Vegan Multivariate Analysis

PCA

2023-08-14

Ordination with vegan

Data

data(dune)
data(dune.env)

data(varespec)
data(varechem)

Analysis

## Correlations and 0's
round(cor(varespec)[c(1:20) ,c(1:11)], 3)

         Callvulg Empenigr Rhodtome Vaccmyrt Vaccviti Pinusylv Descflex Betupube Vacculig Diphcomp Dicrsp
Callvulg    1.000   -0.262   -0.061   -0.093   -0.312   -0.029   -0.076   -0.077   -0.093   -0.066 -0.109
Empenigr   -0.262    1.000    0.529    0.205    0.611    0.072    0.409    0.430    0.007    0.155 -0.172
Rhodtome   -0.061    0.529    1.000    0.676    0.467   -0.042    0.610    0.821    0.015   -0.118 -0.108
Vaccmyrt   -0.093    0.205    0.676    1.000    0.201   -0.091    0.350    0.577   -0.052   -0.142 -0.123
Vaccviti   -0.312    0.611    0.467    0.201    1.000    0.266    0.198    0.464   -0.085    0.170  0.043
Pinusylv   -0.029    0.072   -0.042   -0.091    0.266    1.000   -0.151    0.047   -0.209   -0.125 -0.006
Descflex   -0.076    0.409    0.610    0.350    0.198   -0.151    1.000    0.084    0.088   -0.097 -0.081
Betupube   -0.077    0.430    0.821    0.577    0.464    0.047    0.084    1.000   -0.072   -0.075 -0.023
Vacculig   -0.093    0.007    0.015   -0.052   -0.085   -0.209    0.088   -0.072    1.000    0.259 -0.115
Diphcomp   -0.066    0.155   -0.118   -0.142    0.170   -0.125   -0.097   -0.075    0.259    1.000 -0.083
Dicrsp     -0.109   -0.172   -0.108   -0.123    0.043   -0.006   -0.081   -0.023   -0.115   -0.083  1.000
Dicrfusc    0.182   -0.042    0.138    0.080   -0.128   -0.156    0.108   -0.033    0.042   -0.117 -0.006
Dicrpoly   -0.122    0.257    0.660    0.485    0.456    0.117    0.014    0.851   -0.133   -0.111  0.357
Hylosple   -0.123    0.046    0.251    0.690   -0.027   -0.165    0.583   -0.077   -0.014   -0.103 -0.087
Pleuschr   -0.119   -0.047    0.196    0.536    0.078   -0.121    0.541   -0.134   -0.124   -0.203  0.256
Polypili   -0.074   -0.354   -0.156   -0.181   -0.078    0.299   -0.132   -0.102   -0.134   -0.067 -0.125
Polyjuni   -0.138    0.099   -0.118   -0.124    0.076   -0.155   -0.091    0.020   -0.108   -0.068  0.440
Polycomm   -0.160    0.543    0.700    0.455    0.359   -0.076    0.379    0.703   -0.111   -0.128  0.080
Pohlnuta   -0.160    0.198    0.139    0.067    0.589    0.614   -0.169    0.276   -0.218    0.003  0.273
Ptilcili   -0.077    0.465    0.780    0.542    0.543    0.067    0.058    0.976   -0.106   -0.076 -0.068

mean(cor(varespec))

[1] 0.04888188

# Method 1: PCA - RDA [Vegan] 
pca <- rda(decostand(varespec, method = "hellinger"),
           scale=TRUE,
           center=TRUE)
pca

Call: rda(X = decostand(varespec, method = "hellinger"), scale = TRUE, center = TRUE)

              Inertia Rank
Total              44     
Unconstrained      44   23
Inertia is correlations 

Eigenvalues for unconstrained axes:
  PC1   PC2   PC3   PC4   PC5   PC6   PC7   PC8 
8.603 5.134 4.576 3.714 3.245 2.779 2.626 2.221 
(Showing 8 of 23 unconstrained eigenvalues)

summary(pca) #variable and sites PCs

Call:
rda(X = decostand(varespec, method = "hellinger"), scale = TRUE,      center = TRUE) 

Partitioning of correlations:
              Inertia Proportion
Total              44          1
Unconstrained      44          1

Eigenvalues, and their contribution to the correlations 

Importance of components:
                         PC1    PC2    PC3     PC4     PC5     PC6     PC7     PC8     PC9    PC10    PC11    PC12    PC13
Eigenvalue            8.6028 5.1336 4.5756 3.71393 3.24492 2.77919 2.62560 2.22100 1.67857 1.65627 1.30432 1.03472 0.91190
Proportion Explained  0.1955 0.1167 0.1040 0.08441 0.07375 0.06316 0.05967 0.05048 0.03815 0.03764 0.02964 0.02352 0.02073
Cumulative Proportion 0.1955 0.3122 0.4162 0.50059 0.57434 0.63750 0.69718 0.74765 0.78580 0.82344 0.85309 0.87660 0.89733
                         PC14   PC15   PC16    PC17    PC18     PC19     PC20     PC21     PC22     PC23
Eigenvalue            0.87323 0.7612 0.6336 0.52021 0.51641 0.408841 0.267175 0.206336 0.179715 0.150795
Proportion Explained  0.01985 0.0173 0.0144 0.01182 0.01174 0.009292 0.006072 0.004689 0.004084 0.003427
Cumulative Proportion 0.91718 0.9345 0.9489 0.96070 0.97243 0.981727 0.987799 0.992488 0.996573 1.000000

Scaling 2 for species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions
* General scaling constant of scores:  5.640208 


Species scores

               PC1      PC2        PC3       PC4      PC5      PC6
Callvulg -0.209390  0.09676  0.1334687  0.271038  0.39235 -0.22508
Empenigr  0.414477  0.14879 -0.1791490 -0.230858  0.01279 -0.22115
Rhodtome  0.669705 -0.16259 -0.2039673 -0.067214  0.29904  0.01460
Vaccmyrt  0.618761 -0.18140 -0.2417607  0.121239  0.29656  0.10110
Vaccviti  0.491687  0.41237  0.0148870 -0.171505 -0.14493  0.05757
Pinusylv  0.182972  0.16485  0.5796489  0.195952 -0.09835  0.14666
Descflex  0.454908 -0.29016 -0.4712063  0.083571  0.09812  0.03515
Betupube  0.650032  0.04492  0.0008693 -0.269503  0.12163 -0.20338
Vacculig -0.132051 -0.19853 -0.3864829 -0.243377  0.19854  0.03209
Diphcomp -0.220304 -0.05478 -0.0923936 -0.434865  0.04917 -0.14809
Dicrsp    0.151923  0.19743 -0.0939855  0.291086 -0.39663 -0.02314
Dicrfusc -0.051453  0.31926 -0.3710035  0.324002  0.27879 -0.26547
Dicrpoly  0.587663  0.11455  0.3379986 -0.022813  0.02941  0.18201
Hylosple  0.237918 -0.25728 -0.4272564  0.295589  0.01764  0.31653
Pleuschr  0.277573  0.22017 -0.4067357  0.499839 -0.17005  0.21194
Polypili -0.261233  0.24976  0.0841089 -0.225057 -0.10691  0.50732
Polyjuni  0.027339  0.37730 -0.2483927 -0.175963 -0.54822 -0.23683
Polycomm  0.538187  0.06187 -0.2466995 -0.170137 -0.13745 -0.20292
Pohlnuta  0.359155  0.30110  0.4516514  0.119283  0.01549  0.13491
Ptilcili  0.647061  0.22828  0.1101115 -0.389411  0.04090 -0.04950
Barbhatc  0.685808  0.05221  0.0915309 -0.332084  0.22286 -0.06939
Cladarbu -0.556254  0.29956 -0.1058615 -0.242235  0.26132 -0.05796
Cladrang -0.518584 -0.13326  0.1040149 -0.457258  0.14261  0.24826
Cladstel -0.018246 -0.43021  0.5529033 -0.154171 -0.17653 -0.18109
Cladunci -0.137802  0.49061  0.0871857  0.416022  0.12129 -0.01575
Cladcocc -0.510585  0.27142  0.1097286 -0.068427  0.12258 -0.21640
Cladcorn -0.127282  0.56990 -0.1837898 -0.160663 -0.35755 -0.08154
Cladgrac -0.020914  0.58764 -0.0511522 -0.168551  0.03196  0.18325
Cladfimb -0.019058  0.23667 -0.1357887 -0.152591  0.44459 -0.43717
Cladcris -0.067610  0.65498  0.0965990 -0.006773  0.14544 -0.14292
Cladchlo  0.399861 -0.02603  0.4078287 -0.237811 -0.01428 -0.17938
Cladbotr  0.651167  0.20485 -0.0025678 -0.180037  0.15318  0.08641
Cladamau -0.313478 -0.04797 -0.0957629 -0.491278  0.10816  0.14613
Cladsp   -0.108599 -0.08637  0.0677240  0.098043  0.10789 -0.42847
Cetreric -0.335644  0.25223  0.2582057  0.338371  0.18465 -0.16608
Cetrisla  0.474622  0.02055  0.5732779  0.058596 -0.03994 -0.08223
Flavniva -0.279960 -0.24613  0.1776329 -0.104388 -0.01346 -0.28016
Nepharct -0.035784  0.05223 -0.3827337 -0.089215 -0.47199 -0.37406
Stersp   -0.440612  0.17642 -0.0192955 -0.375922 -0.02681  0.28150
Peltapht  0.043222  0.35282 -0.1459193 -0.179393 -0.40191  0.13167
Icmaeric -0.329988  0.10717 -0.0713723 -0.072648  0.30382  0.14958
Cladcerv -0.150665 -0.29644 -0.0599910  0.023588 -0.32890 -0.40391
Claddefo  0.006309  0.68925 -0.0498109  0.107605  0.26483 -0.02387
Cladphyl -0.040428  0.01750  0.5304810  0.121673 -0.18540 -0.05460


Site scores (weighted sums of species scores)

        PC1      PC2      PC3      PC4      PC5      PC6
18 -0.91305  0.32985 -0.58568 -2.17895  0.54469 -0.07209
15 -0.50706  1.23534 -0.25250  0.96252  0.54984  0.27513
24  0.66103  0.83889  1.12343  1.71303 -1.30869  1.49539
27  1.31240 -1.38724 -2.44161  0.58877  0.03484  0.85869
23  0.33111  3.01887 -0.64293 -1.31965 -1.14514  0.41111
19  0.57358  0.23538 -0.31180 -0.53221 -0.79793  0.09360
22  0.42982 -0.36398 -1.14510  1.09605  1.51185 -0.58867
16 -0.29253  0.47065 -0.11502  1.23158  1.62132 -0.32506
28  0.99500 -1.64123 -1.36928  1.69885  0.06495  1.72194
13 -0.40983  0.11754  0.45491  0.28431  1.55318 -0.85667
14 -0.79516  2.09189  0.08599  1.61187  1.24498 -1.12174
20 -0.02365  1.07206 -0.48804  0.68936  0.45049  0.83243
25  0.15354  0.54680 -2.24733  0.01614 -3.31771 -2.53231
7  -0.94992 -0.60843 -0.84382 -1.50291  0.65673  0.10933
5  -1.89291 -0.11308 -0.15414 -1.72112  0.43956  2.13679
6  -0.91615 -0.04466  0.22541 -0.30006  0.61593 -0.33932
3  -0.86828 -1.15876 -0.16741 -1.34625  0.11599 -0.03727
4  -1.22859 -1.35920  0.70879  0.20333 -0.11205 -1.73840
2  -0.18109 -2.19999  0.21633 -0.02536 -0.97044 -0.15968
9   0.19035 -0.40754  2.01164  0.19876 -0.45206 -1.46022
12  0.25756 -0.36546  1.16652  0.48806 -0.45162  0.41984
10  0.08749 -0.80866  2.01134  0.26070 -0.54180 -0.87010
11 -0.28300  0.25582  1.79382  0.01901 -1.69284  2.23944
21  4.26934  0.24516  0.96646 -2.13583  1.38591 -0.49214

scores(pca) #first two variable PCs

$species
                  PC1         PC2
Callvulg -0.209389881  0.09675599
Empenigr  0.414476536  0.14879137
Rhodtome  0.669705318 -0.16259319
Vaccmyrt  0.618760500 -0.18139933
Vaccviti  0.491687067  0.41236766
Pinusylv  0.182972122  0.16484692
Descflex  0.454907763 -0.29016241
Betupube  0.650032155  0.04492120
Vacculig -0.132051130 -0.19853464
Diphcomp -0.220304037 -0.05478313
Dicrsp    0.151923183  0.19743434
Dicrfusc -0.051452784  0.31925527
Dicrpoly  0.587662732  0.11454661
Hylosple  0.237917550 -0.25727959
Pleuschr  0.277573406  0.22017147
Polypili -0.261233111  0.24975942
Polyjuni  0.027338641  0.37729786
Polycomm  0.538186591  0.06187168
Pohlnuta  0.359154830  0.30110202
Ptilcili  0.647060711  0.22827616
Barbhatc  0.685808377  0.05220801
Cladarbu -0.556254315  0.29956399
Cladrang -0.518584286 -0.13326164
Cladstel -0.018245943 -0.43021390
Cladunci -0.137802436  0.49060821
Cladcocc -0.510584794  0.27141805
Cladcorn -0.127282065  0.56989893
Cladgrac -0.020914171  0.58764171
Cladfimb -0.019058263  0.23667005
Cladcris -0.067610171  0.65498092
Cladchlo  0.399861443 -0.02602741
Cladbotr  0.651167223  0.20484747
Cladamau -0.313477569 -0.04797077
Cladsp   -0.108599334 -0.08637367
Cetreric -0.335643582  0.25222727
Cetrisla  0.474622111  0.02055333
Flavniva -0.279960034 -0.24612796
Nepharct -0.035784315  0.05223138
Stersp   -0.440611810  0.17641802
Peltapht  0.043221881  0.35281557
Icmaeric -0.329987744  0.10716622
Cladcerv -0.150665450 -0.29644481
Claddefo  0.006309459  0.68925195
Cladphyl -0.040427566  0.01750354

$sites
           PC1         PC2
18 -0.91304556  0.32985049
15 -0.50705716  1.23533638
24  0.66102525  0.83888703
27  1.31240402 -1.38724311
23  0.33110848  3.01886645
19  0.57358112  0.23538107
22  0.42982222 -0.36397792
16 -0.29252967  0.47065127
28  0.99500153 -1.64122659
13 -0.40982951  0.11753565
14 -0.79515874  2.09189186
20 -0.02364897  1.07205707
25  0.15354232  0.54679931
7  -0.94991729 -0.60842669
5  -1.89290622 -0.11307838
6  -0.91615379 -0.04465886
3  -0.86828448 -1.15876208
4  -1.22859226 -1.35920455
2  -0.18109099 -2.19998823
9   0.19034568 -0.40754033
12  0.25755942 -0.36546465
10  0.08748571 -0.80866418
11 -0.28299884  0.25582177
21  4.26933773  0.24515723

attr(,"const")
[1] 5.640208

# Ca$eig 
pca.data.PCs <- as.data.frame(pca$CA$eig)

pca.data.Pc1and2 <- as.data.frame(pca$CA$eig[1:2]) #first two PCs

# Variables "Ca$v"
pca.data.species <- as.data.frame(pca$CA$v) #species scores

#Results for sites "Ca$u"
pca.data.sites <- as.data.frame(pca$CA$u) #site scores

screeplot(pca, bstick=TRUE, type = "l", main= NULL)

Plot

biplot(pca, scaling= "symmetric")