7.864605e-05 
## ... Procrustes: rmse 0.1395414  max resid 0.2014377 
## Run 482 stress 7.093423e-05 
## ... Procrustes: rmse 0.2236884  max resid 0.2801549 
## Run 483 stress 9.021826e-05 
## ... Procrustes: rmse 0.2255416  max resid 0.3540517 
## Run 484 stress 8.712607e-05 
## ... Procrustes: rmse 0.2313265  max resid 0.2813314 
## Run 485 stress 9.701111e-05 
## ... Procrustes: rmse 0.2560269  max resid 0.395143 
## Run 486 stress 9.633498e-05 
## ... Procrustes: rmse 0.2339795  max resid 0.2795778 
## Run 487 stress 7.678059e-05 
## ... Procrustes: rmse 0.1286553  max resid 0.2029963 
## Run 488 stress 9.114384e-05 
## ... Procrustes: rmse 0.2573281  max resid 0.4441394 
## Run 489 stress 9.542448e-05 
## ... Procrustes: rmse 0.2756342  max resid 0.4354664 
## Run 490 stress 9.277839e-05 
## ... Procrustes: rmse 0.2533689  max resid 0.392537 
## Run 491 stress 0.0001379902 
## ... Procrustes: rmse 0.1977211  max resid 0.3084087 
## Run 492 stress 8.257375e-05 
## ... Procrustes: rmse 0.275668  max resid 0.4355326 
## Run 493 stress 8.863e-05 
## ... Procrustes: rmse 0.09655526  max resid 0.1399787 
## Run 494 stress 9.847084e-05 
## ... Procrustes: rmse 0.2982617  max resid 0.4178466 
## Run 495 stress 9.04915e-05 
## ... Procrustes: rmse 0.2015843  max resid 0.2986058 
## Run 496 stress 9.873228e-05 
## ... Procrustes: rmse 0.2253865  max resid 0.3540535 
## Run 497 stress 9.902728e-05 
## ... Procrustes: rmse 0.2560512  max resid 0.3733946 
## Run 498 stress 0 
## ... Procrustes: rmse 0.1197349  max resid 0.1784656 
## Run 499 stress 8.842792e-05 
## ... Procrustes: rmse 0.2176721  max resid 0.3159418 
## Run 500 stress 4.204977e-05 
## ... Procrustes: rmse 0.1280962  max resid 0.183641 
## *** Best solution was not repeated -- monoMDS stopping criteria:
##     28: no. of iterations >= maxit
##    471: stress < smin
##      1: stress ratio > sratmax
## Warning in metaMDS(AddiewellPS, noshare = TRUE, autotransform = FALSE, trymax =
## 500): stress is (nearly) zero: you may have insufficient data
## Warning in postMDS(out$points, dis, plot = max(0, plot - 1), ...): skipping
## half-change scaling: too few points below threshold
plot(AddiewellNMDS)

#This is a simple NMDS plot, with the different plant communities as circles and the #red crosses as species.

AddiewellNMDS
## 
## Call:
## metaMDS(comm = AddiewellPS, trymax = 500, autotransform = FALSE,      noshare = TRUE) 
## 
## global Multidimensional Scaling using monoMDS
## 
## Data:     AddiewellPS 
## Distance: bray 
## 
## Dimensions: 2 
## Stress:     0 
## Stress type 1, weak ties
## Best solution was not repeated after 500 tries
## The best solution was from try 1 (random start)
## Scaling: centring, PC rotation 
## Species: expanded scores based on 'AddiewellPS'
plot(AddiewellNMDS, "sites")   # Produces distance 

plot(AddiewellNMDS, "species", xlim = c(-0.5, 0.5), ylim = c(-1.5, 1.0))
orditorp(AddiewellNMDS, "species")

#The orditorp function provides some of the plant species on the site on the graph. #The species are grouped fairly close together, apart from Pleurozium schreberi. It will #be interesting to look at CCAs of the plant and substrate data at Addiewell Bing, to #better visualise the relationship between plants and substrate.

#Now for some CCAS…

AddiewellCCA <- cca(AddiewellPS, AddiewellPC)
## 
## Some constraints or conditions were aliased because they were redundant. This
## can happen if terms are linearly dependent (collinear): 'CaO', 'MgO', 'Na2O',
## 'K2O', 'Cr2O3', 'TiO2', 'MnO', 'P2O5', 'SrO', 'BaO', 'LOI', 'Ag', 'As', 'B',
## 'Be', 'Bi', 'Cd', 'Co', 'Cr', 'Cu', 'Ga', 'Hg', 'La', 'Li', 'Mo', 'Ni', 'Pb',
## 'S', 'Sb', 'Sc', 'Th', 'Ti', 'Tl', 'U', 'V', 'W', 'Zn', 'Akermanite', 'Albite',
## 'Aluminium.oxide.hydroxide', 'Anhydrite', 'Aragonite', 'Biotite', 'Birnessite',
## 'Calcite', 'Clinochlore', 'Cuspidine', 'Diaspore', 'Dickite', 'Gehlenite',
## 'Goethite', 'Haematite', 'Illite', 'Kaolinite', 'Langite', 'Linnaeite',
## 'Magnesioferrite', 'Melilite', 'Merwinite', 'Microcline', 'Mullite',
## 'Muscovite', 'Orthoclase', 'Orthopyroxene', 'Periclase', 'Phengite',
## 'Pseudowollastonite', 'Quartz', 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component
print(AddiewellCCA)
## Call: cca(X = AddiewellPS, Y = AddiewellPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total           1.706      1.000     
## Constrained     1.706      1.000    4
## Unconstrained   0.000      0.000    0
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## Some constraints or conditions were aliased because they were redundant.
## This can happen if terms are linearly dependent (collinear): 'CaO', 'MgO',
## 'Na2O', 'K2O', 'Cr2O3', 'TiO2', 'MnO', 'P2O5', 'SrO', 'BaO', 'LOI', 'Ag',
## 'As', 'B', 'Be', 'Bi', 'Cd', 'Co', 'Cr', 'Cu', 'Ga', 'Hg', 'La', 'Li',
## 'Mo', 'Ni', 'Pb', 'S', 'Sb', 'Sc', 'Th', 'Ti', 'Tl', 'U', 'V', 'W', 'Zn',
## 'Akermanite', 'Albite', 'Aluminium.oxide.hydroxide', 'Anhydrite',
## 'Aragonite', 'Biotite', 'Birnessite', 'Calcite', 'Clinochlore',
## 'Cuspidine', 'Diaspore', 'Dickite', 'Gehlenite', 'Goethite', 'Haematite',
## 'Illite', 'Kaolinite', 'Langite', 'Linnaeite', 'Magnesioferrite',
## 'Melilite', 'Merwinite', 'Microcline', 'Mullite', 'Muscovite',
## 'Orthoclase', 'Orthopyroxene', 'Periclase', 'Phengite',
## 'Pseudowollastonite', 'Quartz', 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component.
## 
## 88 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4 
## 0.6828 0.5091 0.3583 0.1556
plot(AddiewellCCA)

summary(AddiewellCCA)
## 
## Call:
## cca(X = AddiewellPS, Y = AddiewellPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           1.706          1
## Constrained     1.706          1
## Unconstrained   0.000          0
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CCA4
## Eigenvalue            0.6828 0.5091 0.3583 0.15559
## Proportion Explained  0.4003 0.2984 0.2101 0.09121
## Cumulative Proportion 0.4003 0.6987 0.9088 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3    CCA4
## Eigenvalue            0.6828 0.5091 0.3583 0.15559
## Proportion Explained  0.4003 0.2984 0.2101 0.09121
## Cumulative Proportion 0.4003 0.6987 0.9088 1.00000
AddiewellCCA2 <- cca(AddiewellPS ~ Co + Pb + S + As, data = AddiewellPC)
## 
## The model is overfitted with no unconstrained (residual) component
print(AddiewellCCA2)
## Call: cca(formula = AddiewellPS ~ Co + Pb + S + As, data = AddiewellPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total           1.706      1.000     
## Constrained     1.706      1.000    4
## Unconstrained   0.000      0.000    0
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## The model is overfitted with no unconstrained (residual) component.
## 
## 88 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4 
## 0.6828 0.5091 0.3583 0.1556
plot(AddiewellCCA2)

summary(AddiewellCCA2)
## 
## Call:
## cca(formula = AddiewellPS ~ Co + Pb + S + As, data = AddiewellPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           1.706          1
## Constrained     1.706          1
## Unconstrained   0.000          0
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CCA4
## Eigenvalue            0.6828 0.5091 0.3583 0.15559
## Proportion Explained  0.4003 0.2984 0.2101 0.09121
## Cumulative Proportion 0.4003 0.6987 0.9088 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3    CCA4
## Eigenvalue            0.6828 0.5091 0.3583 0.15559
## Proportion Explained  0.4003 0.2984 0.2101 0.09121
## Cumulative Proportion 0.4003 0.6987 0.9088 1.00000
AddiewellCCA3 <- cca(AddiewellPS ~ V + Pb + S + As, data = AddiewellPC)
## 
## The model is overfitted with no unconstrained (residual) component
print(AddiewellCCA3)
## Call: cca(formula = AddiewellPS ~ V + Pb + S + As, data = AddiewellPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total           1.706      1.000     
## Constrained     1.706      1.000    4
## Unconstrained   0.000      0.000    0
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## The model is overfitted with no unconstrained (residual) component.
## 
## 88 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4 
## 0.6828 0.5091 0.3583 0.1556
plot(AddiewellCCA3)

summary(AddiewellCCA3)
## 
## Call:
## cca(formula = AddiewellPS ~ V + Pb + S + As, data = AddiewellPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           1.706          1
## Constrained     1.706          1
## Unconstrained   0.000          0
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CCA4
## Eigenvalue            0.6828 0.5091 0.3583 0.15559
## Proportion Explained  0.4003 0.2984 0.2101 0.09121
## Cumulative Proportion 0.4003 0.6987 0.9088 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3    CCA4
## Eigenvalue            0.6828 0.5091 0.3583 0.15559
## Proportion Explained  0.4003 0.2984 0.2101 0.09121
## Cumulative Proportion 0.4003 0.6987 0.9088 1.00000
AddiewellCCA4 <- cca(AddiewellPS ~ Pb + S + As, data = AddiewellPC)

print(AddiewellCCA4)
## Call: cca(formula = AddiewellPS ~ Pb + S + As, data = AddiewellPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          1.7058     1.0000     
## Constrained    1.3838     0.8112    3
## Unconstrained  0.3220     0.1888    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 88 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.6603 0.4565 0.2669 
## 
## Eigenvalues for unconstrained axes:
##   CA1 
## 0.322
plot(AddiewellCCA4)

summary(AddiewellCCA4)
## 
## Call:
## cca(formula = AddiewellPS ~ Pb + S + As, data = AddiewellPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           1.706     1.0000
## Constrained     1.384     0.8112
## Unconstrained   0.322     0.1888
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.6603 0.4565 0.2669 0.3220
## Proportion Explained  0.3871 0.2676 0.1565 0.1888
## Cumulative Proportion 0.3871 0.6547 0.8112 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.6603 0.4565 0.2669
## Proportion Explained  0.4772 0.3299 0.1929
## Cumulative Proportion 0.4772 0.8071 1.0000
anova(AddiewellCCA4)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = AddiewellPS ~ Pb + S + As, data = AddiewellPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   1.38377 1.4323 0.2417
## Residual  1   0.32203

#F statistic of 1.4323 and p value of 0.1583

AddiewellCCA5 <- cca(AddiewellPS ~ pH_level + Al2O3 + Fe2O3, data = AddiewellPC)

print(AddiewellCCA5)
## Call: cca(formula = AddiewellPS ~ pH_level + Al2O3 + Fe2O3, data =
## AddiewellPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          1.7058     1.0000     
## Constrained    1.4006     0.8211    3
## Unconstrained  0.3052     0.1789    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 88 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.6092 0.5078 0.2836 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.30519
plot(AddiewellCCA5)

summary(AddiewellCCA5)
## 
## Call:
## cca(formula = AddiewellPS ~ pH_level + Al2O3 + Fe2O3, data = AddiewellPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          1.7058     1.0000
## Constrained    1.4006     0.8211
## Unconstrained  0.3052     0.1789
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.6092 0.5078 0.2836 0.3052
## Proportion Explained  0.3572 0.2977 0.1662 0.1789
## Cumulative Proportion 0.3572 0.6549 0.8211 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.6092 0.5078 0.2836
## Proportion Explained  0.4350 0.3626 0.2024
## Cumulative Proportion 0.4350 0.7976 1.0000
anova(AddiewellCCA5)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = AddiewellPS ~ pH_level + Al2O3 + Fe2O3, data = AddiewellPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   1.40062 1.5298    0.2
## Residual  1   0.30519

#F statstic of 1.5298 and p value of 0.15.

AddiewellCCA6 <- cca(AddiewellPS ~ Pb  + Al2O3 + Fe2O3, data = AddiewellPC)

print(AddiewellCCA6)
## Call: cca(formula = AddiewellPS ~ Pb + Al2O3 + Fe2O3, data = AddiewellPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          1.7058     1.0000     
## Constrained    1.4727     0.8633    3
## Unconstrained  0.2331     0.1367    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 88 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.6577 0.5091 0.3059 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.23311
plot(AddiewellCCA6)

summary(AddiewellCCA6)
## 
## Call:
## cca(formula = AddiewellPS ~ Pb + Al2O3 + Fe2O3, data = AddiewellPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          1.7058     1.0000
## Constrained    1.4727     0.8633
## Unconstrained  0.2331     0.1367
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.6577 0.5091 0.3059 0.2331
## Proportion Explained  0.3856 0.2984 0.1794 0.1367
## Cumulative Proportion 0.3856 0.6840 0.8633 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.6577 0.5091 0.3059
## Proportion Explained  0.4466 0.3457 0.2077
## Cumulative Proportion 0.4466 0.7923 1.0000
anova(AddiewellCCA6)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = AddiewellPS ~ Pb + Al2O3 + Fe2O3, data = AddiewellPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   1.47269 2.1058 0.1083
## Residual  1   0.23311

#F statistic of 2.1058 and p value of 0.09167.

AddiewellCCA7 <- cca(AddiewellPS ~ V + S + As, data = AddiewellPC)

print(AddiewellCCA7)
## Call: cca(formula = AddiewellPS ~ V + S + As, data = AddiewellPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          1.7058     1.0000     
## Constrained    1.4584     0.8550    3
## Unconstrained  0.2474     0.1450    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 88 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.6812 0.4874 0.2898 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.24739
plot(AddiewellCCA7)

summary(AddiewellCCA7)
## 
## Call:
## cca(formula = AddiewellPS ~ V + S + As, data = AddiewellPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          1.7058      1.000
## Constrained    1.4584      0.855
## Unconstrained  0.2474      0.145
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.6812 0.4874 0.2898 0.2474
## Proportion Explained  0.3993 0.2858 0.1699 0.1450
## Cumulative Proportion 0.3993 0.6851 0.8550 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.6812 0.4874 0.2898
## Proportion Explained  0.4671 0.3342 0.1987
## Cumulative Proportion 0.4671 0.8013 1.0000
anova(AddiewellCCA7)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = AddiewellPS ~ V + S + As, data = AddiewellPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   1.45842 1.9651 0.1417
## Residual  1   0.24739

#F statistic of 1.9651 and p value of 0.08333.

AddiewellCCA8 <- cca(AddiewellPS ~ V + S + Co, data = AddiewellPC)

print(AddiewellCCA8)
## Call: cca(formula = AddiewellPS ~ V + S + Co, data = AddiewellPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          1.7058     1.0000     
## Constrained    1.4646     0.8586    3
## Unconstrained  0.2412     0.1414    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 88 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.6784 0.4986 0.2876 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.24122
plot(AddiewellCCA8)

summary(AddiewellCCA8)
## 
## Call:
## cca(formula = AddiewellPS ~ V + S + Co, data = AddiewellPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          1.7058     1.0000
## Constrained    1.4646     0.8586
## Unconstrained  0.2412     0.1414
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.6784 0.4986 0.2876 0.2412
## Proportion Explained  0.3977 0.2923 0.1686 0.1414
## Cumulative Proportion 0.3977 0.6900 0.8586 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.6784 0.4986 0.2876
## Proportion Explained  0.4632 0.3405 0.1964
## Cumulative Proportion 0.4632 0.8036 1.0000
anova(AddiewellCCA8)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = AddiewellPS ~ V + S + Co, data = AddiewellPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   1.46459 2.0239   0.15
## Residual  1   0.24122

#F statistic of 2.0239 and p value of 0.09167.

AddiewellCCA9 <- cca(AddiewellPS ~ V + As + Co, data = AddiewellPC)

print(AddiewellCCA9)
## Call: cca(formula = AddiewellPS ~ V + As + Co, data = AddiewellPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          1.7058     1.0000     
## Constrained    1.4096     0.8264    3
## Unconstrained  0.2962     0.1736    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 88 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.6826 0.4787 0.2483 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.29619
plot(AddiewellCCA9)

summary(AddiewellCCA9)
## 
## Call:
## cca(formula = AddiewellPS ~ V + As + Co, data = AddiewellPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          1.7058     1.0000
## Constrained    1.4096     0.8264
## Unconstrained  0.2962     0.1736
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.6826 0.4787 0.2483 0.2962
## Proportion Explained  0.4001 0.2807 0.1456 0.1736
## Cumulative Proportion 0.4001 0.6808 0.8264 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.6826 0.4787 0.2483
## Proportion Explained  0.4842 0.3396 0.1762
## Cumulative Proportion 0.4842 0.8238 1.0000
anova(AddiewellCCA9)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = AddiewellPS ~ V + As + Co, data = AddiewellPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   1.40962 1.5864 0.1417
## Residual  1   0.29619

#F statistic of 1.5864 and p value of 0.1083.

#After doing several CCAs and anovas for the data, using different combinations of varibles, #I have not been able to find any statistically significant CCAs for the Addiewell data. #It can be determined that the NMDS analyses are more appropriate for representation #of the plant data for this field site.

#Penicuik Data#

urlfile9 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/PenicuikPlantSpecies.csv'

PenicuikPS <- read.csv(urlfile9,  header = TRUE, colClasses = c("numeric"))

urlfile10 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/PENICUIK_PLANT_CHEMISTRY_MG_KG.csv'

PenicuikPC <-read.csv(urlfile10, header = TRUE, colClasses = c("numeric"))

head(PenicuikPS)
##   Agrostis.spp. Agrostis.canina Alchemilla.mollis Alopercus.pratensis
## 1             5               3                 0                   0
## 2             3               0                 1                   0
## 3            32               0                 0                   0
## 4            39               0                 0                   0
## 5             0               0                 0                   0
##   Angelica.sylvestris Anthoxanthum.odoratum Anthyllis.vulneraria
## 1                   0                     0                    0
## 2                   1                     0                    0
## 3                   1                     0                    0
## 4                   0                     0                    0
## 5                   0                     0                    0
##   Aphanes.arvensis Arrhenatherum.elatius Atrichum.undulatum Avenula.pratensis
## 1                0                     0                  0                 0
## 2                0                     4                  0                 0
## 3                0                     0                  0                 0
## 4                0                     0                  0                 0
## 5                0                     0                  0                 0
##   Bellis.perennis Betula.pubescens Blackstonia.perfoliata
## 1               0                0                      0
## 2               0                0                      0
## 3               0                0                      0
## 4               0                0                      0
## 5               0                0                      0
##   Brachythecium.albicans Brachythecium.glareosum Brachythecium.mildeanum
## 1                      0                       0                       0
## 2                      0                       0                       0
## 3                      0                       0                       0
## 4                      0                       0                       0
## 5                      0                       0                       0
##   Brachythecium.rutabulum Briza.media Bromus.hordeaceus Bryum.c.f..caespiticium
## 1                       0           0                 0                       0
## 2                      10           0                 0                       0
## 3                      10           0                 0                       0
## 4                       0           0                 0                       0
## 5                       0           0                 0                       0
##   Bryum.c.f..pallescens Bryum.capillare Bryum.spp. Calliergonella.cupsidata
## 1                     0               0          0                        0
## 2                     0               0          0                       50
## 3                     0               0          0                      110
## 4                     0               0          0                        0
## 5                     0               0          0                        0
##   Calypogeia.arguta Campanula.rotundifolia Carex.distans Carex.flacca
## 1                 0                      0             0            0
## 2                 0                      0             0            0
## 3                60                      0             0            0
## 4                 0                      0             0            0
## 5                 0                      0             0            0
##   Carex.panicea Carlina.vulgaris Centaurea.nigra Centaurium.erythraea
## 1             0                0               0                    0
## 2             0                0               0                    0
## 3             0                0               0                    0
## 4             0                0               0                    0
## 5             0                0               0                    0
##   Centaurium.littorale Centaurium.pulchellum Cerastium.fontanum
## 1                    0                     0                  0
## 2                    0                     0                  0
## 3                    0                     0                  0
## 4                    0                     0                  0
## 5                    0                     0                  0
##   Chamaenerion.angustifolium Cirriphyllum.piliferum Cirsium.arvense
## 1                          0                      0               3
## 2                          0                      0               4
## 3                          0                      0               8
## 4                          0                      0               0
## 5                          0                      0               0
##   Cirsium.palustre Crepis.capillaris Cynosurus.cristatus Dactylis.glomerata
## 1                0                 0                   0                  1
## 2                0                 0                   0                  0
## 3                0                 0                   0                  4
## 4                0                 0                   0                 54
## 5                0                 0                   0                  0
##   Dactylorhiza.fuchsii Danthonia.decumbens Daucus.carrota Dicranella.spp.
## 1                    0                   0              0               0
## 2                    0                   0              0               0
## 3                    0                   0              0               0
## 4                    0                   0              0               0
## 5                    0                   0              0               0
##   Dicranum.scoparium Epilobium.montanum Equisetum.arvense Equisteum.variegatum
## 1                  0                  3                 0                    0
## 2                  0                  0                49                    0
## 3                  0                  0                 4                    0
## 4                  0                  0                 0                    0
## 5                  0                  0                 0                    0
##   Erigeron.acer Euphrasia.agg Festuca.ovina Festuca.rubra Festuca.rubra.agg.
## 1             0             0             0             0                  0
## 2             0             0             0             0                  0
## 3             0             0             0             0                  0
## 4             0             0             0             0                  0
## 5             0             0             0             0                  0
##   Filipendula.ulmaria Fissidens.adianthoides Fissidens.dubius Fissidens.exilis
## 1                   3                      0                0                0
## 2                   3                      0                0                0
## 3                   0                      0                0                0
## 4                   0                      0                0                0
## 5                   0                      0                0                0
##   Fragaria.vesca Galium.aparine Galium.arvense Galium.saxatile Galium.verum
## 1              0              0              1               0            0
## 2              0              0              0               0            0
## 3              0              0              0               0            0
## 4             11              0              0               0            0
## 5              0             47              0               0            0
##   Geum.urbanum Glechoma.hederacea Helicotrichon.spp. Heracleum.sphondylium
## 1            0                  0                  0                     0
## 2            0                  0                  0                     0
## 3            0                  0                  0                     0
## 4           48                  5                  0                     0
## 5            0                  0                  0                     1
##   Hieracium.spp. Holcus.spp. Holcus.lanatus Holcus.mollis
## 1              0           0              0            56
## 2              0           0              0            17
## 3              0           0              0             4
## 4              0           0              0             0
## 5              0           0              0             0
##   Homalothecium.lutescens Hylocomium.splendens Hypericum.perforatum
## 1                       0                    0                    0
## 2                       0                    0                    0
## 3                       0                    0                    0
## 4                       0                    0                    0
## 5                       0                    0                    0
##   Hypnum.cupressiforme Hypnum.imponens Hypnum.jutlandicum Hypochaeris.radicata
## 1                    0               0                  0                    0
## 2                    0               0                  0                    0
## 3                    0               0                  0                    0
## 4                    0               0                  0                    0
## 5                    0               0                  0                    0
##   Kindbergia.praelonga Lathyrus.pratensis Leontodon.hispidus
## 1                    0                  0                  0
## 2                    0                  0                  0
## 3                   50                  0                  0
## 4                   50                  0                  0
## 5                    0                  0                  0
##   Leontodon.saxatilis Leucanthemum.vulgare Linum.catharticum Lolium.perenne
## 1                   0                    0                 0              0
## 2                   0                    0                 0              0
## 3                   0                    0                 0              0
## 4                   0                    0                 0              0
## 5                   0                    0                 0              0
##   Lophocolea.semiteres Lotus.corniculatus Luzula.multiflora Lysimachia.maritima
## 1                    0                  0                 0                   0
## 2                    0                  0                 0                   0
## 3                    0                 12                 0                   0
## 4                    0                  0                 0                   0
## 5                    0                  0                 0                   0
##   Medicago.lupulina Myosotis.arvensis Ononis.repens Oxalis.acetosella
## 1                 0                 0             0                 0
## 2                 0                 0             0                 0
## 3                 0                 0             0                 0
## 4                 0                 0             0               113
## 5                 0                 3             0                 0
##   Pastinaca.sativa Pentaglottis.sempervirens Pillosella.officinarum
## 1                0                         0                      0
## 2                0                         0                      0
## 3                0                         0                      0
## 4                0                         0                      0
## 5                0                         4                      0
##   Plantago.coronopus Plantago.lanceolata Pleurozium.schreberi Poa.annua
## 1                  0                   0                    0         0
## 2                  0                   0                    0         0
## 3                  0                   0                    0         0
## 4                  0                   0                    0         0
## 5                  0                   0                    0         0
##   Poa.spp. Polytrichum.commune Polytrichum.commune.agg. Polytrichum.formosum
## 1        0                   0                        0                    0
## 2        0                   0                        0                    0
## 3        0                   0                        0                    0
## 4        0                   0                        0                    0
## 5        0                   0                        0                    0
##   Potentilla.reptans Prunella.vulgaris Pseudoscleropidum.purum
## 1                  0                 0                       0
## 2                  0                 0                       0
## 3                  0                 0                       0
## 4                  0                 0                       0
## 5                  0                 0                       0
##   Pteridium.aquilinum Ranunculus.acris Ranunculus.parviflorus Ranunculus.repens
## 1                   0                0                      0                 0
## 2                   0                0                      0                 0
## 3                   0                0                      0                 0
## 4                   4                0                      0                 0
## 5                   0                0                      0                 0
##   Reseda.lutea Rhinanthus.minor Rhizomnium.punctatum Rhytidadelphus.squarrosus
## 1            0                0                    0                         0
## 2            0                0                    0                       140
## 3            0                0                    0                        20
## 4            0                0                    0                         0
## 5            0                0                    0                         0
##   Rhytidadelphus.triquetris Rubus.fruticosus Sanguisorba.minor.spp.minor
## 1                         0                0                           0
## 2                         0                0                           0
## 3                         0                0                           0
## 4                         0                0                           0
## 5                         0                0                           0
##   Saniona.uncinata Sedum.anglicum Senecio.jacobaea Senecio.vulgaris
## 1                0              0                0                0
## 2                0              0                1                0
## 3                0              0                0                0
## 4                0              0                0                0
## 5                0              0                0                0
##   Sonchus.arvensis Stachys.sylvatica Stellaria.apetala Taraxacum.agg.
## 1                0                 1                 0              0
## 2                0                 1                 0              0
## 3                0                 0                 0              0
## 4                0                 0                 0              0
## 5                0                 0                 0              0
##   Thuidium.tamariscinum Thymus.polytrichus Trichostomum.crispulum
## 1                     0                  0                      0
## 2                     0                  0                      0
## 3                     0                  0                      0
## 4                     0                  0                      0
## 5                     0                  0                      0
##   Trifolium.campestre Trifolium.dubium Trifolium.pratense Trifolium.repens
## 1                   0                0                  0                0
## 2                   0                0                  0                0
## 3                   0                0                  0                0
## 4                   0                0                  0                0
## 5                   0                0                  0                0
##   Trisetum.flavescens Tussilago.farfara Urtica.diocia Veronica.officinalis
## 1                   0                 0             0                    0
## 2                   0                15             0                    0
## 3                   0                 4             0                    0
## 4                   0                 0             0                    0
## 5                   0                 0            55                    0
##   Vicia.sativa Viola.riviniana Weissia.controversa Zygodon.stirtonii
## 1            0               0                   0                 0
## 2            0               0                   0                 0
## 3            0               0                   0                 0
## 4            0               0                   0                 0
## 5            0               0                   0                 0
head(PenicuikPC)
##      pH     SiO2    Al2O3    Fe2O3        CaO      MgO     Na2O       K2O
## 1 8.048 330943.9 55835.91 31054.49  18296.084 1266.375 1261.157 14776.630
## 2 8.075 224368.8 69067.17 28396.68  64393.638 4221.251 4970.441 10459.862
## 3 7.024 272514.6 60863.79 28886.27   8218.944 4040.341 5489.741 11622.069
## 4 5.474 255686.9 58217.54 35460.87   5288.712 4341.858 8160.426  9048.611
## 5 7.222 150514.0 44457.03 21682.19 101486.089 3377.001 3635.099  6475.153
##       Cr2O3     TiO2       MnO      P2O5       SrO      BaO   LOI   Ag As  B
## 1  61.57822 3416.255 1394.0235  899.8838  42.27973 806.0862  6.58 0.20  4  5
## 2 102.63036 4674.875  774.4575 1599.7934  84.55946 626.9560 21.00 0.30  9 10
## 3  95.78834 4495.072  929.3490 2299.7030  84.55946 537.3908 22.80 0.15  8 10
## 4 102.63036 5334.152 1006.7947 1899.7547  84.55946 358.2605 24.70 0.20  9  5
## 5  75.26227 3655.992  464.6745 4199.4577 169.11891 268.6954 39.00 0.30  7 10
##     Be  Bi   Cd Co Cu Ga  Hg La Li  Mo Ni  Pb    S  Sb Sc Th Tl U  V W  Zn
## 1 0.25 1.5 0.70  8 30  5 0.5 10  5 0.5 24  28  300 1.5  4 10  5 5 13 5 257
## 2 1.40 1.5 0.80 14 86 10 0.5 10 20 1.0 35  96  500 1.5  4 10  5 5 40 5 337
## 3 1.00 1.5 0.25 13 35  5 0.5 10 10 1.0 28  66  800 2.0  3 10  5 5 37 5 136
## 4 0.70 1.5 0.25 13 21 10 0.5 10 20 1.0 23  66  700 1.5  1 10  5 5 51 5 141
## 5 1.90 1.5 1.50 13 74  5 0.5 10 10 1.0 77 133 1200 1.5  1 10  5 5 33 5 342
##   Akermanite Albite Aluminium.oxide.hydroxide Anhydrite Aragonite Biotite
## 1          0      0                         0         0         0       0
## 2          0      0                         0         1         0       0
## 3          0      0                         0         0         0       0
## 4          0      0                         0         0         0       0
## 5          0      0                         0         0         0       0
##   Birnessite Calcite Clinochlore Cuspidine Diaspore Dickite Gehlenite Goethite
## 1          0       0           0         0        0       0         0        0
## 2          0       0           0         0        0       0         0        0
## 3          0       0           0         0        0       0         0        0
## 4          0       0           0         0        0       0         0        0
## 5          0       1           0         0        0       0         0        0
##   Haematite Illite Kaolinite Langite Linnaeite Magnesioferrite Melilite
## 1         0      0         1       0         0               0        0
## 2         0      0         1       0         0               0        0
## 3         0      0         1       0         0               0        0
## 4         0      0         1       0         0               0        0
## 5         0      0         1       0         0               0        0
##   Merwinite Microcline Mullite Muscovite Orthoclase Orthopyroxene Periclase
## 1         0          0       0         1          0             0         0
## 2         0          0       0         1          0             0         0
## 3         0          0       0         0          0             0         1
## 4         0          0       0         0          0             0         0
## 5         0          0       0         1          0             0         0
##   Phengite Pseudowollastonite Quartz Staurolite Valentinite
## 1        0                  0      1          0           0
## 2        0                  0      1          0           0
## 3        0                  0      1          0           0
## 4        0                  0      1          0           0
## 5        0                  0      1          0           0
rowSums(PenicuikPS)
## [1]  76 299 319 324 110

#Now for some ANOSIMs…

#anoPSiO2 <- anosim(PenicuikPS, PenicuikPC$SiO2, distance = “bray”, permutations = 9999)

#When this ANOSIM is run, the error message: “there should be replicates within groups” #comes up. This error message came up for other substrate variables for other #data. From now on, only variables that were tested successfully will be included.

anoPCr2O3 <- anosim(PenicuikPS, PenicuikPC$Cr2O3, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoPCr2O3
## 
## Call:
## anosim(x = PenicuikPS, grouping = PenicuikPC$Cr2O3, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.1111 
##       Significance: 0.6 
## 
## Permutation: free
## Number of permutations: 119
anoPSrO <- anosim(PenicuikPS, PenicuikPC$SrO, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoPSrO
## 
## Call:
## anosim(x = PenicuikPS, grouping = PenicuikPC$SrO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.7143 
##       Significance: 0.2 
## 
## Permutation: free
## Number of permutations: 119
#This has a high R statistic of 1, but with a non-significant p value of 0.2

anoPAg <- anosim(PenicuikPS, PenicuikPC$Ag, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoPAg
## 
## Call:
## anosim(x = PenicuikPS, grouping = PenicuikPC$Ag, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.3125 
##       Significance: 0.86667 
## 
## Permutation: free
## Number of permutations: 119
anoPAs <- anosim(PenicuikPS, PenicuikPC$As, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoPAs
## 
## Call:
## anosim(x = PenicuikPS, grouping = PenicuikPC$As, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.1111 
##       Significance: 0.6 
## 
## Permutation: free
## Number of permutations: 119
anoPCd <- anosim(PenicuikPS, PenicuikPC$Cd, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoPCd
## 
## Call:
## anosim(x = PenicuikPS, grouping = PenicuikPC$Cd, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.7778 
##       Significance: 0.2 
## 
## Permutation: free
## Number of permutations: 119
anoPCo <- anosim(PenicuikPS, PenicuikPC$Co, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoPCo
## 
## Call:
## anosim(x = PenicuikPS, grouping = PenicuikPC$Co, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.2381 
##       Significance: 0.6 
## 
## Permutation: free
## Number of permutations: 119
#This has a high R statistic of 1, but with a non-significant p value of 0.1

anoPPb <- anosim(PenicuikPS, PenicuikPC$Pb, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoPPb
## 
## Call:
## anosim(x = PenicuikPS, grouping = PenicuikPC$Pb, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.7778 
##       Significance: 0.2 
## 
## Permutation: free
## Number of permutations: 119
anoPSc <- anosim(PenicuikPS, PenicuikPC$Sc, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoPSc
## 
## Call:
## anosim(x = PenicuikPS, grouping = PenicuikPC$Sc, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.0625 
##       Significance: 0.6 
## 
## Permutation: free
## Number of permutations: 119

#None of the ANOSIM tests led to stastistically significant results. Because of this, #CCAs might not be entirely appropriate to represent the data visually. #NMDS analyses will be utilised instead to visualise the plant data.

PenicuikNMDS <- metaMDS(PenicuikPS)
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0 
## ... Procrustes: rmse 0.1588239  max resid 0.2751202 
## Run 2 stress 0 
## ... Procrustes: rmse 0.2787275  max resid 0.4391253 
## Run 3 stress 0 
## ... Procrustes: rmse 0.2494537  max resid 0.3687649 
## Run 4 stress 0 
## ... Procrustes: rmse 0.2214514  max resid 0.3343612 
## Run 5 stress 0 
## ... Procrustes: rmse 0.1535876  max resid 0.1988528 
## Run 6 stress 8.963861e-05 
## ... Procrustes: rmse 0.2974179  max resid 0.4857913 
## Run 7 stress 0 
## ... Procrustes: rmse 0.3039324  max resid 0.449431 
## Run 8 stress 0 
## ... Procrustes: rmse 0.299959  max resid 0.4700047 
## Run 9 stress 0 
## ... Procrustes: rmse 0.1344095  max resid 0.2117445 
## Run 10 stress 0 
## ... Procrustes: rmse 0.1316192  max resid 0.1933083 
## Run 11 stress 0 
## ... Procrustes: rmse 0.3264276  max resid 0.4058194 
## Run 12 stress 0 
## ... Procrustes: rmse 0.3043311  max resid 0.4089408 
## Run 13 stress 0 
## ... Procrustes: rmse 0.2645414  max resid 0.3669792 
## Run 14 stress 0 
## ... Procrustes: rmse 0.1243563  max resid 0.1700068 
## Run 15 stress 0 
## ... Procrustes: rmse 0.2803937  max resid 0.4341262 
## Run 16 stress 0 
## ... Procrustes: rmse 0.2683513  max resid 0.4773628 
## Run 17 stress 0 
## ... Procrustes: rmse 0.1155863  max resid 0.1910522 
## Run 18 stress 0 
## ... Procrustes: rmse 0.2050943  max resid 0.3011 
## Run 19 stress 0 
## ... Procrustes: rmse 0.3337995  max resid 0.4228298 
## Run 20 stress 0 
## ... Procrustes: rmse 0.1104326  max resid 0.1692845 
## *** Best solution was not repeated -- monoMDS stopping criteria:
##     20: stress < smin
## Warning in metaMDS(PenicuikPS): stress is (nearly) zero: you may have
## insufficient data
## Warning in postMDS(out$points, dis, plot = max(0, plot - 1), ...): skipping
## half-change scaling: too few points below threshold
plot(PenicuikNMDS)

#As in the previous NMDS plots, plant species are represented by red crosses, while
#plant communities are represented by circles.

PenicuikNMDS
## 
## Call:
## metaMDS(comm = PenicuikPS) 
## 
## global Multidimensional Scaling using monoMDS
## 
## Data:     wisconsin(sqrt(PenicuikPS)) 
## Distance: bray 
## 
## Dimensions: 2 
## Stress:     0 
## Stress type 1, weak ties
## Best solution was not repeated after 20 tries
## The best solution was from try 0 (metric scaling or null solution)
## Scaling: centring, PC rotation 
## Species: expanded scores based on 'wisconsin(sqrt(PenicuikPS))'
plot(PenicuikNMDS, "sites")   # Produces distance 

plot(PenicuikNMDS, "species", xlim = c(-0.2, 0.5), ylim = c(-0.4, 0.8))
orditorp(PenicuikNMDS, "species")

#The ordiplot function here shows some differences between species on South Bank Wood in 
#Penicuik. U. dioica, for example, plots separately from all of the other species, although
#not all of the species on-site are represented on this plot.
#It might give further context to look at a CCA of this site as well, especially to look
#at plants and substrate.
PenciuikCCA <- cca(PenicuikPS, PenicuikPC)
## 
## Some constraints or conditions were aliased because they were redundant. This
## can happen if terms are linearly dependent (collinear): 'CaO', 'MgO', 'Na2O',
## 'K2O', 'Cr2O3', 'TiO2', 'MnO', 'P2O5', 'SrO', 'BaO', 'LOI', 'Ag', 'As', 'B',
## 'Be', 'Bi', 'Cd', 'Co', 'Cu', 'Ga', 'Hg', 'La', 'Li', 'Mo', 'Ni', 'Pb', 'S',
## 'Sb', 'Sc', 'Th', 'Tl', 'U', 'V', 'W', 'Zn', 'Akermanite', 'Albite',
## 'Aluminium.oxide.hydroxide', 'Anhydrite', 'Aragonite', 'Biotite', 'Birnessite',
## 'Calcite', 'Clinochlore', 'Cuspidine', 'Diaspore', 'Dickite', 'Gehlenite',
## 'Goethite', 'Haematite', 'Illite', 'Kaolinite', 'Langite', 'Linnaeite',
## 'Magnesioferrite', 'Melilite', 'Merwinite', 'Microcline', 'Mullite',
## 'Muscovite', 'Orthoclase', 'Orthopyroxene', 'Periclase', 'Phengite',
## 'Pseudowollastonite', 'Quartz', 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component
print(PenciuikCCA)
## Call: cca(X = PenicuikPS, Y = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total           2.854      1.000     
## Constrained     2.854      1.000    4
## Unconstrained   0.000      0.000    0
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## Some constraints or conditions were aliased because they were redundant.
## This can happen if terms are linearly dependent (collinear): 'CaO', 'MgO',
## 'Na2O', 'K2O', 'Cr2O3', 'TiO2', 'MnO', 'P2O5', 'SrO', 'BaO', 'LOI', 'Ag',
## 'As', 'B', 'Be', 'Bi', 'Cd', 'Co', 'Cu', 'Ga', 'Hg', 'La', 'Li', 'Mo',
## 'Ni', 'Pb', 'S', 'Sb', 'Sc', 'Th', 'Tl', 'U', 'V', 'W', 'Zn', 'Akermanite',
## 'Albite', 'Aluminium.oxide.hydroxide', 'Anhydrite', 'Aragonite', 'Biotite',
## 'Birnessite', 'Calcite', 'Clinochlore', 'Cuspidine', 'Diaspore', 'Dickite',
## 'Gehlenite', 'Goethite', 'Haematite', 'Illite', 'Kaolinite', 'Langite',
## 'Linnaeite', 'Magnesioferrite', 'Melilite', 'Merwinite', 'Microcline',
## 'Mullite', 'Muscovite', 'Orthoclase', 'Orthopyroxene', 'Periclase',
## 'Phengite', 'Pseudowollastonite', 'Quartz', 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component.
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4 
## 1.0000 0.8144 0.6265 0.4135
plot(PenciuikCCA)

summary(PenciuikCCA)
## 
## Call:
## cca(X = PenicuikPS, Y = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           2.854          1
## Constrained     2.854          1
## Unconstrained   0.000          0
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4
## Eigenvalue            1.0000 0.8144 0.6265 0.4135
## Proportion Explained  0.3503 0.2853 0.2195 0.1449
## Cumulative Proportion 0.3503 0.6357 0.8551 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4
## Eigenvalue            1.0000 0.8144 0.6265 0.4135
## Proportion Explained  0.3503 0.2853 0.2195 0.1449
## Cumulative Proportion 0.3503 0.6357 0.8551 1.0000
PenicuikCCA2 <- cca(PenicuikPS ~ Al2O3 + pH + Fe2O3 + SiO2, data = PenicuikPC)
## 
## The model is overfitted with no unconstrained (residual) component
print(PenicuikCCA2)
## Call: cca(formula = PenicuikPS ~ Al2O3 + pH + Fe2O3 + SiO2, data =
## PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total           2.854      1.000     
## Constrained     2.854      1.000    4
## Unconstrained   0.000      0.000    0
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## The model is overfitted with no unconstrained (residual) component.
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4 
## 1.0000 0.8144 0.6265 0.4135
plot(PenicuikCCA2)

summary(PenicuikCCA2)
## 
## Call:
## cca(formula = PenicuikPS ~ Al2O3 + pH + Fe2O3 + SiO2, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           2.854          1
## Constrained     2.854          1
## Unconstrained   0.000          0
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4
## Eigenvalue            1.0000 0.8144 0.6265 0.4135
## Proportion Explained  0.3503 0.2853 0.2195 0.1449
## Cumulative Proportion 0.3503 0.6357 0.8551 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3   CCA4
## Eigenvalue            1.0000 0.8144 0.6265 0.4135
## Proportion Explained  0.3503 0.2853 0.2195 0.1449
## Cumulative Proportion 0.3503 0.6357 0.8551 1.0000
PenicuikCCA3 <- cca(PenicuikPS ~ Al2O3 + pH + Fe2O3, data = PenicuikPC)

print(PenicuikCCA3)
## Call: cca(formula = PenicuikPS ~ Al2O3 + pH + Fe2O3, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    2.3694     0.8301    3
## Unconstrained  0.4850     0.1699    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9365 0.8070 0.6259 
## 
## Eigenvalues for unconstrained axes:
##   CA1 
## 0.485
plot(PenicuikCCA3)

summary(PenicuikCCA3)
## 
## Call:
## cca(formula = PenicuikPS ~ Al2O3 + pH + Fe2O3, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           2.854     1.0000
## Constrained     2.369     0.8301
## Unconstrained   0.485     0.1699
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.9365 0.8070 0.6259 0.4850
## Proportion Explained  0.3281 0.2827 0.2193 0.1699
## Cumulative Proportion 0.3281 0.6108 0.8301 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.9365 0.8070 0.6259
## Proportion Explained  0.3953 0.3406 0.2642
## Cumulative Proportion 0.3953 0.7358 1.0000
anova(PenicuikCCA3)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ Al2O3 + pH + Fe2O3, data = PenicuikPC)
##          Df ChiSquare      F  Pr(>F)  
## Model     3   2.36939 1.6284 0.01667 *
## Residual  1   0.48501                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.6284 and a low p value of 0.01667.

PenicuikCCA4 <- cca(PenicuikPS ~ Al2O3 + SrO + Fe2O3, data = PenicuikPC)

print(PenicuikCCA4)
## Call: cca(formula = PenicuikPS ~ Al2O3 + SrO + Fe2O3, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    2.3362     0.8185    3
## Unconstrained  0.5182     0.1815    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9824 0.8037 0.5501 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.5182
plot(PenicuikCCA4)

summary(PenicuikCCA4)
## 
## Call:
## cca(formula = PenicuikPS ~ Al2O3 + SrO + Fe2O3, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          2.8544     1.0000
## Constrained    2.3362     0.8185
## Unconstrained  0.5182     0.1815
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.9824 0.8037 0.5501 0.5182
## Proportion Explained  0.3442 0.2816 0.1927 0.1815
## Cumulative Proportion 0.3442 0.6257 0.8185 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.9824 0.8037 0.5501
## Proportion Explained  0.4205 0.3440 0.2355
## Cumulative Proportion 0.4205 0.7645 1.0000
anova(PenicuikCCA4)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ Al2O3 + SrO + Fe2O3, data = PenicuikPC)
##          Df ChiSquare      F Pr(>F)  
## Model     3    2.3362 1.5028   0.05 *
## Residual  1    0.5182                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.5028 and a p value of 0.008333.

PenicuikCCA5 <- cca(PenicuikPS ~ pH + SrO + Fe2O3, data = PenicuikPC)

print(PenicuikCCA5)
## Call: cca(formula = PenicuikPS ~ pH + SrO + Fe2O3, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    2.1812     0.7641    3
## Unconstrained  0.6732     0.2359    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9529 0.8141 0.4142 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.6732
plot(PenicuikCCA5)

summary(PenicuikCCA5)
## 
## Call:
## cca(formula = PenicuikPS ~ pH + SrO + Fe2O3, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          2.8544     1.0000
## Constrained    2.1812     0.7641
## Unconstrained  0.6732     0.2359
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.9529 0.8141 0.4142 0.6732
## Proportion Explained  0.3338 0.2852 0.1451 0.2359
## Cumulative Proportion 0.3338 0.6190 0.7641 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.9529 0.8141 0.4142
## Proportion Explained  0.4369 0.3732 0.1899
## Cumulative Proportion 0.4369 0.8101 1.0000
anova(PenicuikCCA5)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ pH + SrO + Fe2O3, data = PenicuikPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   2.18115 1.0799 0.2083
## Residual  1   0.67325

#An F statistic of 1.0799 and a p value of 0.2.

PenicuikCCA6 <- cca(PenicuikPS ~ pH + SrO + Al2O3, data = PenicuikPC)

print(PenicuikCCA6)
## Call: cca(formula = PenicuikPS ~ pH + SrO + Al2O3, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    2.3811     0.8342    3
## Unconstrained  0.4733     0.1658    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9925 0.8118 0.5768 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.4733
plot(PenicuikCCA6)

summary(PenicuikCCA6)
## 
## Call:
## cca(formula = PenicuikPS ~ pH + SrO + Al2O3, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          2.8544     1.0000
## Constrained    2.3811     0.8342
## Unconstrained  0.4733     0.1658
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.9925 0.8118 0.5768 0.4733
## Proportion Explained  0.3477 0.2844 0.2021 0.1658
## Cumulative Proportion 0.3477 0.6321 0.8342 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.9925 0.8118 0.5768
## Proportion Explained  0.4168 0.3409 0.2423
## Cumulative Proportion 0.4168 0.7577 1.0000
anova(PenicuikCCA6)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ pH + SrO + Al2O3, data = PenicuikPC)
##          Df ChiSquare      F   Pr(>F)   
## Model     3   2.38108 1.6768 0.008333 **
## Residual  1   0.47332                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.6768 and a p value of 0.008333.

PenicuikCCA7 <- cca(PenicuikPS ~ MgO + SrO + As, data = PenicuikPC)

print(PenicuikCCA7)
## Call: cca(formula = PenicuikPS ~ MgO + SrO + As, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    2.0683     0.7246    3
## Unconstrained  0.7861     0.2754    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9997 0.6551 0.4135 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.7861
plot(PenicuikCCA7)

summary(PenicuikCCA7)
## 
## Call:
## cca(formula = PenicuikPS ~ MgO + SrO + As, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          2.8544     1.0000
## Constrained    2.0683     0.7246
## Unconstrained  0.7861     0.2754
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.9997 0.6551 0.4135 0.7861
## Proportion Explained  0.3502 0.2295 0.1449 0.2754
## Cumulative Proportion 0.3502 0.5797 0.7246 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.9997 0.6551 0.4135
## Proportion Explained  0.4834 0.3167 0.1999
## Cumulative Proportion 0.4834 0.8001 1.0000
anova(PenicuikCCA7)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ MgO + SrO + As, data = PenicuikPC)
##          Df ChiSquare     F Pr(>F)
## Model     3   2.06828 0.877 0.5917
## Residual  1   0.78612

#An F statistic of 0.877 and a p value of 0.4833.

PenicuikCCA8 <- cca(PenicuikPS ~ pH + SrO + As, data = PenicuikPC)

print(PenicuikCCA8)
## Call: cca(formula = PenicuikPS ~ pH + SrO + As, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    2.3787     0.8333    3
## Unconstrained  0.4757     0.1667    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9920 0.8118 0.5749 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.4757
plot(PenicuikCCA8)

summary(PenicuikCCA8)
## 
## Call:
## cca(formula = PenicuikPS ~ pH + SrO + As, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          2.8544     1.0000
## Constrained    2.3787     0.8333
## Unconstrained  0.4757     0.1667
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.9920 0.8118 0.5749 0.4757
## Proportion Explained  0.3475 0.2844 0.2014 0.1667
## Cumulative Proportion 0.3475 0.6319 0.8333 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.9920 0.8118 0.5749
## Proportion Explained  0.4171 0.3413 0.2417
## Cumulative Proportion 0.4171 0.7583 1.0000
anova(PenicuikCCA8)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ pH + SrO + As, data = PenicuikPC)
##          Df ChiSquare      F  Pr(>F)  
## Model     3    2.3787 1.6668 0.01667 *
## Residual  1    0.4757                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.6668 and a p value of 0.008333.

PenicuikCCA9 <- cca(PenicuikPS ~ Al2O3 + SrO + As, data = PenicuikPC)

print(PenicuikCCA9)
## Call: cca(formula = PenicuikPS ~ Al2O3 + SrO + As, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    2.3803     0.8339    3
## Unconstrained  0.4741     0.1661    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9920 0.8125 0.5758 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.4741
plot(PenicuikCCA9)

summary(PenicuikCCA9)
## 
## Call:
## cca(formula = PenicuikPS ~ Al2O3 + SrO + As, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          2.8544     1.0000
## Constrained    2.3803     0.8339
## Unconstrained  0.4741     0.1661
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.9920 0.8125 0.5758 0.4741
## Proportion Explained  0.3475 0.2846 0.2017 0.1661
## Cumulative Proportion 0.3475 0.6322 0.8339 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.9920 0.8125 0.5758
## Proportion Explained  0.4168 0.3413 0.2419
## Cumulative Proportion 0.4168 0.7581 1.0000
anova(PenicuikCCA9)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ Al2O3 + SrO + As, data = PenicuikPC)
##          Df ChiSquare      F   Pr(>F)   
## Model     3   2.38029 1.6735 0.008333 **
## Residual  1   0.47411                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.6735 and a p value of 0.008333.

PenicuikCCA10 <- cca(PenicuikPS ~ pH + SrO + Co, data = PenicuikPC)

print(PenicuikCCA10)
## Call: cca(formula = PenicuikPS ~ pH + SrO + Co, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    2.4085     0.8438    3
## Unconstrained  0.4459     0.1562    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9973 0.8116 0.5997 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.4459
plot(PenicuikCCA10)

summary(PenicuikCCA10)
## 
## Call:
## cca(formula = PenicuikPS ~ pH + SrO + Co, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          2.8544     1.0000
## Constrained    2.4085     0.8438
## Unconstrained  0.4459     0.1562
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.9973 0.8116 0.5997 0.4459
## Proportion Explained  0.3494 0.2843 0.2101 0.1562
## Cumulative Proportion 0.3494 0.6337 0.8438 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.9973 0.8116 0.5997
## Proportion Explained  0.4141 0.3370 0.2490
## Cumulative Proportion 0.4141 0.7510 1.0000
anova(PenicuikCCA10)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ pH + SrO + Co, data = PenicuikPC)
##          Df ChiSquare      F   Pr(>F)   
## Model     3   2.40854 1.8007 0.008333 **
## Residual  1   0.44586                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.8007 and a p value of 0.008333.

PenicuikCCA11 <- cca(PenicuikPS ~ pH + SrO + Pb, data = PenicuikPC)

print(PenicuikCCA11)
## Call: cca(formula = PenicuikPS ~ pH + SrO + Pb, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    2.2654     0.7937    3
## Unconstrained  0.5890     0.2063    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9714 0.8128 0.4812 
## 
## Eigenvalues for unconstrained axes:
##   CA1 
## 0.589
plot(PenicuikCCA11)

summary(PenicuikCCA11)
## 
## Call:
## cca(formula = PenicuikPS ~ pH + SrO + Pb, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           2.854     1.0000
## Constrained     2.265     0.7937
## Unconstrained   0.589     0.2063
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.9714 0.8128 0.4812 0.5890
## Proportion Explained  0.3403 0.2848 0.1686 0.2063
## Cumulative Proportion 0.3403 0.6251 0.7937 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.9714 0.8128 0.4812
## Proportion Explained  0.4288 0.3588 0.2124
## Cumulative Proportion 0.4288 0.7876 1.0000
anova(PenicuikCCA11)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ pH + SrO + Pb, data = PenicuikPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   2.26542 1.2821 0.1583
## Residual  1   0.58898

#An F statistic of 1.2821 and a p value of 0.1.

PenicuikCCA12 <- cca(PenicuikPS ~ pH + SrO + V, data = PenicuikPC)

print(PenicuikCCA12)
## Call: cca(formula = PenicuikPS ~ pH + SrO + V, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    2.3476     0.8224    3
## Unconstrained  0.5068     0.1776    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9863 0.8120 0.5493 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.5068
plot(PenicuikCCA12)

summary(PenicuikCCA12)
## 
## Call:
## cca(formula = PenicuikPS ~ pH + SrO + V, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          2.8544     1.0000
## Constrained    2.3476     0.8224
## Unconstrained  0.5068     0.1776
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.9863 0.8120 0.5493 0.5068
## Proportion Explained  0.3455 0.2845 0.1924 0.1776
## Cumulative Proportion 0.3455 0.6300 0.8224 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.9863 0.8120 0.5493
## Proportion Explained  0.4201 0.3459 0.2340
## Cumulative Proportion 0.4201 0.7660 1.0000
anova(PenicuikCCA12)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ pH + SrO + V, data = PenicuikPC)
##          Df ChiSquare     F  Pr(>F)  
## Model     3   2.34759 1.544 0.01667 *
## Residual  1   0.50681                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.544 and a p value of 0.01667.

PenicuikCCA13 <- cca(PenicuikPS ~ pH + SrO, data = PenicuikPC)

print(PenicuikCCA13)
## Call: cca(formula = PenicuikPS ~ pH + SrO, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    1.7630     0.6176    2
## Unconstrained  1.0914     0.3824    2
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2 
## 0.9515 0.8115 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2 
## 0.6734 0.4180
plot(PenicuikCCA13)

summary(PenicuikCCA13)
## 
## Call:
## cca(formula = PenicuikPS ~ pH + SrO, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total           2.854     1.0000
## Constrained     1.763     0.6176
## Unconstrained   1.091     0.3824
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2    CA1    CA2
## Eigenvalue            0.9515 0.8115 0.6734 0.4180
## Proportion Explained  0.3333 0.2843 0.2359 0.1464
## Cumulative Proportion 0.3333 0.6176 0.8536 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2
## Eigenvalue            0.9515 0.8115
## Proportion Explained  0.5397 0.4603
## Cumulative Proportion 0.5397 1.0000
anova(PenicuikCCA13)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ pH + SrO, data = PenicuikPC)
##          Df ChiSquare      F   Pr(>F)   
## Model     2    1.7630 1.6153 0.008333 **
## Residual  2    1.0914                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.6153 and a p value of 0.008333.

PenicuikCCA14 <- cca(PenicuikPS ~ pH + SrO + BaO, data = PenicuikPC)

print(PenicuikCCA14)
## Call: cca(formula = PenicuikPS ~ pH + SrO + BaO, data = PenicuikPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8544     1.0000     
## Constrained    2.2647     0.7934    3
## Unconstrained  0.5897     0.2066    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 112 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9712 0.8128 0.4806 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.5897
plot(PenicuikCCA14)

summary(PenicuikCCA14)
## 
## Call:
## cca(formula = PenicuikPS ~ pH + SrO + BaO, data = PenicuikPC) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          2.8544     1.0000
## Constrained    2.2647     0.7934
## Unconstrained  0.5897     0.2066
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                         CCA1   CCA2   CCA3    CA1
## Eigenvalue            0.9712 0.8128 0.4806 0.5897
## Proportion Explained  0.3403 0.2848 0.1684 0.2066
## Cumulative Proportion 0.3403 0.6250 0.7934 1.0000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2   CCA3
## Eigenvalue            0.9712 0.8128 0.4806
## Proportion Explained  0.4289 0.3589 0.2122
## Cumulative Proportion 0.4289 0.7878 1.0000
anova(PenicuikCCA14)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 119
## 
## Model: cca(formula = PenicuikPS ~ pH + SrO + BaO, data = PenicuikPC)
##          Df ChiSquare      F Pr(>F)
## Model     3   2.26468 1.2801 0.1583
## Residual  1   0.58972

#An F statistic of 1.2801 and a p value of 0.1083.

#After doing multiple CCAs, the one with the highest F statistic and lowest p value is #PenicuikCCA10. However, the plot for this has a very short arrow for Co, which indicates #that Co may not be such an important variable for the CCA. PenicuikCCA6, meanwhile, has #a lower F statistic of 1.6768, the same p value of 0.00833 and BaO and longer arrows #for each of the variables. The plot for PenicuikCCA14 can be improved to better show the #relationships between substrate and plant species.

options(max.print=1000000)

PenicuikCCA6$CCA$v
##                                 CCA1        CCA2        CCA3
## Agrostis.spp.             -0.3170951 -0.57943764 -0.30710845
## Agrostis.canina           -0.5240142  1.50571071 -4.28411086
## Alchemilla.mollis         -0.3633211  1.20199944  1.35332240
## Angelica.sylvestris       -0.2521188  0.65770840  0.58100562
## Arrhenatherum.elatius     -0.3633211  1.20199944  1.35332240
## Brachythecium.rutabulum   -0.2521188  0.65770840  0.58100562
## Calliergonella.cupsidata  -0.2104180  0.45359926  0.29138682
## Calypogeia.arguta         -0.1409166  0.11341736 -0.19131116
## Cirsium.arvense           -0.2768440  0.68216459 -0.59796882
## Dactylis.glomerata        -0.4134295 -1.38753418 -0.10386446
## Epilobium.montanum        -0.5240142  1.50571071 -4.28411086
## Equisetum.arvense         -0.3465359  1.11984231  1.23674628
## Filipendula.ulmaria       -0.4436677  1.35385508 -1.46539423
## Fragaria.vesca            -0.4315678 -1.55229439 -0.01997496
## Galium.aparine             3.0294405 -0.06426004 -0.10500748
## Galium.arvense            -0.5240142  1.50571071 -4.28411086
## Geum.urbanum              -0.4315678 -1.55229439 -0.01997496
## Glechoma.hederacea        -0.4315678 -1.55229439 -0.01997496
## Heracleum.sphondylium      3.0294405 -0.06426004 -0.10500748
## Holcus.mollis             -0.4686354  1.36633065 -2.82686977
## Kindbergia.praelonga      -0.2862422 -0.71943851 -0.10564306
## Lotus.corniculatus        -0.1409166  0.11341736 -0.19131116
## Myosotis.arvensis          3.0294405 -0.06426004 -0.10500748
## Oxalis.acetosella         -0.4315678 -1.55229439 -0.01997496
## Pentaglottis.sempervirens  3.0294405 -0.06426004 -0.10500748
## Pteridium.aquilinum       -0.4315678 -1.55229439 -0.01997496
## Rhytidadelphus.squarrosus -0.3355205  1.06592668  1.16024320
## Senecio.jacobaea          -0.3633211  1.20199944  1.35332240
## Stachys.sylvatica         -0.4436677  1.35385508 -1.46539423
## Tussilago.farfara         -0.3164991  0.97282427  1.02813638
## Urtica.diocia              3.0294405 -0.06426004 -0.10500748
## attr(,"na.action")
##         Alopercus.pratensis       Anthoxanthum.odoratum 
##                           4                           6 
##        Anthyllis.vulneraria            Aphanes.arvensis 
##                           7                           8 
##          Atrichum.undulatum           Avenula.pratensis 
##                          10                          11 
##             Bellis.perennis            Betula.pubescens 
##                          12                          13 
##      Blackstonia.perfoliata      Brachythecium.albicans 
##                          14                          15 
##     Brachythecium.glareosum     Brachythecium.mildeanum 
##                          16                          17 
##                 Briza.media           Bromus.hordeaceus 
##                          19                          20 
##     Bryum.c.f..caespiticium       Bryum.c.f..pallescens 
##                          21                          22 
##             Bryum.capillare                  Bryum.spp. 
##                          23                          24 
##      Campanula.rotundifolia               Carex.distans 
##                          27                          28 
##                Carex.flacca               Carex.panicea 
##                          29                          30 
##            Carlina.vulgaris             Centaurea.nigra 
##                          31                          32 
##        Centaurium.erythraea        Centaurium.littorale 
##                          33                          34 
##       Centaurium.pulchellum          Cerastium.fontanum 
##                          35                          36 
##  Chamaenerion.angustifolium      Cirriphyllum.piliferum 
##                          37                          38 
##            Cirsium.palustre           Crepis.capillaris 
##                          40                          41 
##         Cynosurus.cristatus        Dactylorhiza.fuchsii 
##                          42                          44 
##         Danthonia.decumbens              Daucus.carrota 
##                          45                          46 
##             Dicranella.spp.          Dicranum.scoparium 
##                          47                          48 
##        Equisteum.variegatum               Erigeron.acer 
##                          51                          52 
##               Euphrasia.agg               Festuca.ovina 
##                          53                          54 
##               Festuca.rubra          Festuca.rubra.agg. 
##                          55                          56 
##      Fissidens.adianthoides            Fissidens.dubius 
##                          58                          59 
##            Fissidens.exilis             Galium.saxatile 
##                          60                          64 
##                Galium.verum          Helicotrichon.spp. 
##                          65                          68 
##              Hieracium.spp.                 Holcus.spp. 
##                          70                          71 
##              Holcus.lanatus     Homalothecium.lutescens 
##                          72                          74 
##        Hylocomium.splendens        Hypericum.perforatum 
##                          75                          76 
##        Hypnum.cupressiforme             Hypnum.imponens 
##                          77                          78 
##          Hypnum.jutlandicum        Hypochaeris.radicata 
##                          79                          80 
##          Lathyrus.pratensis          Leontodon.hispidus 
##                          82                          83 
##         Leontodon.saxatilis        Leucanthemum.vulgare 
##                          84                          85 
##           Linum.catharticum              Lolium.perenne 
##                          86                          87 
##        Lophocolea.semiteres           Luzula.multiflora 
##                          88                          90 
##         Lysimachia.maritima           Medicago.lupulina 
##                          91                          92 
##               Ononis.repens            Pastinaca.sativa 
##                          94                          96 
##      Pillosella.officinarum          Plantago.coronopus 
##                          98                          99 
##         Plantago.lanceolata        Pleurozium.schreberi 
##                         100                         101 
##                   Poa.annua                    Poa.spp. 
##                         102                         103 
##         Polytrichum.commune    Polytrichum.commune.agg. 
##                         104                         105 
##        Polytrichum.formosum          Potentilla.reptans 
##                         106                         107 
##           Prunella.vulgaris     Pseudoscleropidum.purum 
##                         108                         109 
##            Ranunculus.acris      Ranunculus.parviflorus 
##                         111                         112 
##           Ranunculus.repens                Reseda.lutea 
##                         113                         114 
##            Rhinanthus.minor        Rhizomnium.punctatum 
##                         115                         116 
##   Rhytidadelphus.triquetris            Rubus.fruticosus 
##                         118                         119 
## Sanguisorba.minor.spp.minor            Saniona.uncinata 
##                         120                         121 
##              Sedum.anglicum            Senecio.vulgaris 
##                         122                         124 
##            Sonchus.arvensis           Stellaria.apetala 
##                         125                         127 
##              Taraxacum.agg.       Thuidium.tamariscinum 
##                         128                         129 
##          Thymus.polytrichus      Trichostomum.crispulum 
##                         130                         131 
##         Trifolium.campestre            Trifolium.dubium 
##                         132                         133 
##          Trifolium.pratense            Trifolium.repens 
##                         134                         135 
##         Trisetum.flavescens        Veronica.officinalis 
##                         136                         139 
##                Vicia.sativa             Viola.riviniana 
##                         140                         141 
##         Weissia.controversa           Zygodon.stirtonii 
##                         142                         143 
## attr(,"class")
## [1] "exclude"
#The "v values" show the positions of individual species on the graph, with the CCA1 value
#representing the x axis and the CCA2 value representing the y axis, in the case of the
#graph created in R.

plot(PenicuikCCA6, xlim = c(-5, 5), ylim = c(-5, 5)) 

#Increasing the xlim and ylim to give more room for writing on graph

plot(PenicuikCCA6, choices = c(1,2), display = c("wa", "bp"), xlim = c(-4, 3),
     ylim = c(-3, 2))

#Increasing the xlim and ylim to give more room for writing on graph

points(x = -0.4315678, y = -1.55229439, pch = 15, col = "black")

#This point represents Glechoma hederacea

text('G. hederacea', x = -0.4315678, y = -1.55229439, cex = 0.88, pos = 2, col = "black")

#Adding text to this point.

points(x = -0.5240142 , y = 1.50571071, pch = 15, col = "black")

#This point represents Epilobium montanum

text('E. montanum', x = -0.5240142 , y = 1.50571071, cex = 0.88, pos = 2, col = "black")

#Adding text to this point

points(x = 3.0421284 , y = 1.075808e-15, pch = 15, col = "black")

#This point represents Heracleum sphondylium

text('H. sphondylium', x = 3.0294405, y = -0.06426004, cex = 0.88, pos = 2, col = "black")

#Adding text to this point

points(x = 3.0294405 , y = -0.06426004, pch = 15, col = "black")

#This point represents Angelica sylvestris

text('A. sylvestris', x = -0.2521188, y = 0.65770840, cex = 0.88, pos = 2, col = "black")

#Adding text to this point

points(x = -0.2521188, y = 0.65770840, pch = 15, col = "black")

##Carnforth Data

urlfile11 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/CarnforthPlantSpecies.csv'

CarnforthPS <- read.csv(urlfile11, header = TRUE, colClasses = c("numeric"))

urlfile12 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/CARNFORTH_PLANT_CHEMISTRY_MG_KG.csv'

CarnforthPC <-read.csv(urlfile12, header = TRUE, colClasses = c("numeric"))

head(CarnforthPS)
##   Agrostis.spp. Agrostis.canina Alchemilla.mollis Alopercus.pratensis
## 1             0               0                 0                   0
## 2             0               0                 0                   0
## 3             0               0                 0                   0
## 4             0               0                 0                   0
## 5             0               0                 0                   0
## 6             0               0                 0                  27
##   Angelica.sylvestris Anthoxanthum.odoratum Anthyllis.vulneraria
## 1                   0                     0                    0
## 2                   0                     0                    0
## 3                   0                     0                    0
## 4                   0                     0                    0
## 5                   0                     0                    0
## 6                   0                     0                    0
##   Aphanes.arvensis Arrhenatherum.elatius Atrichum.undulatum Avenula.pratensis
## 1                0                     1                  0                 0
## 2                0                     0                  0                 0
## 3                0                     0                  0                 0
## 4                0                     0                  0                 0
## 5                0                     0                  0                 0
## 6                0                     0                  0                11
##   Bellis.perennis Betula.pubescens Blackstonia.perfoliata
## 1               0                0                      0
## 2               0                0                      0
## 3              11                0                      0
## 4               0                0                      0
## 5               0                0                      0
## 6              10                0                      0
##   Brachythecium.albicans Brachythecium.glareosum Brachythecium.mildeanum
## 1                      0                       0                       0
## 2                      0                       0                       0
## 3                      0                       0                       0
## 4                      0                       0                       0
## 5                      0                       0                       0
## 6                      0                       0                       0
##   Brachythecium.rutabulum Briza.media Bromus.hordeaceus Bryum.c.f..caespiticium
## 1                       0           0                 0                       0
## 2                       0           0                 0                       0
## 3                       0           0                 0                       0
## 4                       0           0                 0                       0
## 5                       0           0                 0                       0
## 6                       0           0                 0                       0
##   Bryum.c.f..pallescens Bryum.capillare Bryum.spp. Calliergonella.cupsidata
## 1                    60               0          0                        0
## 2                     0               0          0                        0
## 3                     0               0          0                        0
## 4                     0               0         20                      120
## 5                     0               0          0                        0
## 6                     0               0          0                       10
##   Calypogeia.arguta Campanula.rotundifolia Carex.distans Carex.flacca
## 1                 0                      0             0            0
## 2                 0                      0             0            0
## 3                 0                      0            23            0
## 4                 0                      0             0           24
## 5                 0                      0             0            0
## 6                 0                      0             0            0
##   Carex.panicea Carlina.vulgaris Centaurea.nigra Centaurium.erythraea
## 1             0               11               0                    0
## 2             0                5               0                    0
## 3             0                4               0                    0
## 4             0                0               0                    0
## 5             0                0               0                    0
## 6             0                0               0                    0
##   Centaurium.littorale Centaurium.pulchellum Cerastium.fontanum
## 1                    0                     0                  1
## 2                    0                     0                  0
## 3                    0                     0                  0
## 4                    0                     0                  0
## 5                    0                     0                  0
## 6                    0                     0                  0
##   Chamaenerion.angustifolium Cirriphyllum.piliferum Cirsium.arvense
## 1                          0                      0               0
## 2                          0                      0               0
## 3                          0                      0               0
## 4                          0                      0               0
## 5                          0                      0               0
## 6                          0                      0               0
##   Cirsium.palustre Crepis.capillaris Cynosurus.cristatus Dactylis.glomerata
## 1                0                 0                   0                  0
## 2                0                 0                   0                  0
## 3                0                 0                   0                  0
## 4                0                 0                   0                  0
## 5                0                 0                   0                  0
## 6                0                 0                   0                  0
##   Dactylorhiza.fuchsii Danthonia.decumbens Daucus.carrota Dicranella.spp.
## 1                    0                   0              0               0
## 2                    0                   0              0               0
## 3                    0                   0              0               0
## 4                    0                   0              0               0
## 5                    0                   0              0               0
## 6                    0                   0              0               0
##   Dicranum.scoparium Epilobium.montanum Equisetum.arvense Equisteum.variegatum
## 1                  0                  0                 0                    0
## 2                  0                  0                 0                    0
## 3                  0                  0                 0                    0
## 4                  0                  0                 0                    0
## 5                  0                  0                 0                    0
## 6                  0                  0                 0                    0
##   Erigeron.acer Euphrasia.agg Festuca.ovina Festuca.rubra Festuca.rubra.agg.
## 1             0            16             0             0                  0
## 2             0             0             0             0                  0
## 3             0             0            17             0                  0
## 4             0             0            55             0                  0
## 5             0             0            27             0                  0
## 6             0             0             5             0                  0
##   Filipendula.ulmaria Fissidens.adianthoides Fissidens.dubius Fissidens.exilis
## 1                   0                      0                0                0
## 2                   0                      0                0                0
## 3                   0                      0                0                0
## 4                   0                      0               20                0
## 5                   0                      0                0                0
## 6                   0                      0                0                0
##   Fragaria.vesca Galium.aparine Galium.arvense Galium.saxatile Galium.verum
## 1              0              0              0               0            0
## 2              0              0              0               0            0
## 3              0              0              0               0            0
## 4              0              0              0               0            0
## 5              0              0              0               1            0
## 6              0              0              0               0            0
##   Geum.urbanum Glechoma.hederacea Helicotrichon.spp. Heracleum.sphondylium
## 1            0                  0                  0                     0
## 2            0                  0                  0                     0
## 3            0                  0                  0                     0
## 4            0                  0                  0                     0
## 5            0                  0                  0                     0
## 6            0                  0                  0                     0
##   Hieracium.spp. Holcus.spp. Holcus.lanatus Holcus.mollis
## 1              0          42              0             0
## 2              0           0              0             0
## 3              0          40              8             0
## 4              0          58              3             0
## 5              0          70              0             0
## 6              0          23              0             0
##   Homalothecium.lutescens Hylocomium.splendens Hypericum.perforatum
## 1                       0                    0                    0
## 2                       0                    0                    0
## 3                       0                    0                    0
## 4                       0                    0                    0
## 5                     160                    0                    0
## 6                      10                    0                    0
##   Hypnum.cupressiforme Hypnum.imponens Hypnum.jutlandicum Hypochaeris.radicata
## 1                   60               0                  0                    0
## 2                  150               0                  0                    0
## 3                   60               0                  0                    0
## 4                    0               0                  0                    0
## 5                    0               0                  0                    0
## 6                    0               0                  0                    0
##   Kindbergia.praelonga Lathyrus.pratensis Leontodon.hispidus
## 1                    0                  0                  0
## 2                    0                  0                  0
## 3                    0                  0                  0
## 4                    0                  0                  0
## 5                    0                  0                  0
## 6                    0                  0                  0
##   Leontodon.saxatilis Leucanthemum.vulgare Linum.catharticum Lolium.perenne
## 1                   0                    0                 5              0
## 2                   0                    0                 0              0
## 3                   0                    0                 0              0
## 4                   0                    0                 0              0
## 5                   0                    0                 0              0
## 6                   0                    0                 0              0
##   Lophocolea.semiteres Lotus.corniculatus Luzula.multiflora Lysimachia.maritima
## 1                    0                  0                 0                   0
## 2                    0                  0                 0                   0
## 3                    0                220                 0                   0
## 4                    0                 19                 0                   0
## 5                    0                  0                 0                   0
## 6                    0                  0                 0                   0
##   Medicago.lupulina Myosotis.arvensis Ononis.repens Oxalis.acetosella
## 1                 0                 0             0                 0
## 2                 0                 1             0                 0
## 3                 5                 0             0                 0
## 4                 0                 0             0                 0
## 5                 0                 6             2                 0
## 6                 0                 4            63                 0
##   Pastinaca.sativa Pentaglottis.sempervirens Pillosella.officinarum
## 1                0                         0                     33
## 2                0                         0                    286
## 3                0                         0                      2
## 4                0                         0                      0
## 5                0                         0                     54
## 6                0                         0                      0
##   Plantago.coronopus Plantago.lanceolata Pleurozium.schreberi Poa.annua
## 1                  0                   1                    0         0
## 2                  0                   0                    0         0
## 3                  0                   0                    0         0
## 4                  1                   0                    0         0
## 5                 19                   0                    0         0
## 6                  0                   1                    0         0
##   Poa.spp. Polytrichum.commune Polytrichum.commune.agg. Polytrichum.formosum
## 1        0                   0                        0                    0
## 2        0                   0                        0                    0
## 3        0                   0                        0                    0
## 4        0                   0                        0                    0
## 5        0                   0                        0                    0
## 6        0                   0                        0                    0
##   Potentilla.reptans Prunella.vulgaris Pseudoscleropidum.purum
## 1                  0                 0                       0
## 2                  0                 0                       0
## 3                  0                 0                       0
## 4                  0                 0                       0
## 5                  0                 0                      30
## 6                  0                 0                       0
##   Pteridium.aquilinum Ranunculus.acris Ranunculus.parviflorus Ranunculus.repens
## 1                   0                0                      0                 0
## 2                   0                0                      0                 0
## 3                   0                0                      0                 0
## 4                   0                0                      0                 0
## 5                   0                0                      0                 0
## 6                   0                0                      0                 0
##   Reseda.lutea Rhinanthus.minor Rhizomnium.punctatum Rhytidadelphus.squarrosus
## 1            0                0                    0                        60
## 2            0                0                    0                         0
## 3            0                0                    0                         0
## 4            0                0                    0                         0
## 5            0                0                    0                       140
## 6            0                0                    0                        20
##   Rhytidadelphus.triquetris Rubus.fruticosus Sanguisorba.minor.spp.minor
## 1                         0                0                           0
## 2                         0                0                           0
## 3                         0                0                           0
## 4                         0                0                           0
## 5                         0                0                           0
## 6                         0                0                           0
##   Saniona.uncinata Sedum.anglicum Senecio.jacobaea Senecio.vulgaris
## 1                0              0                0                0
## 2                0              0                0                0
## 3                0              0                0                0
## 4                0              0                0                0
## 5                0              0                0                0
## 6                0              0                0                0
##   Sonchus.arvensis Stachys.sylvatica Stellaria.apetala Taraxacum.agg.
## 1                0                 0                 0              0
## 2                0                 0                 0              1
## 3                0                 0                 0              3
## 4                0                 0                 0              2
## 5                0                 0                 0              1
## 6                0                 0                 0              0
##   Thuidium.tamariscinum Thymus.polytrichus Trichostomum.crispulum
## 1                     0                283                     60
## 2                     0                  7                      0
## 3                     0                159                      0
## 4                     0                  0                      0
## 5                     0                  0                      0
## 6                     0                 20                      0
##   Trifolium.campestre Trifolium.dubium Trifolium.pratense Trifolium.repens
## 1                   0              162                  0                0
## 2                   0              118                  0                0
## 3                   0                0                  0                0
## 4                   0                0                  0                0
## 5                   0                0                  0                0
## 6                   0                0                  0                2
##   Trisetum.flavescens Tussilago.farfara Urtica.diocia Veronica.officinalis
## 1                   0                 0             0                    0
## 2                   0                 0             0                    0
## 3                   0                 0             0                    0
## 4                   0                 0             0                    0
## 5                   0                 0             7                    0
## 6                   0                 0             0                    0
##   Vicia.sativa Viola.riviniana Weissia.controversa Zygodon.stirtonii
## 1            0               0                   0                 0
## 2            0               0                   0                 0
## 3            0               0                   0                 0
## 4            0               0                   0                 0
## 5            0               0                   0                 0
## 6            0               0                   0                 0
head(CarnforthPC)
##   pH_level     SiO2    Al2O3      Fe2O3      CaO      MgO     Na2O       K2O
## 1    9.008 182299.6 47632.53 153873.611 164378.9 6030.359 2967.428 10791.921
## 2   10.175 159862.7 52131.16   7903.508 262291.5 8924.931 2151.385  3486.621
## 3   10.589 170613.7 44139.48  20283.340 204401.6 8140.985 2299.756  5561.990
## 4    9.516 181832.2 35936.10   7833.566 200828.1 8080.681 2596.499  4648.828
## 5   10.133 142567.7 43927.78   4826.036 250141.8 9769.182 1186.971  2407.429
## 6    8.790 200997.0 31755.02 181850.631 121497.4 6030.359 3709.284 13282.364
##       Cr2O3     TiO2      MnO     P2O5      SrO       BaO   LOI   Ag As  B   Be
## 1 342.10121 3596.057 5421.202 999.8709 287.5021 1791.3027 22.86 0.00  0  0  0.0
## 2  27.36810 4495.072 1858.698 399.9484 338.2378 1433.0422 13.90 0.15  3 50 12.8
## 3  20.52607 2637.109 1936.144 599.9225 253.6784  716.5211 19.00 1.30 11 60  8.4
## 4  41.05215 2457.306 1781.252 499.9354 253.6784  985.2165 20.70 0.30  7 40  8.6
## 5  13.68405 3356.320  929.349 599.9225 253.6784  716.5211 22.20 0.30  3 40 11.4
## 6  68.42024 1798.029 2323.372 999.8709 211.3986  806.0862 20.61 0.00  0  0  0.0
##    Bi   Cd Co Cu Ga  Hg La Li  Mo Ni  Pb     S   Sb Sc Th Tl  U   V W   Zn
## 1 0.0 0.00  0  0  0 0.0  0  0 0.0  0   0 10000  0.0  0  0  0  0 100 0 6000
## 2 1.5 0.25  1 14  5 0.5 30 50 0.5  7  11  6000  2.0 11 10  5 10  10 5   36
## 3 2.0 2.70  3 53 10 0.5 30 40 0.5  8 212  4300 16.0  7 10  5  5  12 5  503
## 4 1.5 0.60 36 30  5 0.5 20 40 0.5  6  71  2700  2.0  5 10  5  5  11 5  120
## 5 1.5 0.25  4 17  5 0.5 30 40 0.5  3  28  8100  1.5  8 10  5  5   5 5   46
## 6 0.0 0.00  0  0  0 0.0  0  0 0.0  0   0  5000  0.0  0  0  0  0 100 0 2000
##   Akermanite Albite Aluminium.oxide.hydroxide Anhydrite Aragonite Biotite
## 1          1      0                         0         0         0       1
## 2          0      0                         0         0         0       0
## 3          0      0                         0         0         0       0
## 4          0      0                         0         0         0       0
## 5          1      0                         0         0         0       0
## 6          0      0                         0         0         0       0
##   Birnessite Calcite Clinochlore Cuspidine Diaspore Dickite Gehlenite Goethite
## 1          0       1           0         0        0       0         0        0
## 2          0       1           0         1        0       0         1        0
## 3          0       1           0         1        0       0         1        0
## 4          0       1           0         0        0       0         1        0
## 5          0       1           0         1        0       0         0        0
## 6          0       1           0         0        0       0         0        0
##   Haematite Illite Kaolinite Langite Linnaeite Magnesioferrite Melilite
## 1         0      0         0       0         0               0        0
## 2         0      0         0       0         0               0        0
## 3         0      0         0       0         0               0        0
## 4         0      0         0       0         0               0        0
## 5         0      0         0       0         0               0        0
## 6         0      0         0       0         0               1        0
##   Merwinite Microcline Mullite Muscovite Orthoclase Orthopyroxene Periclase
## 1         0          0       0         0          0             0         0
## 2         0          0       0         0          0             0         1
## 3         0          0       0         0          0             0         0
## 4         0          0       0         0          0             0         0
## 5         0          0       0         1          0             0         1
## 6         1          0       0         0          0             0         0
##   Phengite Pseudowollastonite Quartz Staurolite Valentinite
## 1        0                  1      1          0           0
## 2        0                  0      1          0           0
## 3        0                  0      1          0           0
## 4        0                  0      1          0           0
## 5        0                  0      0          0           0
## 6        0                  0      1          0           0
rowSums(CarnforthPS)
## [1] 795 568 552 322 517 206 319 343

#Now for some ANOSIMs…

#anoCSiO2 <- anosim(CarnforthPS, CarnforthPC$SiO2, distance = “bray”, permutations = 9999)

#When this ANOSIM is run, the error message: “there should be replicates within groups” #comes up. This error message comes up for another substrate variables for the Barrow #data. From now on, only variables that were tested successfully will be included.

anoCMgO <- anosim(CarnforthPS, CarnforthPC$MgO, distance = "bray", permutations = 9999)

anoCMgO
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$MgO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1852 
##       Significance: 0.4287 
## 
## Permutation: free
## Number of permutations: 9999
anoCCr2O3 <- anosim(CarnforthPS, CarnforthPC$Cr2O3, distance = "bray", permutations = 9999)

anoCCr2O3
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$Cr2O3, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:    -0 
##       Significance: 0.5006 
## 
## Permutation: free
## Number of permutations: 9999
anoCP2O5 <- anosim(CarnforthPS, CarnforthPC$P2O5, distance = "bray", permutations = 9999)

anoCP2O5
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$P2O5, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.03846 
##       Significance: 0.4723 
## 
## Permutation: free
## Number of permutations: 9999
anoCSrO <- anosim(CarnforthPS, CarnforthPC$SrO, distance = "bray", permutations = 9999)

anoCSrO
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$SrO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.07576 
##       Significance: 0.5985 
## 
## Permutation: free
## Number of permutations: 9999
anoCBaO <- anosim(CarnforthPS, CarnforthPC$BaO, distance = "bray", permutations = 9999)

anoCBaO
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$BaO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.1923 
##       Significance: 0.6727 
## 
## Permutation: free
## Number of permutations: 9999
anoCAg <- anosim(CarnforthPS, CarnforthPC$Ag, distance = "bray", permutations = 9999)

anoCAg
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$Ag, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.01333 
##       Significance: 0.497 
## 
## Permutation: free
## Number of permutations: 9999
anoCAs <- anosim(CarnforthPS, CarnforthPC$As, distance = "bray", permutations = 9999)

anoCAs
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$As, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:    -0 
##       Significance: 0.4966 
## 
## Permutation: free
## Number of permutations: 9999
anoCB <- anosim(CarnforthPS, CarnforthPC$B, distance = "bray", permutations = 9999)

anoCB
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$B, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.1875 
##       Significance: 0.7076 
## 
## Permutation: free
## Number of permutations: 9999
anoCBe <- anosim(CarnforthPS, CarnforthPC$Be, distance = "bray", permutations = 9999)

anoCBe
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$Be, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1852 
##       Significance: 0.4274 
## 
## Permutation: free
## Number of permutations: 9999
anoCCd <- anosim(CarnforthPS, CarnforthPC$Cd, distance = "bray", permutations = 9999)

anoCCd
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$Cd, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.1042 
##       Significance: 0.6296 
## 
## Permutation: free
## Number of permutations: 9999
anoCCo <- anosim(CarnforthPS, CarnforthPC$Co, distance = "bray", permutations = 9999)

anoCCo
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$Co, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1538 
##       Significance: 0.3512 
## 
## Permutation: free
## Number of permutations: 9999
anoCCu <- anosim(CarnforthPS, CarnforthPC$Cu, distance = "bray", permutations = 9999)

anoCCu
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$Cu, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1852 
##       Significance: 0.4232 
## 
## Permutation: free
## Number of permutations: 9999
anoCMo <- anosim(CarnforthPS, CarnforthPC$Mo, distance = "bray", permutations = 9999)

anoCMo
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$Mo, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.3542 
##       Significance: 0.8562 
## 
## Permutation: free
## Number of permutations: 9999
anoCNi <- anosim(CarnforthPS, CarnforthPC$Ni, distance = "bray", permutations = 9999)

anoCNi
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$Ni, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.2267 
##       Significance: 0.7544 
## 
## Permutation: free
## Number of permutations: 9999
anoCPb <- anosim(CarnforthPS, CarnforthPC$Pb, distance = "bray", permutations = 9999)

anoCPb
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$Pb, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1852 
##       Significance: 0.4296 
## 
## Permutation: free
## Number of permutations: 9999
anoCSb <- anosim(CarnforthPS, CarnforthPC$Sb, distance = "bray", permutations = 9999)

anoCSb
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$Sb, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.01333 
##       Significance: 0.5111 
## 
## Permutation: free
## Number of permutations: 9999
anoCSc <- anosim(CarnforthPS, CarnforthPC$Sc, distance = "bray", permutations = 9999)

anoCSc
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$Sc, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1852 
##       Significance: 0.4217 
## 
## Permutation: free
## Number of permutations: 9999
anoCV <- anosim(CarnforthPS, CarnforthPC$V, distance = "bray", permutations = 9999)

anoCV
## 
## Call:
## anosim(x = CarnforthPS, grouping = CarnforthPC$V, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.1852 
##       Significance: 0.4271 
## 
## Permutation: free
## Number of permutations: 9999
#None of the ANOSIM tests led to stastistically significant results. Because of this,
#CCAs might not be entirely appropriate to represent the data visually.
#NMDS analyses will be utilised to visualise the plant data.
CarnforthNMDS <- metaMDS(CarnforthPS)
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1027624 
## Run 1 stress 0.1175384 
## Run 2 stress 0.05547408 
## ... New best solution
## ... Procrustes: rmse 0.2042017  max resid 0.4524411 
## Run 3 stress 0.1027624 
## Run 4 stress 0.1027625 
## Run 5 stress 0.186362 
## Run 6 stress 0.05547398 
## ... New best solution
## ... Procrustes: rmse 4.411432e-05  max resid 7.488946e-05 
## ... Similar to previous best
## Run 7 stress 0.05547398 
## ... New best solution
## ... Procrustes: rmse 6.750473e-06  max resid 1.270373e-05 
## ... Similar to previous best
## Run 8 stress 0.05547398 
## ... New best solution
## ... Procrustes: rmse 6.782685e-06  max resid 1.228053e-05 
## ... Similar to previous best
## Run 9 stress 0.190284 
## Run 10 stress 0.05547399 
## ... Procrustes: rmse 3.218193e-05  max resid 5.714836e-05 
## ... Similar to previous best
## Run 11 stress 0.055474 
## ... Procrustes: rmse 5.876103e-05  max resid 0.0001036368 
## ... Similar to previous best
## Run 12 stress 0.05547398 
## ... Procrustes: rmse 5.877481e-06  max resid 1.059789e-05 
## ... Similar to previous best
## Run 13 stress 0.08975528 
## Run 14 stress 0.2848522 
## Run 15 stress 0.055474 
## ... Procrustes: rmse 5.699742e-05  max resid 9.960538e-05 
## ... Similar to previous best
## Run 16 stress 0.1027624 
## Run 17 stress 0.05547399 
## ... Procrustes: rmse 2.927659e-05  max resid 5.150946e-05 
## ... Similar to previous best
## Run 18 stress 0.3083098 
## Run 19 stress 0.05547399 
## ... Procrustes: rmse 2.263375e-05  max resid 3.966542e-05 
## ... Similar to previous best
## Run 20 stress 0.05547399 
## ... Procrustes: rmse 3.515576e-05  max resid 6.215593e-05 
## ... Similar to previous best
## *** Best solution repeated 8 times
plot(CarnforthNMDS)

#As in the other NMDS plots, species are represented by red crosses and communities are #represented by circles.

CarnforthNMDS
## 
## Call:
## metaMDS(comm = CarnforthPS) 
## 
## global Multidimensional Scaling using monoMDS
## 
## Data:     wisconsin(sqrt(CarnforthPS)) 
## Distance: bray 
## 
## Dimensions: 2 
## Stress:     0.05547398 
## Stress type 1, weak ties
## Best solution was repeated 8 times in 20 tries
## The best solution was from try 8 (random start)
## Scaling: centring, PC rotation, halfchange scaling 
## Species: expanded scores based on 'wisconsin(sqrt(CarnforthPS))'
plot(CarnforthNMDS, "sites")   # Produces distance 

plot(CarnforthNMDS, "species")
orditorp(CarnforthNMDS, "species")

#What is interesting about this NMDS is that most of the species are separated out, with #very little clustering or ‘clumping’. This contrasts greatly with the NMDS plots #for Fallin Bing, Addiewell Bing and South Bank Wood (Penicuik). It might still be #useful to look at a CCA for Carnforth as well…

CarnforthCCA <- cca(CarnforthPS, CarnforthPC)
## 
## Some constraints or conditions were aliased because they were redundant. This
## can happen if terms are linearly dependent (collinear): 'K2O', 'Cr2O3', 'TiO2',
## 'MnO', 'P2O5', 'SrO', 'BaO', 'LOI', 'Ag', 'As', 'B', 'Be', 'Bi', 'Cd', 'Co',
## 'Cu', 'Ga', 'Hg', 'La', 'Li', 'Mo', 'Ni', 'Pb', 'S', 'Sb', 'Sc', 'Th', 'Tl',
## 'U', 'V', 'W', 'Zn', 'Akermanite', 'Albite', 'Aluminium.oxide.hydroxide',
## 'Anhydrite', 'Aragonite', 'Biotite', 'Birnessite', 'Calcite', 'Clinochlore',
## 'Cuspidine', 'Diaspore', 'Dickite', 'Gehlenite', 'Goethite', 'Haematite',
## 'Illite', 'Kaolinite', 'Langite', 'Linnaeite', 'Magnesioferrite', 'Melilite',
## 'Merwinite', 'Microcline', 'Mullite', 'Muscovite', 'Orthoclase',
## 'Orthopyroxene', 'Periclase', 'Phengite', 'Pseudowollastonite', 'Quartz',
## 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component
print(CarnforthCCA)
## Call: cca(X = CarnforthPS, Y = CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total           3.868      1.000     
## Constrained     3.868      1.000    7
## Unconstrained   0.000      0.000    0
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## Some constraints or conditions were aliased because they were redundant.
## This can happen if terms are linearly dependent (collinear): 'K2O',
## 'Cr2O3', 'TiO2', 'MnO', 'P2O5', 'SrO', 'BaO', 'LOI', 'Ag', 'As', 'B', 'Be',
## 'Bi', 'Cd', 'Co', 'Cu', 'Ga', 'Hg', 'La', 'Li', 'Mo', 'Ni', 'Pb', 'S',
## 'Sb', 'Sc', 'Th', 'Tl', 'U', 'V', 'W', 'Zn', 'Akermanite', 'Albite',
## 'Aluminium.oxide.hydroxide', 'Anhydrite', 'Aragonite', 'Biotite',
## 'Birnessite', 'Calcite', 'Clinochlore', 'Cuspidine', 'Diaspore', 'Dickite',
## 'Gehlenite', 'Goethite', 'Haematite', 'Illite', 'Kaolinite', 'Langite',
## 'Linnaeite', 'Magnesioferrite', 'Melilite', 'Merwinite', 'Microcline',
## 'Mullite', 'Muscovite', 'Orthoclase', 'Orthopyroxene', 'Periclase',
## 'Phengite', 'Pseudowollastonite', 'Quartz', 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component.
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6   CCA7 
## 0.8089 0.6910 0.6454 0.5739 0.4932 0.4219 0.2338
plot(CarnforthCCA)

CarnforthCCA1 <- cca(CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Calcite,
                     data = CarnforthPC)

print(CarnforthCCA1)
## Call: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Calcite, data =
## CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          3.8682     1.0000     
## Constrained    3.0308     0.7835    5
## Unconstrained  0.8374     0.2165    2
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5 
## 0.7958 0.6891 0.6261 0.5340 0.3858 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2 
## 0.5070 0.3303
plot(CarnforthCCA1)

anova(CarnforthCCA1)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Calcite, data = CarnforthPC)
##          Df ChiSquare      F Pr(>F)   
## Model     5   3.03084 1.4478  0.005 **
## Residual  2   0.83737                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##An F statistic of 1.4478 and a low p value of 0.008.

CarnforthCCA2 <- cca(CarnforthPS ~ Na2O + Co +SrO + Al2O3 + Calcite + MgO,
                     data = CarnforthPC)

print(CarnforthCCA2)
## Call: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Calcite + MgO,
## data = CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total         3.86821    1.00000     
## Constrained   3.52185    0.91046    6
## Unconstrained 0.34635    0.08954    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.7968 0.6898 0.6295 0.5737 0.4903 0.3417 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.3464
plot(CarnforthCCA2)

anova(CarnforthCCA2)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Calcite + MgO, data = CarnforthPC)
##          Df ChiSquare      F Pr(>F)    
## Model     6    3.5219 1.6947  0.001 ***
## Residual  1    0.3464                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##An F statistic of 1.6947 and a low p value of 0.002.

CarnforthCCA3 <- cca(CarnforthPS ~ Na2O + Co + P2O5 + Al2O3, data = CarnforthPC)
print(CarnforthCCA3)
## Call: cca(formula = CarnforthPS ~ Na2O + Co + P2O5 + Al2O3, data =
## CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          3.8682     1.0000     
## Constrained    2.2333     0.5774    4
## Unconstrained  1.6349     0.4226    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4 
## 0.7660 0.6623 0.5402 0.2648 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.6517 0.5161 0.4670
plot(CarnforthCCA3)

anova(CarnforthCCA3)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = CarnforthPS ~ Na2O + Co + P2O5 + Al2O3, data = CarnforthPC)
##          Df ChiSquare      F Pr(>F)
## Model     4    2.2333 1.0245  0.332
## Residual  3    1.6349

#An F statistic of 1.0245 and a p value of 0.382.

CarnforthCCA4 <- cca(CarnforthPS ~ pH_level + Co +SrO + Al2O3 + Calcite + MgO,
                     data = CarnforthPC)

print(CarnforthCCA4)
## Call: cca(formula = CarnforthPS ~ pH_level + Co + SrO + Al2O3 + Calcite +
## MgO, data = CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          3.8682     1.0000     
## Constrained    3.4512     0.8922    6
## Unconstrained  0.4170     0.1078    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.8029 0.6899 0.6387 0.5456 0.4825 0.2915 
## 
## Eigenvalues for unconstrained axes:
##   CA1 
## 0.417
plot(CarnforthCCA4)

anova(CarnforthCCA4)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = CarnforthPS ~ pH_level + Co + SrO + Al2O3 + Calcite + MgO, data = CarnforthPC)
##          Df ChiSquare      F Pr(>F)   
## Model     6    3.4512 1.3792  0.004 **
## Residual  1    0.4170                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.3792 and a p value of 0.01.

CarnforthCCA5 <- cca(CarnforthPS ~ pH_level + Co + As + Al2O3 + Calcite + MgO,
                     data = CarnforthPC)

print(CarnforthCCA5)
## Call: cca(formula = CarnforthPS ~ pH_level + Co + As + Al2O3 + Calcite +
## MgO, data = CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          3.8682     1.0000     
## Constrained    3.4109     0.8818    6
## Unconstrained  0.4573     0.1182    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.8071 0.6868 0.6199 0.5552 0.4863 0.2556 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.4573
plot(CarnforthCCA5)

anova(CarnforthCCA5)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = CarnforthPS ~ pH_level + Co + As + Al2O3 + Calcite + MgO, data = CarnforthPC)
##          Df ChiSquare     F Pr(>F)  
## Model     6    3.4109 1.243  0.075 .
## Residual  1    0.4573               
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.243 and a p value of 0.089.

CarnforthCCA6 <- cca(CarnforthPS ~ Na2O + Co +SrO + Al2O3 + Calcite + V,
                     data = CarnforthPC)

print(CarnforthCCA6)
## Call: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Calcite + V,
## data = CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          3.8682     1.0000     
## Constrained    3.3915     0.8768    6
## Unconstrained  0.4767     0.1232    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.7998 0.6892 0.6332 0.5414 0.4791 0.2487 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.4767
plot(CarnforthCCA6)

anova(CarnforthCCA6)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Calcite + V, data = CarnforthPC)
##          Df ChiSquare      F Pr(>F)
## Model     6    3.3915 1.1857    0.1
## Residual  1    0.4767

#An F statistic of 1.1857 and a p value of 0.104.

CarnforthCCA7 <- cca(CarnforthPS ~ Na2O + Co +SrO + Al2O3 + Ag + MgO,
                     data = CarnforthPC)

print(CarnforthCCA7)
## Call: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Ag + MgO, data
## = CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total         3.86821    1.00000     
## Constrained   3.50666    0.90653    6
## Unconstrained 0.36155    0.09347    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.8011 0.6893 0.6378 0.5672 0.4924 0.3189 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.3615
plot(CarnforthCCA7)

anova(CarnforthCCA7)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Ag + MgO, data = CarnforthPC)
##          Df ChiSquare      F Pr(>F)   
## Model     6    3.5067 1.6165  0.002 **
## Residual  1    0.3615                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.6165 and a p value of 0.003.

CarnforthCCA8 <- cca(CarnforthPS ~ Na2O + Co +SrO + Al2O3 + BaO + MgO,
                     data = CarnforthPC)

print(CarnforthCCA8)
## Call: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + BaO + MgO, data
## = CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          3.8682     1.0000     
## Constrained    3.3792     0.8736    6
## Unconstrained  0.4890     0.1264    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.8089 0.6901 0.6451 0.5427 0.4532 0.2392 
## 
## Eigenvalues for unconstrained axes:
##   CA1 
## 0.489
plot(CarnforthCCA8)

anova(CarnforthCCA8)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + BaO + MgO, data = CarnforthPC)
##          Df ChiSquare      F Pr(>F)
## Model     6    3.3792 1.1518  0.184
## Residual  1    0.4890

#An F statistic of 1.1518 and a p value of 0.147.

CarnforthCCA9 <- cca(CarnforthPS ~ Na2O + Co +SrO + Al2O3 + Cr2O3 + MgO,
                     data = CarnforthPC)

print(CarnforthCCA9)
## Call: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Cr2O3 + MgO,
## data = CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          3.8682     1.0000     
## Constrained    3.3565     0.8677    6
## Unconstrained  0.5117     0.1323    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.8077 0.6905 0.6435 0.5408 0.4375 0.2365 
## 
## Eigenvalues for unconstrained axes:
##    CA1 
## 0.5117
plot(CarnforthCCA9)

anova(CarnforthCCA9)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Cr2O3 + MgO, data = CarnforthPC)
##          Df ChiSquare      F Pr(>F)
## Model     6    3.3565 1.0933  0.285
## Residual  1    0.5117

#An F statistic of 1.6442 and a p value of 0.002.

CarnforthCCA9 <- cca(CarnforthPS ~ Na2O + Co +SrO + Al2O3 + Cd + MgO,
                     data = CarnforthPC)

print(CarnforthCCA9)
## Call: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Cd + MgO, data
## = CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total         3.86821    1.00000     
## Constrained   3.51219    0.90796    6
## Unconstrained 0.35601    0.09204    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.8002 0.6893 0.6361 0.5695 0.4930 0.3240 
## 
## Eigenvalues for unconstrained axes:
##   CA1 
## 0.356
plot(CarnforthCCA9)

anova(CarnforthCCA9)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Al2O3 + Cd + MgO, data = CarnforthPC)
##          Df ChiSquare      F Pr(>F)   
## Model     6    3.5122 1.6442  0.003 **
## Residual  1    0.3560                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.634 and a low p value of 0.002.

CarnforthCCA10 <- cca(CarnforthPS ~ Na2O + Co +SrO + Cd + Calcite + MgO,
                     data = CarnforthPC)

print(CarnforthCCA10)
## Call: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Cd + Calcite + MgO,
## data = CarnforthPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total         3.86821    1.00000     
## Constrained   3.51017    0.90744    6
## Unconstrained 0.35804    0.09256    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 102 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.8014 0.6909 0.6376 0.5676 0.4932 0.3195 
## 
## Eigenvalues for unconstrained axes:
##   CA1 
## 0.358
plot(CarnforthCCA10)

anova(CarnforthCCA10)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = CarnforthPS ~ Na2O + Co + SrO + Cd + Calcite + MgO, data = CarnforthPC)
##          Df ChiSquare     F Pr(>F)   
## Model     6    3.5102 1.634  0.003 **
## Residual  1    0.3580                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#An F statistic of 1.6287 and a low p value of 0.001.

#After doing several CCAs with different combinations of chemical variables, the one with #the highest F statistic, 1.6947, is CarnforthCCA2. This CCA also has a low p value of #0.002. The plot for this one looks good, but it can be made to be a little neater and #easier to interpret…

options(max.print=1000000)

CarnforthCCA2$CCA$v
##                                  CCA1       CCA2        CCA3        CCA4
## Alopercus.pratensis        0.70197267  1.9144914  0.58018924 -3.19668010
## Arrhenatherum.elatius     -0.92434356 -0.3623170 -0.30215207  0.13427454
## Avenula.pratensis          0.70197267  1.9144914  0.58018924 -3.19668010
## Bellis.perennis            0.25570592  1.0509552  0.19022470 -0.86331856
## Brachythecium.mildeanum    2.78627371 -2.1170901  0.13902509  0.32569124
## Bryum.c.f..pallescens     -0.97459212 -0.7902055 -1.38783174 -0.32053435
## Bryum.spp.                 1.08992217  2.5870088 -1.28669429  1.76431490
## Calliergonella.cupsidata   1.06007990  2.5352767 -1.14308786  1.38269990
## Carex.distans              1.88581916 -1.3862996  0.04600892  0.61157449
## Carex.flacca               1.08992217  2.5870088 -1.28669429  1.76431490
## Carlina.vulgaris          -0.76941458 -0.3533724 -0.05304103  0.32526965
## Centaurium.pulchellum      2.78627371 -2.1170901  0.13902509  0.32569124
## Cerastium.fontanum        -0.92434356 -0.3623170 -0.30215207  0.13427454
## Dicranella.spp.           -1.03489039 -1.3036717 -2.69064735 -0.86630502
## Euphrasia.agg             -0.92434356 -0.3623170 -0.30215207  0.13427454
## Festuca.ovina              1.06512484  0.8841181 -0.43752785  0.47189414
## Fissidens.dubius           1.08992217  2.5870088 -1.28669429  1.76431490
## Fissidens.exilis          -1.03489039 -1.3036717 -2.69064735 -0.86630502
## Galium.saxatile            0.25327885  0.3925877  0.39790464 -1.84098085
## Holcus.spp.                0.35971488  0.7701560 -0.20685038 -0.16208029
## Holcus.lanatus             0.18816704  0.8989459 -0.47039918  1.39602713
## Homalothecium.lutescens    0.27967260  0.4821115  0.40862726 -1.92072787
## Hypnum.cupressiforme      -0.66364332 -0.1652824  1.09999378  0.70620087
## Linum.catharticum         -0.92434356 -0.3623170 -0.30215207  0.13427454
## Lotus.corniculatus        -0.05142062  0.4504439 -0.25351743  1.29817661
## Lysimachia.maritima        2.78627371 -2.1170901  0.13902509  0.32569124
## Medicago.lupulina         -0.14999113  0.2659224 -0.16428852  1.25791922
## Myosotis.arvensis          0.32388542  0.8867765  0.62497725 -2.10166559
## Ononis.repens              0.68816670  1.8676636  0.57458048 -3.15496628
## Pillosella.officinarum    -0.63005543 -0.1744372  1.67056970  0.29508742
## Plantago.coronopus         2.41445838 -1.7261350  0.16509219  0.02921254
## Plantago.lanceolata       -0.11118545  0.7760872  0.13901858 -1.53120278
## Pseudoscleropidum.purum    1.26647679 -0.6112834  0.29435282 -0.97431202
## Rhytidadelphus.squarrosus -0.02710055  0.3250595  0.22355141 -1.42552022
## Taraxacum.agg.             0.17404653  0.8722031 -0.07168349  0.88224152
## Thymus.polytrichus        -0.62903152 -0.1603932 -0.40066206  0.27255158
## Trichostomum.crispulum    -0.99587386 -0.9714288 -1.84764902 -0.51315929
## Trifolium.campestre        2.78627371 -2.1170901  0.13902509  0.32569124
## Trifolium.dubium          -0.85711750 -0.3187554  0.73823585  0.37870712
## Trifolium.repens           0.70197267  1.9144914  0.58018924 -3.19668010
## Urtica.diocia              0.25327885  0.3925877  0.39790464 -1.84098085
##                                  CCA5        CCA6
## Alopercus.pratensis        2.23753647 -2.73079659
## Arrhenatherum.elatius      0.39151162 -1.93124381
## Avenula.pratensis          2.23753647 -2.73079659
## Bellis.perennis            2.36187593 -0.19603802
## Brachythecium.mildeanum    0.05140906 -0.77970802
## Bryum.c.f..pallescens     -0.30152871 -0.74573425
## Bryum.spp.                -1.85436517 -0.70523196
## Calliergonella.cupsidata  -1.53960351 -0.86104462
## Carex.distans              0.79461657  0.10594407
## Carex.flacca              -1.85436517 -0.70523196
## Carlina.vulgaris           0.20674996 -0.49095930
## Centaurium.pulchellum      0.05140906 -0.77970802
## Cerastium.fontanum         0.39151162 -1.93124381
## Dicranella.spp.           -1.13317712  0.67687722
## Euphrasia.agg              0.39151162 -1.93124381
## Festuca.ovina             -0.57422053  0.23471256
## Fissidens.dubius          -1.85436517 -0.70523196
## Fissidens.exilis          -1.13317712  0.67687722
## Galium.saxatile           -0.98632494  2.45820246
## Holcus.spp.               -0.03668418  0.24977834
## Holcus.lanatus             1.29419989  1.34096433
## Homalothecium.lutescens   -0.79668603  2.15296723
## Hypnum.cupressiforme      -0.03540532 -0.01756412
## Linum.catharticum          0.39151162 -1.93124381
## Lotus.corniculatus         2.13074333  1.88461900
## Lysimachia.maritima        0.05140906 -0.77970802
## Medicago.lupulina          2.47491179  2.10828794
## Myosotis.arvensis          0.16562703  0.33850867
## Ononis.repens              2.13834073 -2.57113508
## Pillosella.officinarum    -1.01774072  0.11864224
## Plantago.coronopus        -0.10995452 -0.32004552
## Plantago.lanceolata        1.31452405 -2.33102020
## Pseudoscleropidum.purum   -0.57123134  1.16303827
## Rhytidadelphus.squarrosus -0.31747302  0.78935357
## Taraxacum.agg.             0.21705445  1.03859562
## Thymus.polytrichus         0.95251835 -0.45952861
## Trichostomum.crispulum    -0.59505168 -0.24363609
## Trifolium.campestre        0.05140906 -0.77970802
## Trifolium.dubium          -0.28353711 -1.16053071
## Trifolium.repens           2.23753647 -2.73079659
## Urtica.diocia             -0.98632494  2.45820246
## attr(,"na.action")
##               Agrostis.spp.             Agrostis.canina 
##                           1                           2 
##           Alchemilla.mollis         Angelica.sylvestris 
##                           3                           5 
##       Anthoxanthum.odoratum        Anthyllis.vulneraria 
##                           6                           7 
##            Aphanes.arvensis          Atrichum.undulatum 
##                           8                          10 
##            Betula.pubescens      Blackstonia.perfoliata 
##                          13                          14 
##      Brachythecium.albicans     Brachythecium.glareosum 
##                          15                          16 
##     Brachythecium.rutabulum                 Briza.media 
##                          18                          19 
##           Bromus.hordeaceus     Bryum.c.f..caespiticium 
##                          20                          21 
##             Bryum.capillare           Calypogeia.arguta 
##                          23                          26 
##      Campanula.rotundifolia               Carex.panicea 
##                          27                          30 
##             Centaurea.nigra        Centaurium.erythraea 
##                          32                          33 
##        Centaurium.littorale  Chamaenerion.angustifolium 
##                          34                          37 
##      Cirriphyllum.piliferum             Cirsium.arvense 
##                          38                          39 
##            Cirsium.palustre           Crepis.capillaris 
##                          40                          41 
##         Cynosurus.cristatus          Dactylis.glomerata 
##                          42                          43 
##        Dactylorhiza.fuchsii         Danthonia.decumbens 
##                          44                          45 
##              Daucus.carrota          Dicranum.scoparium 
##                          46                          48 
##          Epilobium.montanum           Equisetum.arvense 
##                          49                          50 
##        Equisteum.variegatum               Erigeron.acer 
##                          51                          52 
##               Festuca.rubra          Festuca.rubra.agg. 
##                          55                          56 
##         Filipendula.ulmaria      Fissidens.adianthoides 
##                          57                          58 
##              Fragaria.vesca              Galium.aparine 
##                          61                          62 
##              Galium.arvense                Galium.verum 
##                          63                          65 
##                Geum.urbanum          Glechoma.hederacea 
##                          66                          67 
##          Helicotrichon.spp.       Heracleum.sphondylium 
##                          68                          69 
##              Hieracium.spp.               Holcus.mollis 
##                          70                          73 
##        Hylocomium.splendens        Hypericum.perforatum 
##                          75                          76 
##             Hypnum.imponens          Hypnum.jutlandicum 
##                          78                          79 
##        Hypochaeris.radicata        Kindbergia.praelonga 
##                          80                          81 
##          Lathyrus.pratensis          Leontodon.hispidus 
##                          82                          83 
##         Leontodon.saxatilis        Leucanthemum.vulgare 
##                          84                          85 
##              Lolium.perenne        Lophocolea.semiteres 
##                          87                          88 
##           Luzula.multiflora           Oxalis.acetosella 
##                          90                          95 
##            Pastinaca.sativa   Pentaglottis.sempervirens 
##                          96                          97 
##        Pleurozium.schreberi                   Poa.annua 
##                         101                         102 
##                    Poa.spp.         Polytrichum.commune 
##                         103                         104 
##    Polytrichum.commune.agg.        Polytrichum.formosum 
##                         105                         106 
##          Potentilla.reptans           Prunella.vulgaris 
##                         107                         108 
##         Pteridium.aquilinum            Ranunculus.acris 
##                         110                         111 
##      Ranunculus.parviflorus           Ranunculus.repens 
##                         112                         113 
##                Reseda.lutea            Rhinanthus.minor 
##                         114                         115 
##        Rhizomnium.punctatum   Rhytidadelphus.triquetris 
##                         116                         118 
##            Rubus.fruticosus Sanguisorba.minor.spp.minor 
##                         119                         120 
##            Saniona.uncinata              Sedum.anglicum 
##                         121                         122 
##            Senecio.jacobaea            Senecio.vulgaris 
##                         123                         124 
##            Sonchus.arvensis           Stachys.sylvatica 
##                         125                         126 
##           Stellaria.apetala       Thuidium.tamariscinum 
##                         127                         129 
##          Trifolium.pratense         Trisetum.flavescens 
##                         134                         136 
##           Tussilago.farfara        Veronica.officinalis 
##                         137                         139 
##                Vicia.sativa             Viola.riviniana 
##                         140                         141 
##         Weissia.controversa           Zygodon.stirtonii 
##                         142                         143 
## attr(,"class")
## [1] "exclude"
#The "v values" show the positions of individual species on the graph, with the CCA1 value
#representing the x axis and the CCA2 value representing the y axis, in the case of the
#graph created in R.

plot(CarnforthCCA2, xlim = c(-5, 5), ylim = c(-5, 5)) 

#Increasing the xlim and ylim to give more room for writing on graph

plot(CarnforthCCA2, choices = c(1,2), display = c("wa", "bp"), xlim = c(-4, 3),
     ylim = c(-3, 2))

#Increasing the xlim and ylim to give more room for writing on graph Note that Community
#1 and Community 2 are grouped/clustered together in this CCA plot.

points(x = 0.70197267, y = 1.9144914, pch = 15, col = "black")

#This point represents Alopercus pratensis

text('A. pratensis', x = 0.70197267, y = 1.9144914, cex = 0.88, pos = 2, col = "black")

#Adding text to this point.

points(x = -0.63005543, y = -0.1744372, pch = 15, col = "black")

#This point represents Pilosella officinarum

text('P. officinarum', x = -0.63005543, y = -0.1744372, cex = 0.88, pos = 2, col = "black")

#Adding text to this point

points(x = 2.78627371 , y = -2.1170901, pch = 15, col = "black")

#This point represents Centaurium pulchellum

text('C. pulchellum', x = 2.78627371, y = -2.1170901, cex = 0.88, pos = 2, col = "black")

#Adding text to this point

points(x = -1.03489039, y = -1.3036717, pch = 15, col = "black")

#This point represents Fissidens exilis

text('F. exilis', x = -1.03489039, y = -1.3036717, cex = 0.88, pos = 2, col = "black")

#Adding text to this point

points(x = 0.27967260, y = 0.4821115, pch = 15, col = "black")

#This point represents Homalothecium lutescens

text('H. lutescens', x = 0.27967260, y = 0.4821115, cex = 0.88, pos = 2, col = "black")

#Adding text to this point

##Hodbarrow Data##

urlfile13 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/HodbarrowPlantSpecies.csv'

HodbarrowPS <- read.csv(urlfile13,  header = TRUE, colClasses = c("numeric"))

urlfile14 <- 'https://raw.githubusercontent.com/Savannankvm/Canonical-Correspondence-analyses-six-study-sites-PhD/PhD-files/HODBARROW_PLANT_CHEMISTRY_MG_KG.csv'

HodbarrowPC <-read.csv(urlfile14, header = TRUE, 
                       colClasses = c("numeric"))

head(HodbarrowPS)
##   Agrostis.spp. Agrostis.canina Alchemilla.mollis Alopercus.pratensis
## 1             0               0                 0                   0
## 2             0               0                 0                   0
## 3             0               0                 0                   0
## 4             0               0                 0                   0
## 5             0               0                 0                   0
## 6             0               0                 0                   0
##   Angelica.sylvestris Anthoxanthum.odoratum Anthyllis.vulneraria
## 1                   0                     0                    0
## 2                   0                     0                   70
## 3                   0                     0                  189
## 4                   0                     7                    0
## 5                   0                     0                    0
## 6                   0                     0                    0
##   Aphanes.arvensis Arrhenatherum.elatius Atrichum.undulatum Avenula.pratensis
## 1                0                     0                  0                 0
## 2                0                     0                  0                 0
## 3                0                     0                  0                 0
## 4                0                     0                  0                 0
## 5                0                     0                  0                 0
## 6                0                     0                  0                 0
##   Bellis.perennis Betula.pubescens Blackstonia.perfoliata
## 1               0                0                      0
## 2               0                0                      0
## 3               1                0                      0
## 4               0                0                      0
## 5               0                0                      0
## 6               0                0                      0
##   Brachythecium.albicans Brachythecium.glareosum Brachythecium.mildeanum
## 1                      0                       0                       0
## 2                      0                       0                       0
## 3                      0                       0                       0
## 4                      0                       0                       0
## 5                      0                       0                       0
## 6                      0                       0                       0
##   Brachythecium.rutabulum Briza.media Bromus.hordeaceus Bryum.c.f..caespiticium
## 1                       0           0                 0                       0
## 2                       0           0                 0                       0
## 3                       0           0                 0                       0
## 4                       0           0                 0                       0
## 5                       0           0                 0                       0
## 6                       0           0                 0                       0
##   Bryum.c.f..pallescens Bryum.capillare Bryum.spp. Calliergonella.cupsidata
## 1                     0               0          0                        0
## 2                     0               0          0                        0
## 3                     0               0         60                        0
## 4                     0               0          0                        0
## 5                     0               0          0                        0
## 6                     0               0          0                        0
##   Calypogeia.arguta Campanula.rotundifolia Carex.distans Carex.flacca
## 1                 0                      0             0            0
## 2                 0                      0             0            0
## 3                 0                      0             0            0
## 4                 0                     42             0            0
## 5                 0                      0             0            3
## 6                 0                      0             0            0
##   Carex.panicea Carlina.vulgaris Centaurea.nigra Centaurium.erythraea
## 1             0                0               0                    0
## 2             0                0               0                    0
## 3             1                0               0                    0
## 4             0                3               0                    0
## 5             0                2               1                    0
## 6             0                1               0                    0
##   Centaurium.littorale Centaurium.pulchellum Cerastium.fontanum
## 1                    0                     0                  0
## 2                    4                     0                  0
## 3                    0                     0                  0
## 4                    4                     0                  1
## 5                    5                     0                  0
## 6                    0                     0                  0
##   Chamaenerion.angustifolium Cirriphyllum.piliferum Cirsium.arvense
## 1                          0                      0               0
## 2                          0                      0               0
## 3                          0                      0               0
## 4                          0                      0               0
## 5                          0                      0               0
## 6                          0                      0               0
##   Cirsium.palustre Crepis.capillaris Cynosurus.cristatus Dactylis.glomerata
## 1                0                 0                   0                  0
## 2                0                 0                   0                  0
## 3                0                 0                   0                  0
## 4                0                 0                   0                  0
## 5                0                 0                   0                  0
## 6                0                 0                   0                  0
##   Dactylorhiza.fuchsii Danthonia.decumbens Daucus.carrota Dicranella.spp.
## 1                    0                   0              0               0
## 2                    0                   0              0               0
## 3                    0                   0              0               0
## 4                    0                   0              0               0
## 5                    0                   0              0               0
## 6                    0                   0              0               0
##   Dicranum.scoparium Epilobium.montanum Equisetum.arvense Equisteum.variegatum
## 1                  0                  0                 0                    0
## 2                  0                  0                 0                    0
## 3                  0                  0                 0                    0
## 4                  0                  0                10                   31
## 5                  0                  0                 0                    0
## 6                  0                  0                 0                    0
##   Erigeron.acer Euphrasia.agg Festuca.ovina Festuca.rubra Festuca.rubra.agg.
## 1             0             0             0            10                  0
## 2             0             0             0             0                  0
## 3             0             0             0             4                  0
## 4             0             0             0             2                  0
## 5             0            36             0            44                  0
## 6             0             0             0             0                  0
##   Filipendula.ulmaria Fissidens.adianthoides Fissidens.dubius Fissidens.exilis
## 1                   0                      0                0                0
## 2                   0                      0                0                0
## 3                   0                      0                0                0
## 4                   0                      0                0                0
## 5                   0                      0                0                0
## 6                   0                      0                0                0
##   Fragaria.vesca Galium.aparine Galium.arvense Galium.saxatile Galium.verum
## 1              0              0              0               0            0
## 2              0              0              0               0            0
## 3              0              0              0               0            0
## 4              0              0              0               0            0
## 5              0              0              0               0            0
## 6              0              0              0               0            0
##   Geum.urbanum Glechoma.hederacea Helicotrichon.spp. Heracleum.sphondylium
## 1            0                  0                  0                     0
## 2            0                  0                  0                     0
## 3            0                  0                  0                     0
## 4            0                  0                  0                     0
## 5            0                  0                  0                     0
## 6            0                  0                  0                     0
##   Hieracium.spp. Holcus.spp. Holcus.lanatus Holcus.mollis
## 1              0          47              0             0
## 2              0           0              0             0
## 3              0           0              0             0
## 4              0           0             18             0
## 5              0          23              0             0
## 6              0          78              0             0
##   Homalothecium.lutescens Hylocomium.splendens Hypericum.perforatum
## 1                       0                    0                    0
## 2                       0                    0                    0
## 3                       0                    0                    0
## 4                       0                    0                    0
## 5                       0                    0                    0
## 6                       0                    0                    0
##   Hypnum.cupressiforme Hypnum.imponens Hypnum.jutlandicum Hypochaeris.radicata
## 1                    0               0                  0                    0
## 2                    0               0                  0                    0
## 3                    0               0                  0                    0
## 4                  160               0                  0                    0
## 5                    0               0                  0                    0
## 6                    0               0                  0                    0
##   Kindbergia.praelonga Lathyrus.pratensis Leontodon.hispidus
## 1                    0                  0                  0
## 2                    0                  0                  0
## 3                    0                  0                  0
## 4                    0                  0                  0
## 5                    0                  0                 16
## 6                    0                  0                  2
##   Leontodon.saxatilis Leucanthemum.vulgare Linum.catharticum Lolium.perenne
## 1                   0                    2                 0              0
## 2                   0                    0                 2              0
## 3                   0                    2                 0              0
## 4                   0                    1                 0              0
## 5                   0                    6                 1              0
## 6                   0                    0                 6              0
##   Lophocolea.semiteres Lotus.corniculatus Luzula.multiflora Lysimachia.maritima
## 1                    0                  0                 0                   2
## 2                    0                  0                 0                   0
## 3                    0                  0                 0                   0
## 4                    0                  0                 0                   0
## 5                    0                 57                 0                   0
## 6                    0                  0                 0                   0
##   Medicago.lupulina Myosotis.arvensis Ononis.repens Oxalis.acetosella
## 1                 0                 0             0                 0
## 2                 0                 0             5                 0
## 3                 0                 0             1                 0
## 4                91                 0           111                 0
## 5                 0                 0             2                 0
## 6                 0                 0             0                 0
##   Pastinaca.sativa Pentaglottis.sempervirens Pillosella.officinarum
## 1                0                         0                      2
## 2                0                         0                      0
## 3                0                         0                      0
## 4                0                         0                     91
## 5                0                         0                     39
## 6                0                         0                      0
##   Plantago.coronopus Plantago.lanceolata Pleurozium.schreberi Poa.annua
## 1                  0                   0                    0         0
## 2                  0                   0                    0        69
## 3                  0                   0                    0        46
## 4                  0                   5                    0         0
## 5                 50                  20                    0        55
## 6                  0                   0                    0         0
##   Poa.spp. Polytrichum.commune Polytrichum.commune.agg. Polytrichum.formosum
## 1        0                   0                        0                    0
## 2        0                   0                        0                    0
## 3        0                   0                        0                    0
## 4        0                   0                        0                    0
## 5        0                   0                        0                    0
## 6        0                   0                        0                    0
##   Potentilla.reptans Prunella.vulgaris Pseudoscleropidum.purum
## 1                  0                 0                       0
## 2                  0                 0                       0
## 3                  0                 0                       0
## 4                  0                 0                       0
## 5                  0                 0                       0
## 6                  0                 0                       0
##   Pteridium.aquilinum Ranunculus.acris Ranunculus.parviflorus Ranunculus.repens
## 1                   0                0                      0                 0
## 2                   0                0                      0                 0
## 3                   0                0                      0                 0
## 4                   0                0                      0                 0
## 5                   0                0                      0                 0
## 6                   0                0                      0                 0
##   Reseda.lutea Rhinanthus.minor Rhizomnium.punctatum Rhytidadelphus.squarrosus
## 1            0                0                    0                         0
## 2            0                0                    0                         0
## 3            0                0                    0                         0
## 4            0                0                    0                         0
## 5            0                0                    0                         0
## 6            0                0                    0                         0
##   Rhytidadelphus.triquetris Rubus.fruticosus Sanguisorba.minor.spp.minor
## 1                         0                0                           0
## 2                         0                0                           0
## 3                         0                0                           0
## 4                         0                0                           0
## 5                         0                0                           0
## 6                         0                0                           0
##   Saniona.uncinata Sedum.anglicum Senecio.jacobaea Senecio.vulgaris
## 1                0              0                0                0
## 2                0              0                0                0
## 3                0              0                0                0
## 4                0              0                0                0
## 5                0              0                0                0
## 6                0              0                0                0
##   Sonchus.arvensis Stachys.sylvatica Stellaria.apetala Taraxacum.agg.
## 1                0                 0                 0              0
## 2                0                 0                 0              0
## 3                0                 0                 0              0
## 4                0                 0                 0              0
## 5                0                 0                 0              0
## 6                0                 0                 0              2
##   Thuidium.tamariscinum Thymus.polytrichus Trichostomum.crispulum
## 1                     0                  0                    150
## 2                     0                216                     30
## 3                     0                253                     60
## 4                     0                  0                      0
## 5                     0                  0                     70
## 6                     0                  7                      0
##   Trifolium.campestre Trifolium.dubium Trifolium.pratense Trifolium.repens
## 1                   0                0                  0                0
## 2                   0                0                  0                0
## 3                   0                0                  0                0
## 4                   0                0                  0                0
## 5                   0                0                  0                0
## 6                   0                0                  0                0
##   Trisetum.flavescens Tussilago.farfara Urtica.diocia Veronica.officinalis
## 1                   0                 0             0                    0
## 2                   0                 0             0                    0
## 3                   0                 0             0                    0
## 4                   0                 0             0                    0
## 5                   0                 3             0                    0
## 6                   0                 0             0                    0
##   Vicia.sativa Viola.riviniana Weissia.controversa Zygodon.stirtonii
## 1            0               0                   0                 0
## 2            0               0                   0                 0
## 3            0               0                   0                 0
## 4            0               0                   0                 0
## 5            0               0                   0                 0
## 6            0               0                   0                10
head(HodbarrowPC)
##       pH     SiO2    Al2O3     Fe2O3       CaO       MgO      Na2O       K2O
## 1 10.660 153318.7 46679.88  7833.566 265864.97 14111.040  2077.199  4067.724
## 2  8.381 324399.8 36782.90 26648.112  18867.84  5487.627  6379.969 14278.542
## 3  8.873 324399.8 37947.25 30005.354  27086.78  6754.002  6899.269 14029.497
## 4  8.806 284667.9 52660.41 25039.433  45096.99 13930.129 13353.424 14444.571
## 5 10.346 203334.2 43980.70 14128.395 162234.80  8201.288  8605.540  8052.433
## 6  9.966 134153.8 47579.61  7413.910 260862.13 12603.450  1854.642  2739.488
##       Cr2O3     TiO2       MnO      P2O5       SrO       BaO   LOI   Ag As  B
## 1  13.68405 1258.620 1781.2522  199.9742 338.23782 4746.9523 15.05 0.30  6 70
## 2  68.42024 2697.043  774.4575  999.8709  84.55946  716.5211 11.80 0.20 16 10
## 3  68.42024 2816.912  929.3490  999.8709  84.55946  716.5211  9.88 0.20 19 10
## 4 109.47239 3056.649  929.3490 1699.7805 169.11891 1343.4771 11.55 0.15  7 10
## 5  20.52607 1138.752 1239.1320  699.9096 169.11891 2866.0844 17.55 0.40 10 40
## 6  13.68405 1258.620 1471.4692  199.9742 253.67837 3134.7798 22.00 0.30  6 30
##     Be  Bi   Cd Co Cu Ga  Hg La Li  Mo Ni Pb    S  Sb Sc Th Tl U  V W Zn
## 1 11.4 1.5 0.25  1 17  5 0.5 40 80 0.5  5 74 7400 3.0 10 10  5 5  6 5 73
## 2  1.8 1.5 0.25  5 14  5 0.5 10 20 1.0 13 39  700 5.0  2 10  5 5 18 5 61
## 3  2.0 1.5 0.25  6 18  5 0.5 10 20 1.0 13 51  700 6.0  3 10  5 5 19 5 74
## 4  1.9 1.5 0.25 10 24 10 0.5 20 30 0.5 33 16 1100 1.5  3 10  5 5 31 5 46
## 5  6.8 1.5 0.25  2 22  5 0.5 20 40 0.5  6 56 5300 4.0  6 10  5 5  7 5 58
## 6 11.6 1.5 0.25  1 18  5 0.5 50 60 0.5  4 41 3500 3.0 12 10  5 5  4 5 51
##   Akermanite Albite Aluminium.oxide.hydroxide Anhydrite Aragonite Biotite
## 1          0      0                         0         0         0       0
## 2          0      0                         0         0         0       0
## 3          0      0                         0         0         0       0
## 4          0      1                         0         0         0       0
## 5          0      0                         0         0         0       0
## 6          0      0                         0         0         0       0
##   Birnessite Calcite Clinochlore Cuspidine Diaspore Dickite Gehlenite Goethite
## 1          0       1           0         0        0       0         1        0
## 2          0       0           0         0        0       0         0        0
## 3          0       0           0         0        0       0         0        0
## 4          0       0           0         0        0       0         0        0
## 5          0       1           0         1        0       0         1        0
## 6          0       1           0         0        0       1         0        0
##   Haematite Illite Kaolinite Langite Linnaeite Magnesioferrite Melilite
## 1         0      0         0       0         0               0        0
## 2         0      0         0       0         0               0        0
## 3         0      0         0       0         0               0        0
## 4         0      0         0       0         0               0        0
## 5         0      0         0       0         0               0        0
## 6         0      0         0       0         1               0        0
##   Merwinite Microcline Mullite Muscovite Orthoclase Orthopyroxene Periclase
## 1         0          0       0         0          0             0         0
## 2         0          0       0         0          0             1         0
## 3         0          0       0         0          0             0         0
## 4         0          0       0         0          1             0         0
## 5         0          0       0         0          0             0         0
## 6         0          0       0         0          0             0         0
##   Phengite Pseudowollastonite Quartz Staurolite Valentinite
## 1        0                  0      1          0           0
## 2        0                  0      1          0           0
## 3        0                  0      1          0           1
## 4        0                  0      1          0           0
## 5        0                  0      1          0           0
## 6        0                  0      0          0           0
rowSums(HodbarrowPS)
## [1] 213 396 617 577 433 106 216
#Again, ANOSIMs will be carried out to see if there are any statistically significant
#differences between plants in different concentrations of elements.

anoHSiO2 <- anosim(HodbarrowPS, HodbarrowPC$SiO2, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHSiO2
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$SiO2, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:     1 
##       Significance: 0.047619 
## 
## Permutation: free
## Number of permutations: 5039
#This ANOSIM has a high ANOSIM statistic of 1 and a low p value of 0.047619, showing that
#there are statistically significant differences between plants in different silicon
#concentrations on the Hodbarrow site.

#anoHAl2O3 <- anosim(HodbarrowPS, HodbarrowPC$Al2O3, distance = "bray", permutations = 9999)

#When this ANOSIM is run, the error message: "there should be replicates within groups"
#comes up. This error message comes up for another substrate variables for the Hodbarrow
#data. From now on, only variables that were tested successfully will be included.

anoHCr2O3 <- anosim(HodbarrowPS, HodbarrowPC$Cr2O3, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHCr2O3
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$Cr2O3, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.963 
##       Significance: 0.0095238 
## 
## Permutation: free
## Number of permutations: 5039
#This ANOSIM has a high R statistic of 0.963 and a low p value of 0.0095238. This shows that
#there are significant differences between plants growing in different concentrations of
#Cr2O3.

anoHTiO2 <- anosim(HodbarrowPS, HodbarrowPC$TiO2, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHTiO2
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$TiO2, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:   0.7 
##       Significance: 0.19048 
## 
## Permutation: free
## Number of permutations: 5039
anoHMnO <- anosim(HodbarrowPS, HodbarrowPC$MnO, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHMnO
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$MnO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.5263 
##       Significance: 0.91429 
## 
## Permutation: free
## Number of permutations: 5039
anoHP2O5 <- anosim(HodbarrowPS, HodbarrowPC$P2O5, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHP2O5
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$P2O5, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.963 
##       Significance: 0.0095238 
## 
## Permutation: free
## Number of permutations: 5039
#This ANOSIM has a high R statistic of 0.963 and a low p value of 0.0095238. There are
#significant differences between plants in different concentrations of P2O5 in
#Hodbarrow.

anoHSrO <- anosim(HodbarrowPS, HodbarrowPC$SrO, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHSrO
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$SrO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.5556 
##       Significance: 0.047619 
## 
## Permutation: free
## Number of permutations: 5039
#This ANOSIM has an R statistic of 0.5556 and a p value of 0.047619. This shows that there
#are significant differences between plants growing in different concentrations of SrO
#in Hodbarrow, although the R statistic indicates that this isn't quite as strong as the
#differences seen in, say, SiO2, or Cr2O3.

anoHBaO <- anosim(HodbarrowPS, HodbarrowPC$BaO, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHBaO
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$BaO, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.4737 
##       Significance: 0.15238 
## 
## Permutation: free
## Number of permutations: 5039
anoHAg <- anosim(HodbarrowPS, HodbarrowPC$Ag, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHAg
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$Ag, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.8947 
##       Significance: 0.028571 
## 
## Permutation: free
## Number of permutations: 5039
#This ANOSIM has a high R statistic of 0.8947 and a low p value of 0.028571. This 
#demonstrates that plants are significantly different in differing concentrations of Ag
#at Hodbarrow.

anoHAs <- anosim(HodbarrowPS, HodbarrowPC$As, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHAs
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$As, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:   0.7 
##       Significance: 0.19048 
## 
## Permutation: free
## Number of permutations: 5039
anoHB <- anosim(HodbarrowPS, HodbarrowPC$B, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHB
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$B, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: -0.1481 
##       Significance: 0.57143 
## 
## Permutation: free
## Number of permutations: 5039
anoHCo <- anosim(HodbarrowPS, HodbarrowPC$Co, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHCo
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$Co, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.8421 
##       Significance: 0.038095 
## 
## Permutation: free
## Number of permutations: 5039
#This ANOSIM has a high R statistic of 0.8421 and a low p value of 0.038095. This
#demonstrates that plants are significantly different in differing concentrations of Co at
#Hodbarrow.

anoHCu <- anosim(HodbarrowPS, HodbarrowPC$Cu, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHCu
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$Cu, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:  -0.4 
##       Significance: 0.71429 
## 
## Permutation: free
## Number of permutations: 5039
anoHNi <- anosim(HodbarrowPS, HodbarrowPC$Ni, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHNi
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$Ni, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:     1 
##       Significance: 0.047619 
## 
## Permutation: free
## Number of permutations: 5039
#This ANOSIM has a high R statistic of 1 and a low p value of 0.047619. This demonstrates
#significant differences between plants growing in different concentrations of Ni at
#Hodbarrow.

anoHS <- anosim(HodbarrowPS, HodbarrowPC$S, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHS
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$S, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:     1 
##       Significance: 0.047619 
## 
## Permutation: free
## Number of permutations: 5039
#With a high R statistic of 1 and a low p value of 0.047619, this ANOSIM shows that there
#are significant differences between plants growing in different concentraitons of S at
#Hodbarrow.

anoHSb <- anosim(HodbarrowPS, HodbarrowPC$Sb, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHSb
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$Sb, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R: 0.8421 
##       Significance: 0.038095 
## 
## Permutation: free
## Number of permutations: 5039
#This ANOSIM has a high R statistic of 0.8421 and a low p value of 0.038095, showing that
#plants significantly differ in different concentrations of Sb at Hodbarrow.

anoHSc <- anosim(HodbarrowPS, HodbarrowPC$Sc, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHSc
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$Sc, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:  -0.9 
##       Significance: 0.95238 
## 
## Permutation: free
## Number of permutations: 5039
anoHTi <- anosim(HodbarrowPS, HodbarrowPC$Ti, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHTi
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$Ti, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:   0.7 
##       Significance: 0.19048 
## 
## Permutation: free
## Number of permutations: 5039
anoHV <- anosim(HodbarrowPS, HodbarrowPC$V, distance = "bray", permutations = 9999)
## 'nperm' >= set of all permutations: complete enumeration.
## Set of permutations < 'minperm'. Generating entire set.
anoHV
## 
## Call:
## anosim(x = HodbarrowPS, grouping = HodbarrowPC$V, permutations = 9999,      distance = "bray") 
## Dissimilarity: bray 
## 
## ANOSIM statistic R:   0.9 
##       Significance: 0.095238 
## 
## Permutation: free
## Number of permutations: 5039
#After carrying ANOSIMs for all of the geochemical variables, several of them demonstrated
#significant differences in terms of their relation to plant growth. CCA plots will better
#represent the data than NMDS plots, so some will be generated now to find the most
#appropriate CCA for the data.
HodbarrowCCA <- cca(HodbarrowPS, HodbarrowPC)
## 
## Some constraints or conditions were aliased because they were redundant. This
## can happen if terms are linearly dependent (collinear): 'Na2O', 'K2O', 'Cr2O3',
## 'TiO2', 'MnO', 'P2O5', 'SrO', 'BaO', 'LOI', 'Ag', 'As', 'B', 'Be', 'Bi', 'Cd',
## 'Co', 'Cu', 'Ga', 'Hg', 'La', 'Li', 'Mo', 'Ni', 'Pb', 'S', 'Sb', 'Sc', 'Th',
## 'Tl', 'U', 'V', 'W', 'Zn', 'Akermanite', 'Albite', 'Aluminium.oxide.hydroxide',
## 'Anhydrite', 'Aragonite', 'Biotite', 'Birnessite', 'Calcite', 'Clinochlore',
## 'Cuspidine', 'Diaspore', 'Dickite', 'Gehlenite', 'Goethite', 'Haematite',
## 'Illite', 'Kaolinite', 'Langite', 'Linnaeite', 'Magnesioferrite', 'Melilite',
## 'Merwinite', 'Microcline', 'Mullite', 'Muscovite', 'Orthoclase',
## 'Orthopyroxene', 'Periclase', 'Phengite', 'Pseudowollastonite', 'Quartz',
## 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component
print(HodbarrowCCA)
## Call: cca(X = HodbarrowPS, Y = HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total           2.811      1.000     
## Constrained     2.811      1.000    6
## Unconstrained   0.000      0.000    0
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## Some constraints or conditions were aliased because they were redundant.
## This can happen if terms are linearly dependent (collinear): 'Na2O', 'K2O',
## 'Cr2O3', 'TiO2', 'MnO', 'P2O5', 'SrO', 'BaO', 'LOI', 'Ag', 'As', 'B', 'Be',
## 'Bi', 'Cd', 'Co', 'Cu', 'Ga', 'Hg', 'La', 'Li', 'Mo', 'Ni', 'Pb', 'S',
## 'Sb', 'Sc', 'Th', 'Tl', 'U', 'V', 'W', 'Zn', 'Akermanite', 'Albite',
## 'Aluminium.oxide.hydroxide', 'Anhydrite', 'Aragonite', 'Biotite',
## 'Birnessite', 'Calcite', 'Clinochlore', 'Cuspidine', 'Diaspore', 'Dickite',
## 'Gehlenite', 'Goethite', 'Haematite', 'Illite', 'Kaolinite', 'Langite',
## 'Linnaeite', 'Magnesioferrite', 'Melilite', 'Merwinite', 'Microcline',
## 'Mullite', 'Muscovite', 'Orthoclase', 'Orthopyroxene', 'Periclase',
## 'Phengite', 'Pseudowollastonite', 'Quartz', 'Staurolite', 'Valentinite'
## 
## The model is overfitted with no unconstrained (residual) component.
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5   CCA6 
## 0.9051 0.7597 0.5296 0.3423 0.1971 0.0769
plot(HodbarrowCCA)

HodbarrowCCA1 <- cca(HodbarrowPS ~ CaO + Al2O3 + SiO2,
                     data = HodbarrowPC)

print(HodbarrowCCA1)
## Call: cca(formula = HodbarrowPS ~ CaO + Al2O3 + SiO2, data = HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8108     1.0000     
## Constrained    2.1059     0.7492    3
## Unconstrained  0.7048     0.2508    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.9009 0.7536 0.4514 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.4050 0.2115 0.0883
plot(HodbarrowCCA1)

anova(HodbarrowCCA1)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ CaO + Al2O3 + SiO2, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)    
## Model     3   2.10594 2.9878  0.001 ***
## Residual  3   0.70484                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#High F statistic of 2.9878 and low p value of 0.001.

#With such a high F statistic, it may be tempting to say that this is the most suitable #CCA, but a few more can be constructed, including with some of the variables that #were shown to be significant in the ANOSIMs.

HodbarrowCCA2 <- cca(HodbarrowPS ~ SiO2 + Cr2O3 + P2O5,
                     data = HodbarrowPC)

print(HodbarrowCCA2)
## Call: cca(formula = HodbarrowPS ~ SiO2 + Cr2O3 + P2O5, data = HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8108     1.0000     
## Constrained    2.0587     0.7324    3
## Unconstrained  0.7521     0.2676    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.8796 0.7534 0.4257 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.3760 0.2961 0.0800
plot(HodbarrowCCA2)

anova(HodbarrowCCA2)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ SiO2 + Cr2O3 + P2O5, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)   
## Model     3   2.05870 2.7373  0.003 **
## Residual  3   0.75208                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#High F statistic of 2.7373 and low p value of 0.003.

HodbarrowCCA3 <- cca(HodbarrowPS ~ SrO + Co + Ni,
                     data = HodbarrowPC)

print(HodbarrowCCA3)
## Call: cca(formula = HodbarrowPS ~ SrO + Co + Ni, data = HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total           2.811      1.000     
## Constrained     1.748      0.622    3
## Unconstrained   1.063      0.378    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.8780 0.6717 0.1984 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.5164 0.3677 0.1785
plot(HodbarrowCCA3)

anova(HodbarrowCCA3)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ SrO + Co + Ni, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)  
## Model     3    1.7482 1.6452  0.075 .
## Residual  3    1.0626                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.6452 and p value of 0.05.

HodbarrowCCA3 <- cca(HodbarrowPS ~ SrO + Co + Ni,
                     data = HodbarrowPC)

print(HodbarrowCCA3)
## Call: cca(formula = HodbarrowPS ~ SrO + Co + Ni, data = HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total           2.811      1.000     
## Constrained     1.748      0.622    3
## Unconstrained   1.063      0.378    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.8780 0.6717 0.1984 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.5164 0.3677 0.1785
plot(HodbarrowCCA3)

anova(HodbarrowCCA3)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ SrO + Co + Ni, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)  
## Model     3    1.7482 1.6452  0.073 .
## Residual  3    1.0626                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.6452 and p value of 0.053.

HodbarrowCCA4 <- cca(HodbarrowPS ~ S + Sb + Ni,
                     data = HodbarrowPC)

print(HodbarrowCCA4)
## Call: cca(formula = HodbarrowPS ~ S + Sb + Ni, data = HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8108     1.0000     
## Constrained    1.8699     0.6653    3
## Unconstrained  0.9409     0.3347    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.8873 0.6816 0.3010 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.5717 0.2049 0.1643
plot(HodbarrowCCA4)

anova(HodbarrowCCA4)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ S + Sb + Ni, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)  
## Model     3   1.86990 1.9874   0.02 *
## Residual  3   0.94087                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#High F statistic of 1.9874 and p value of 0.015.

HodbarrowCCA5 <- cca(HodbarrowPS ~ Ag + Al2O3 + As,
                     data = HodbarrowPC)

print(HodbarrowCCA5)
## Call: cca(formula = HodbarrowPS ~ Ag + Al2O3 + As, data = HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8108     1.0000     
## Constrained    1.8945     0.6740    3
## Unconstrained  0.9163     0.3260    3
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3 
## 0.8562 0.7281 0.3102 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2    CA3 
## 0.4214 0.2884 0.2065
plot(HodbarrowCCA5)

anova(HodbarrowCCA5)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Ag + Al2O3 + As, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)   
## Model     3   1.89445 2.0674  0.006 **
## Residual  3   0.91632                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#High F statistic of 2.0674 and low p value of 0.001.

HodbarrowCCA6 <- cca(HodbarrowPS ~ Ag + Al2O3 + As + SiO2,
                     data = HodbarrowPC)

print(HodbarrowCCA6)
## Call: cca(formula = HodbarrowPS ~ Ag + Al2O3 + As + SiO2, data =
## HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8108     1.0000     
## Constrained    2.2526     0.8014    4
## Unconstrained  0.5582     0.1986    2
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4 
## 0.9044 0.7482 0.5126 0.0874 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2 
## 0.3508 0.2074
plot(HodbarrowCCA6)

anova(HodbarrowCCA6)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Ag + Al2O3 + As + SiO2, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)  
## Model     4   2.25255 2.0176  0.017 *
## Residual  2   0.55822                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#High F statistic of 2.0176 and low p value of 0.018.

HodbarrowCCA7 <- cca(HodbarrowPS ~ Ag + SrO + As + Cr2O3,
                     data = HodbarrowPC)

print(HodbarrowCCA7)
## Call: cca(formula = HodbarrowPS ~ Ag + SrO + As + Cr2O3, data =
## HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8108     1.0000     
## Constrained    2.3134     0.8230    4
## Unconstrained  0.4974     0.1770    2
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4 
## 0.8793 0.7505 0.4893 0.1942 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2 
## 0.3884 0.1090
plot(HodbarrowCCA7)

anova(HodbarrowCCA7)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Ag + SrO + As + Cr2O3, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)   
## Model     4   2.31341 2.3256   0.01 **
## Residual  2   0.49737                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#High F statistic of 2.3256 and low p value of 0.003.

HodbarrowCCA8 <- cca(HodbarrowPS ~ SiO2 + SrO + As + Cr2O3,
                     data = HodbarrowPC)

print(HodbarrowCCA8)
## Call: cca(formula = HodbarrowPS ~ SiO2 + SrO + As + Cr2O3, data =
## HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8108     1.0000     
## Constrained    2.1942     0.7807    4
## Unconstrained  0.6165     0.2193    2
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4 
## 0.8831 0.7572 0.3596 0.1944 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2 
## 0.4734 0.1431
plot(HodbarrowCCA8)

anova(HodbarrowCCA8)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ SiO2 + SrO + As + Cr2O3, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)  
## Model     4   2.19424 1.7795  0.049 *
## Residual  2   0.61653                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.7795 and p value of 0.024.

HodbarrowCCA9 <- cca(HodbarrowPS ~ Ag + SrO + As + P2O5,
                     data = HodbarrowPC)

print(HodbarrowCCA9)
## Call: cca(formula = HodbarrowPS ~ Ag + SrO + As + P2O5, data = HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8108     1.0000     
## Constrained    2.3322     0.8297    4
## Unconstrained  0.4786     0.1703    2
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4 
## 0.8963 0.7483 0.4980 0.1896 
## 
## Eigenvalues for unconstrained axes:
##    CA1    CA2 
## 0.3691 0.1094
plot(HodbarrowCCA9)

anova(HodbarrowCCA9)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Ag + SrO + As + P2O5, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)   
## Model     4   2.33219 2.4366  0.004 **
## Residual  2   0.47858                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#High F statistic of 2.4366 and low p value of 0.005.

HodbarrowCCA10 <- cca(HodbarrowPS ~ Ag + SrO + As + Cr2O3 + SiO2,
                     data = HodbarrowPC)

print(HodbarrowCCA10)
## Call: cca(formula = HodbarrowPS ~ Ag + SrO + As + Cr2O3 + SiO2, data =
## HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total         2.81078    1.00000     
## Constrained   2.58639    0.92017    5
## Unconstrained 0.22438    0.07983    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5 
## 0.8831 0.7596 0.5080 0.2421 0.1937 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.22438
plot(HodbarrowCCA10)

anova(HodbarrowCCA10)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Ag + SrO + As + Cr2O3 + SiO2, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)  
## Model     5   2.58639 2.3054  0.027 *
## Residual  1   0.22438                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 2.3054 and p value of 0.008.

HodbarrowCCA11 <- cca(HodbarrowPS ~ Cd + Mo + BaO + V + Na2O,
                      data = HodbarrowPC)

print(HodbarrowCCA11)
## Call: cca(formula = HodbarrowPS ~ Cd + Mo + BaO + V + Na2O, data =
## HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total         2.81078    1.00000     
## Constrained   2.72396    0.96911    5
## Unconstrained 0.08682    0.03089    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5 
## 0.9037 0.7596 0.5262 0.3394 0.1950 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.08682
plot(HodbarrowCCA11)

anova(HodbarrowCCA11)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Cd + Mo + BaO + V + Na2O, data = HodbarrowPC)
##          Df ChiSquare     F Pr(>F)  
## Model     5   2.72396 6.275   0.03 *
## Residual  1   0.08682               
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Particularly high F statistic of 6.275 and p value of 0.001.

HodbarrowCCA12 <- cca(HodbarrowPS ~ Cr2O3 + Be + BaO + Zn + TiO2,
                      data = HodbarrowPC)

print(HodbarrowCCA12)
## Call: cca(formula = HodbarrowPS ~ Cr2O3 + Be + BaO + Zn + TiO2, data =
## HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8108     1.0000     
## Constrained    2.5217     0.8971    5
## Unconstrained  0.2891     0.1029    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5 
## 0.9047 0.7359 0.5184 0.2112 0.1515 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.28911
plot(HodbarrowCCA12)

anova(HodbarrowCCA12)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Cr2O3 + Be + BaO + Zn + TiO2, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)  
## Model     5   2.52167 1.7444  0.069 .
## Residual  1   0.28911                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.7444 and p value of 0.053.

HodbarrowCCA13 <- cca(HodbarrowPS ~ Cr2O3 + Be + BaO + SiO2 + TiO2,
                      data = HodbarrowPC)

print(HodbarrowCCA13)
## Call: cca(formula = HodbarrowPS ~ Cr2O3 + Be + BaO + SiO2 + TiO2, data =
## HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total         2.81078    1.00000     
## Constrained   2.72222    0.96850    5
## Unconstrained 0.08855    0.03150    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5 
## 0.9031 0.7595 0.5294 0.3337 0.1966 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.08855
plot(HodbarrowCCA13)

anova(HodbarrowCCA13)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Cr2O3 + Be + BaO + SiO2 + TiO2, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)   
## Model     5   2.72222 6.1483  0.002 **
## Residual  1   0.08855                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#High F statistic of 6.1483 and p value of 0.001.

HodbarrowCCA14 <- cca(HodbarrowPS ~ Cr2O3 + SiO2 + BaO + Zn + TiO2,
                      data = HodbarrowPC)

print(HodbarrowCCA14)
## Call: cca(formula = HodbarrowPS ~ Cr2O3 + SiO2 + BaO + Zn + TiO2, data =
## HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total         2.81078    1.00000     
## Constrained   2.63479    0.93739    5
## Unconstrained 0.17598    0.06261    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5 
## 0.9045 0.7532 0.4861 0.2961 0.1949 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.17598
plot(HodbarrowCCA14)

anova(HodbarrowCCA14)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Cr2O3 + SiO2 + BaO + Zn + TiO2, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)  
## Model     5   2.63479 2.9944  0.018 *
## Residual  1   0.17598                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#High F statistic of 2.9944 and p value of 0.006.

HodbarrowCCA15 <- cca(HodbarrowPS ~ Cr2O3 + SiO2 + BaO + TiO2 + pH,
                      data = HodbarrowPC)

print(HodbarrowCCA15)
## Call: cca(formula = HodbarrowPS ~ Cr2O3 + SiO2 + BaO + TiO2 + pH, data =
## HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8108     1.0000     
## Constrained    2.5082     0.8924    5
## Unconstrained  0.3026     0.1076    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5 
## 0.9035 0.7506 0.3828 0.2748 0.1965 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.30257
plot(HodbarrowCCA15)

anova(HodbarrowCCA15)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Cr2O3 + SiO2 + BaO + TiO2 + pH, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)  
## Model     5   2.50821 1.6579  0.096 .
## Residual  1   0.30257                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#F statistic of 1.6579 and p value of 0.052.

HodbarrowCCA16 <- cca(HodbarrowPS ~ Cr2O3 + SiO2 + Be + TiO2 + pH,
                      data = HodbarrowPC)

print(HodbarrowCCA16)
## Call: cca(formula = HodbarrowPS ~ Cr2O3 + SiO2 + Be + TiO2 + pH, data =
## HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total          2.8108     1.0000     
## Constrained    2.5183     0.8959    5
## Unconstrained  0.2925     0.1041    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5 
## 0.9050 0.7591 0.4787 0.2668 0.1087 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.29251
plot(HodbarrowCCA16)

anova(HodbarrowCCA16)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Cr2O3 + SiO2 + Be + TiO2 + pH, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)  
## Model     5   2.51827 1.7218  0.083 .
## Residual  1   0.29251                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#This CCA has a somewhat high F statistic of 1.7218 and a p value of 0.056.

HodbarrowCCA17 <- cca(HodbarrowPS ~ Na2O + SiO2 + Be + BaO + TiO2,
                      data = HodbarrowPC)

print(HodbarrowCCA17)
## Call: cca(formula = HodbarrowPS ~ Na2O + SiO2 + Be + BaO + TiO2, data =
## HodbarrowPC)
## 
## -- Model Summary --
## 
##               Inertia Proportion Rank
## Total         2.81078    1.00000     
## Constrained   2.70680    0.96301    5
## Unconstrained 0.10397    0.03699    1
## 
## Inertia is scaled Chi-square
## 
## -- Note --
## 
## 106 species (variables) deleted due to missingness.
## 
## -- Eigenvalues --
## 
## Eigenvalues for constrained axes:
##   CCA1   CCA2   CCA3   CCA4   CCA5 
## 0.8977 0.7589 0.5140 0.3406 0.1955 
## 
## Eigenvalues for unconstrained axes:
##     CA1 
## 0.10397
plot(HodbarrowCCA17)

anova(HodbarrowCCA17)
## Set of permutations < 'minperm'. Generating entire set.
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 5039
## 
## Model: cca(formula = HodbarrowPS ~ Na2O + SiO2 + Be + BaO + TiO2, data = HodbarrowPC)
##          Df ChiSquare      F Pr(>F)   
## Model     5   2.70680 5.2067  0.008 **
## Residual  1   0.10397                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#This CCA has a high F statistic of 5.2067 and a low p value of 0.003.

#After doing a few more CCAs, the one with the highest F statistic (6.1483) is #HodbarrowCCA13. The p value of this one is also low, at 0.001. #The plot for this CCA looks OK, but it can be modified to make it easier #to interpret what is going on with some of the different plant species and communities.

options(max.print=1000000)

HodbarrowCCA13$CCA$v
##                              CCA1         CCA2         CCA3       CCA4
## Anthoxanthum.odoratum  -1.8808682  0.515930843 -0.144904225 -0.1398460
## Anthyllis.vulneraria    0.8513919  1.041042224  0.226654799 -0.5136023
## Bellis.perennis         0.9116973  1.047100739  0.187480527 -0.7875399
## Bryum.spp.              0.9116973  1.047100739  0.187480527 -0.7875399
## Campanula.rotundifolia -1.8808682  0.515930843 -0.144904225 -0.1398460
## Carex.flacca            0.1419301 -1.586688931  1.350916103  0.1033922
## Carex.panicea           0.9116973  1.047100739  0.187480527 -0.7875399
## Carlina.vulgaris       -0.3164334 -1.387531027  0.971548823 -1.3666677
## Centaurea.nigra         0.1630491 -1.163737359  0.694471519  1.7013144
## Centaurium.littorale   -0.2745504 -0.134095913  0.468430358  0.4684153
## Cerastium.fontanum     -1.8808682  0.515930843 -0.144904225 -0.1398460
## Dactylis.glomerata      0.1102516 -2.221116290  2.335582980 -2.2934911
## Equisetum.arvense      -1.8808682  0.515930843 -0.144904225 -0.1398460
## Equisteum.variegatum   -1.8808682  0.515930843 -0.144904225 -0.1398460
## Euphrasia.agg           0.1386204 -1.652972387  1.453791747 -0.1470284
## Festuca.rubra           0.1705365 -1.375764205  0.923216137  0.3245228
## Holcus.spp.             0.3971040 -1.412117935 -2.719427123 -1.1910307
## Holcus.lanatus         -1.8808682  0.515930843 -0.144904225 -0.1398460
## Hypnum.cupressiforme   -1.8808682  0.515930843 -0.144904225 -0.1398460
## Leontodon.hispidus      0.1346201 -1.927026434  1.675332121 -1.3244222
## Leucanthemum.vulgare    0.1775724 -0.555027518 -0.004501243  1.3982298
## Linum.catharticum       0.3192237 -1.513567295 -0.844415940 -2.6519716
## Lotus.corniculatus      0.1493355 -1.438381237  1.120734236  0.6637026
## Lysimachia.maritima     0.5162381 -0.866505432 -2.223199809  3.4437837
## Medicago.lupulina      -1.8808682  0.515930843 -0.144904225 -0.1398460
## Ononis.repens          -1.7150902  0.513540930 -0.107948056 -0.0989720
## Pillosella.officinarum -1.2406638 -0.001280767  0.071603827  0.4584307
## Plantago.coronopus      0.1630491 -1.163737359  0.694471519  1.7013144
## Plantago.lanceolata    -0.0545567 -1.576064174  1.498089179 -0.6145219
## Poa.annua               0.5789231  0.322731125  0.410337564  0.4290675
## Prunella.vulgaris       0.1102516 -2.221116290  2.335582980 -2.2934911
## Taraxacum.agg.          0.3241573 -1.880643518 -2.336923359 -3.8947193
## Thymus.polytrichus      0.8033777  0.996376956  0.181773550 -0.3850685
## Trichostomum.crispulum  0.5297032 -0.380228576 -0.850468946  1.9199615
## Trifolium.pratense      0.1102516 -2.221116290  2.335582980 -2.2934911
## Tussilago.farfara       0.1630491 -1.163737359  0.694471519  1.7013144
## Zygodon.stirtonii       0.4311102 -1.710407131 -4.673176528 -4.6953334
##                               CCA5
## Anthoxanthum.odoratum  -0.23832396
## Anthyllis.vulneraria   -0.15012954
## Bellis.perennis        -0.37461452
## Bryum.spp.             -0.37461452
## Campanula.rotundifolia -0.23832396
## Carex.flacca            0.76411901
## Carex.panicea          -0.37461452
## Carlina.vulgaris       -1.13534521
## Centaurea.nigra         3.56015015
## Centaurium.littorale    1.08867477
## Cerastium.fontanum     -0.23832396
## Dactylis.glomerata     -3.42992771
## Equisetum.arvense      -0.23832396
## Equisteum.variegatum   -0.23832396
## Euphrasia.agg           0.32593502
## Festuca.rubra          -0.01541101
## Holcus.spp.             0.42885209
## Holcus.lanatus         -0.23832396
## Hypnum.cupressiforme   -0.23832396
## Leontodon.hispidus     -1.39073989
## Leucanthemum.vulgare    1.07181145
## Linum.catharticum       0.06404070
## Lotus.corniculatus      1.74454551
## Lysimachia.maritima    -4.29171098
## Medicago.lupulina      -0.23832396
## Ononis.repens          -0.14645693
## Pillosella.officinarum  0.82253753
## Plantago.coronopus      3.56015015
## Plantago.lanceolata    -0.54549112
## Poa.annua               1.23552120
## Prunella.vulgaris      -3.42992771
## Taraxacum.agg.          0.75314264
## Thymus.polytrichus      0.04963641
## Trichostomum.crispulum -1.30110842
## Trifolium.pratense     -3.42992771
## Tussilago.farfara       3.56015015
## Zygodon.stirtonii       2.84467781
## attr(,"na.action")
##               Agrostis.spp.             Agrostis.canina 
##                           1                           2 
##           Alchemilla.mollis         Alopercus.pratensis 
##                           3                           4 
##         Angelica.sylvestris            Aphanes.arvensis 
##                           5                           8 
##       Arrhenatherum.elatius          Atrichum.undulatum 
##                           9                          10 
##           Avenula.pratensis            Betula.pubescens 
##                          11                          13 
##      Blackstonia.perfoliata      Brachythecium.albicans 
##                          14                          15 
##     Brachythecium.glareosum     Brachythecium.mildeanum 
##                          16                          17 
##     Brachythecium.rutabulum                 Briza.media 
##                          18                          19 
##           Bromus.hordeaceus     Bryum.c.f..caespiticium 
##                          20                          21 
##       Bryum.c.f..pallescens             Bryum.capillare 
##                          22                          23 
##    Calliergonella.cupsidata           Calypogeia.arguta 
##                          25                          26 
##               Carex.distans        Centaurium.erythraea 
##                          28                          33 
##       Centaurium.pulchellum  Chamaenerion.angustifolium 
##                          35                          37 
##      Cirriphyllum.piliferum             Cirsium.arvense 
##                          38                          39 
##            Cirsium.palustre           Crepis.capillaris 
##                          40                          41 
##         Cynosurus.cristatus        Dactylorhiza.fuchsii 
##                          42                          44 
##         Danthonia.decumbens              Daucus.carrota 
##                          45                          46 
##             Dicranella.spp.          Dicranum.scoparium 
##                          47                          48 
##          Epilobium.montanum               Erigeron.acer 
##                          49                          52 
##               Festuca.ovina          Festuca.rubra.agg. 
##                          54                          56 
##         Filipendula.ulmaria      Fissidens.adianthoides 
##                          57                          58 
##            Fissidens.dubius            Fissidens.exilis 
##                          59                          60 
##              Fragaria.vesca              Galium.aparine 
##                          61                          62 
##              Galium.arvense             Galium.saxatile 
##                          63                          64 
##                Galium.verum                Geum.urbanum 
##                          65                          66 
##          Glechoma.hederacea          Helicotrichon.spp. 
##                          67                          68 
##       Heracleum.sphondylium              Hieracium.spp. 
##                          69                          70 
##               Holcus.mollis     Homalothecium.lutescens 
##                          73                          74 
##        Hylocomium.splendens        Hypericum.perforatum 
##                          75                          76 
##             Hypnum.imponens          Hypnum.jutlandicum 
##                          78                          79 
##        Hypochaeris.radicata        Kindbergia.praelonga 
##                          80                          81 
##          Lathyrus.pratensis         Leontodon.saxatilis 
##                          82                          84 
##              Lolium.perenne        Lophocolea.semiteres 
##                          87                          88 
##           Luzula.multiflora           Myosotis.arvensis 
##                          90                          93 
##           Oxalis.acetosella            Pastinaca.sativa 
##                          95                          96 
##   Pentaglottis.sempervirens        Pleurozium.schreberi 
##                          97                         101 
##                    Poa.spp.         Polytrichum.commune 
##                         103                         104 
##    Polytrichum.commune.agg.        Polytrichum.formosum 
##                         105                         106 
##          Potentilla.reptans     Pseudoscleropidum.purum 
##                         107                         109 
##         Pteridium.aquilinum            Ranunculus.acris 
##                         110                         111 
##      Ranunculus.parviflorus           Ranunculus.repens 
##                         112                         113 
##                Reseda.lutea            Rhinanthus.minor 
##                         114                         115 
##        Rhizomnium.punctatum   Rhytidadelphus.squarrosus 
##                         116                         117 
##   Rhytidadelphus.triquetris            Rubus.fruticosus 
##                         118                         119 
## Sanguisorba.minor.spp.minor            Saniona.uncinata 
##                         120                         121 
##              Sedum.anglicum            Senecio.jacobaea 
##                         122                         123 
##            Senecio.vulgaris            Sonchus.arvensis 
##                         124                         125 
##           Stachys.sylvatica           Stellaria.apetala 
##                         126                         127 
##       Thuidium.tamariscinum         Trifolium.campestre 
##                         129                         132 
##            Trifolium.dubium            Trifolium.repens 
##                         133                         135 
##         Trisetum.flavescens               Urtica.diocia 
##                         136                         138 
##        Veronica.officinalis                Vicia.sativa 
##                         139                         140 
##             Viola.riviniana         Weissia.controversa 
##                         141                         142 
## attr(,"class")
## [1] "exclude"
#The "v values" show the positions of individual species on the graph, with the CCA1 value
#representing the x axis and the CCA2 value representing the y axis, in the case of the
#graph created in R.

plot(HodbarrowCCA13, xlim = c(-5, 5), ylim = c(-5, 5)) 

#Increasing the xlim and ylim to give more room for writing on graph

plot(HodbarrowCCA13, choices = c(1,2), display = c("wa", "bp"), xlim = c(-4, 3),
     ylim = c(-3, 2))

#Increasing the xlim and ylim to give more room for writing on graph Note that Community
#2 and Community 3 are grouped/clustered together in this CCA plot and that Communities
#1, 5, 6 and 7 are grouped together.

points(x = -1.8808682 , y = 0.515930843, pch = 15, col = "black")

#This point represents Equisetum variegatum

text('E. variegatum', x = -1.8808682, y = 0.515930843, cex = 0.88, pos = 2, col = "black")

#Adding text to this point.

points(x = 0.5789231 , y = 0.322731125, pch = 15, col = "black")

#This point represents Poa annua

text('P. annua', x = 0.5789231 , y = 0.322731125, cex = 0.88, pos = 2, col = "black")

#Adding text to this point

points(x = 0.1102516, y = -2.221116290, pch = 15, col = "black")

#This point represents Trifolium pratense

text('T. pratense', x = 0.1102516, y = -2.221116290, cex = 0.88, pos = 2, col = "black")

#Adding text to this point

points(x = 0.3192237, y = -1.513567295, pch = 15, col = "black")

#This point represents Linum catharticum

text('L. catharticum', x = 0.3192237, y = -1.513567295, cex = 0.88, pos = 2, col = "black")

#Adding text to this point

points(x = 0.8513919, y = 1.041042224, pch = 15, col = "black")

#This point represents Anthyllis vulneraria

text('A. vulneraria', x = 0.8513919, y = 1.041042224, cex = 0.88, pos = 2, col = "black")

#Adding text to this point