Canonical Correspondence Analysis in R using the vegan library

cca.r

library(vegan)
library(labdsv)

data(varespec)
data(varechem)

vare.cca <- cca(varespec ~ Baresoil+Humdepth+pH+N+P+K+Ca+Mg+S+Al+Fe, data=varechem)
vare.cca
plot(vare.cca)
summary(vare.cca)

// See also http://ecology.msu.montana.edu/labdsv/R/labs/lab12/lab12.html

cca_example.png

example_output.txt

> vare.cca
Call: cca(formula = varespec ~ Baresoil + Humdepth + pH + N + P + K + Ca + Mg + S + Al + Fe, data = varechem)

              Inertia Proportion Rank
Total          2.0832     1.0000     
Constrained    1.2154     0.5834   11
Unconstrained  0.8678     0.4166   12
Inertia is mean squared contingency coefficient 

Eigenvalues for constrained axes:
    CCA1     CCA2     CCA3     CCA4     CCA5     CCA6     CCA7     CCA8     CCA9    CCA10    CCA11 
0.410865 0.255619 0.146158 0.131515 0.091575 0.078525 0.060261 0.019134 0.008944 0.006849 0.005946 

Eigenvalues for unconstrained axes:
     CA1      CA2      CA3      CA4      CA5      CA6      CA7      CA8      CA9     CA10     CA11     CA12 
0.253513 0.151934 0.126683 0.093370 0.075393 0.049632 0.037929 0.026435 0.021758 0.014304 0.009052 0.007806 


> plot(vare.cca)
> summary(vare.cca)

Call:
cca(formula = varespec ~ Baresoil + Humdepth + pH + N + P + K +      Ca + Mg + S + Al + Fe, data = varechem) 

Partitioning of mean squared contingency coefficient:
              Inertia Proportion
Total          2.0832     1.0000
Constrained    1.2154     0.5834
Unconstrained  0.8678     0.4166

Eigenvalues, and their contribution to the mean squared contingency coefficient 

Importance of components:
                        CCA1   CCA2    CCA3    CCA4    CCA5    CCA6    CCA7    CCA8
Eigenvalue            0.4109 0.2556 0.14616 0.13152 0.09158 0.07852 0.06026 0.01913
Proportion Explained  0.1972 0.1227 0.07016 0.06313 0.04396 0.03769 0.02893 0.00918
Cumulative Proportion 0.1972 0.3199 0.39009 0.45322 0.49718 0.53488 0.56381 0.57299
                          CCA9    CCA10    CCA11    CA1     CA2     CA3     CA4     CA5
Eigenvalue            0.008944 0.006849 0.005946 0.2535 0.15193 0.12668 0.09337 0.07539
Proportion Explained  0.004290 0.003290 0.002850 0.1217 0.07293 0.06081 0.04482 0.03619
Cumulative Proportion 0.577280 0.580570 0.583430 0.7051 0.77805 0.83886 0.88368 0.91988
                          CA6     CA7     CA8     CA9    CA10     CA11     CA12
Eigenvalue            0.04963 0.03793 0.02643 0.02176 0.01430 0.009052 0.007806
Proportion Explained  0.02382 0.01821 0.01269 0.01044 0.00687 0.004350 0.003750
Cumulative Proportion 0.94370 0.96191 0.97460 0.98504 0.99191 0.996250 1.000000

Accumulated constrained eigenvalues
Importance of components:
                        CCA1   CCA2   CCA3   CCA4    CCA5    CCA6    CCA7    CCA8
Eigenvalue            0.4109 0.2556 0.1462 0.1315 0.09158 0.07852 0.06026 0.01913
Proportion Explained  0.3381 0.2103 0.1203 0.1082 0.07535 0.06461 0.04958 0.01574
Cumulative Proportion 0.3381 0.5484 0.6686 0.7768 0.85218 0.91679 0.96637 0.98211
                          CCA9    CCA10    CCA11
Eigenvalue            0.008944 0.006849 0.005946
Proportion Explained  0.007360 0.005630 0.004890
Cumulative Proportion 0.989470 0.995110 1.000000

Scaling 2 for species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions


Species scores

              CCA1     CCA2     CCA3     CCA4      CCA5     CCA6
Cal.vul  0.2579826 -0.80872  1.94560 -0.35626  0.697113 -0.74258
Emp.nig -0.2704679 -0.05299 -0.14437 -0.32584 -0.170125 -0.04192
Led.pal -0.9762750 -0.37214 -0.06644 -0.75402 -0.697058  0.06306
Vac.myr -1.3055169 -0.11479  0.17137  0.27104 -0.599337  0.07048
Vac.vit -0.1929037  0.08757 -0.21288 -0.35303 -0.066669 -0.10932
Pin.syl  0.2380445  0.22966  0.05686 -0.39593 -0.019382  0.07840
Des.fle -1.4062903  0.38398  0.39272  0.39030 -0.101391  0.30965
Bet.pub -0.5960443 -0.95617 -0.72698 -1.67618 -1.588060 -0.32047
Vac.uli  0.3926825 -0.94198 -0.39399  0.58151 -0.228095 -0.14642
Dip.mon  0.0229110 -0.49673 -0.89897 -0.40174 -0.174258 -0.26730
Dic.sp  -0.4868957  0.65851 -1.26929  0.02094  1.419951 -0.57922
Dic.fus -0.4861256 -0.47490  0.52892 -0.51872  0.229919  0.59969
Dic.pol -0.3223530 -0.20367 -1.05718 -0.83490 -0.119395 -0.73626
Hyl.spl -1.8827323  0.65465  0.49959  1.53295 -0.308169  0.16247
Ple.sch -0.9252145  0.28944  0.09530  0.27152  0.053829 -0.02879
Pol.pil  0.2594323 -0.52462 -0.49858  0.08717  0.163650  0.43618
Pol.jun -0.7366157  0.12464 -0.27517 -0.14649 -0.314192  0.31794
Pol.com -0.9458638 -0.14755 -0.27373 -0.71188 -0.855045 -0.28475
Poh.nut -0.0348872  0.21735 -0.33522 -0.36923  0.179971 -0.30020
Pti.cil -0.5533110 -0.80045 -0.73937 -1.41351 -1.316239 -0.52927
Bar.lyc -0.5655746 -1.05360 -0.79808 -1.74760 -1.740288 -0.58626
Cla.arb  0.3082534 -0.56549 -0.03583  0.08219 -0.096060 -0.13535
Cla.ran  0.4695611 -0.53152 -0.16623  0.29331  0.037571  0.13895
Cla.ste  0.7627157  0.70289  0.12199 -0.02713 -0.053315  0.10624
Cla.unc -0.0840257 -0.04106 -0.16775 -0.54249  0.443329 -0.24384
Cla.coc  0.1998745 -0.11892  0.05746 -0.11248  0.073434  0.09607
Cla.cor -0.3377207  0.00630 -0.30418 -0.13082  0.007785 -0.09738
Cla.gra -0.0591848 -0.14946 -0.27214 -0.18229  0.113776 -0.19158
Cla.fim -0.0005966 -0.11638  0.03219 -0.27266 -0.185276  0.01141
Cla.cri -0.2353142 -0.13014  0.04825 -0.44966 -0.082457 -0.30900
Cla.chl  0.2960198  0.43031 -0.44880 -0.45712 -0.026098 -0.32614
Cla.bot -0.6121890 -0.67705 -0.17531 -1.05814 -0.701290 -0.74162
Cla.ama  0.0339234 -0.89659 -1.10581 -0.06753  0.078437  0.24184
Cla.sp   0.6893702  0.73032  0.49452 -0.39382  0.126202 -0.21620
Cet.eri  0.2703176  0.10341 -0.30842 -0.06482  0.593267 -0.44989
Cet.isl  0.1448207  0.10344 -0.31552 -0.70305 -0.482515 -0.22317
Cet.niv  1.3069886 -0.01489  0.54845  1.61791 -1.099398 -2.15267
Nep.arc -0.8040582  0.39185 -0.06934 -0.02375 -0.746439  1.04971
Ste.sp   0.2935602 -1.44392 -0.78477  0.79952  0.694834  0.72962
Pel.aph -0.6296777  0.05166 -0.34405 -0.15437 -0.058790 -0.21384
Ich.eri  0.3228067 -1.83898 -0.44899  0.64843  0.595119  0.78301
Cla.cer  0.9088477  0.22411  0.50813  1.00260 -0.582433 -0.84668
Cla.def -0.3460925 -0.21145 -0.11090 -0.54258  0.007175 -0.33724
Cla.phy  0.7223026  1.12784 -0.05001 -0.23188  0.099363  0.06092


Site scores (weighted averages of species scores)

      CCA1    CCA2     CCA3      CCA4     CCA5     CCA6
18  0.2368 -1.0455 -0.79083 -0.149031 -0.49251 -0.35212
15 -0.9799 -0.2750  0.34407  0.111139  0.63356  0.30849
24 -1.0983  0.8478 -2.51016 -0.080535  4.40120 -2.69293
27 -1.6399  0.4846  0.31083  1.033926 -0.68668  0.16045
23 -0.6573 -0.3813 -0.70171 -0.837942 -0.50965 -0.35934
19 -0.2220  0.6886 -0.03737 -0.002568 -0.65742  0.07187
22 -1.1371 -0.7562  1.68441 -1.251373  0.68408  1.82825
16 -0.7322 -0.9683  1.38438 -0.848066  1.09474  1.52365
28 -2.4224  0.8605  0.77192  2.459293 -1.07010  0.02053
13  0.5930 -1.4057  2.91790 -0.312366  1.59649 -2.08999
14 -0.3296 -0.8773  0.53603 -1.974878  1.81909 -0.90880
20 -0.5440 -0.3236 -0.58922 -0.198890  0.30072 -0.50529
25 -1.2792  0.4454 -1.17274 -0.360068  1.82086  0.33613
7   0.7264 -1.9319 -0.98918  1.155440 -0.49232 -0.08616
5   0.9323 -2.3201 -1.39730  2.072908  0.83123  1.69279
6   0.7454 -1.2134 -0.56548  0.372969 -0.26442 -0.15445
3   1.3118  0.5893 -0.06894  0.401225 -0.39972  0.94502
4   1.3726 -0.1616  0.83676  1.878597 -1.28329 -3.05924
2   1.3068  1.3075  0.11566 -0.055773 -0.47463  1.05104
9   1.1513  1.9030  0.25604 -0.576516 -0.64079  0.50208
12  0.9003  1.2149  0.03147 -0.437409 -0.44022  0.54418
10  1.2566  1.7341  0.25151 -0.507033 -0.60207  0.74947
11  0.4809  0.1232 -0.01664  0.339108  0.09187  0.24062
21 -0.8258 -0.3306 -1.27405 -2.712570 -3.96294 -1.33584


Site constraints (linear combinations of constraining variables)

       CCA1     CCA2      CCA3     CCA4     CCA5     CCA6
18 -0.51001 -0.86277 -1.265868 -0.84832  0.00585 -0.55362
15 -0.11359  0.47962  0.292164 -0.71983 -1.13275 -0.12336
24 -0.22365  0.90898 -2.201280  0.15538  2.96165 -1.67268
27 -1.64472  0.76232  0.420020  0.74263 -0.06008  0.22434
23 -1.32539 -0.30282 -0.919558 -0.37197  0.23629 -0.78394
19 -1.07981  0.11303 -0.113499 -0.60422 -0.19793 -1.29585
22 -0.80792 -0.42650  1.084574 -0.98064  1.21790  1.50140
16 -0.09523 -1.62392  0.407793 -0.06884 -0.07282  0.33619
28 -2.23615  0.64537  0.663728  2.48585 -0.46791  0.25333
13  0.42015 -1.10098  3.235920 -0.54956  1.29688 -1.38806
14 -0.14558 -0.43109  0.310536 -0.84389  0.19863 -0.03026
20 -0.46785  0.19132 -0.309976 -1.55804 -0.35312 -0.83013
25 -0.94343  0.48338 -0.020181 -0.08962 -0.75201  1.14075
7   1.13410 -1.71592 -0.683778  1.28206 -0.45511 -0.70628
5   0.46572 -2.30802 -1.130203  1.25890  1.45704  1.70523
6   0.86525  0.07408 -0.448437 -0.03867 -0.80286  1.09713
3   1.05262  0.42467 -0.654573  0.68815 -1.10660  0.89967
4   1.39514 -0.07478  0.728546  1.89627 -1.33345 -2.59477
2   1.33321  0.54940  0.492977  0.24130  0.78232  0.74187
9   1.29092  1.95150  0.005342 -0.81565  0.26355  0.18074
12  0.41778  0.20237  0.558481 -0.57975 -0.17713  0.78064
10  0.48239  1.37874 -0.125838  0.29170  0.38215 -0.13758
11  0.56717  0.36508 -0.101642 -0.04929 -0.36747  0.15785
21 -0.55130 -1.11370 -0.928444 -1.85875 -1.87942 -0.58312


Biplot scores for constraining variables

             CCA1     CCA2     CCA3     CCA4     CCA5     CCA6
Baresoil -0.52916 -0.39394 -0.08617 -0.48990 -0.17135 -0.47822
Humdepth -0.74502  0.09330  0.17115 -0.23030 -0.12889 -0.16495
pH        0.50738  0.14614 -0.26885  0.17600 -0.10593  0.17747
N        -0.18023 -0.58693  0.04837  0.36820  0.15022  0.16997
P        -0.36138  0.63661  0.04617  0.32849  0.17792 -0.38565
K        -0.39232  0.31726  0.55953  0.12491  0.25046 -0.48506
Ca       -0.48559  0.41273  0.01284 -0.06856  0.28471 -0.24271
Mg       -0.45563  0.35145 -0.07675 -0.07944  0.47484 -0.50687
S        -0.03901  0.50851  0.36649  0.02615  0.41656 -0.63216
Al        0.80742  0.10327  0.25002  0.22841 -0.03898 -0.35763
Fe        0.67570  0.02563  0.09560  0.24078 -0.08059 -0.04175