Title: PCA and RDA ordinations
Name: Tammy L. Elliott
Date: March 14, 2015
R version 3.1.0
# set global chunk options:
library(knitr)
opts_chunk$set(cache=FALSE, fig.align='center')Species distributions and diversity indices
# Species distribution, all species confounded
(ab <- table(unlist(abd.sp.allsp)))##
## 0 0.253807106598985 0.263852242744063 0.269541778975741
## 20190 5 3 1
## 0.292397660818713 0.323624595469256 0.363636363636364 0.364963503649635
## 2 1 4 1
## 0.3690036900369 0.371747211895911 0.403225806451613 0.411522633744856
## 4 2 4 1
## 0.416666666666667 0.431034482758621 0.436681222707424 0.448430493273543
## 6 2 3 3
## 0.45045045045045 0.462962962962963 0.465116279069767 0.467289719626168
## 1 2 1 3
## 0.4739336492891 0.48780487804878 0.5 0.505050505050505
## 7 5 2 6
## 0.50761421319797 0.523560209424084 0.531914893617021 0.539083557951483
## 3 4 2 2
## 0.543478260869565 0.546448087431694 0.549450549450549 0.555555555555556
## 3 2 2 2
## 0.564971751412429 0.578034682080925 0.581395348837209 0.584795321637427
## 4 3 7 2
## 0.588235294117647 0.595238095238095 0.602409638554217 0.609756097560976
## 5 6 8 2
## 0.613496932515337 0.632911392405063 0.647249190938511 0.649350649350649
## 1 7 2 3
## 0.657894736842105 0.666666666666667 0.671140939597315 0.684931506849315
## 1 4 2 8
## 0.689655172413793 0.694444444444444 0.709219858156028 0.719424460431655
## 1 4 4 9
## 0.72463768115942 0.72992700729927 0.738007380073801 0.743494423791822
## 2 2 3 4
## 0.746268656716418 0.75187969924812 0.761421319796954 0.763358778625954
## 2 15 1 1
## 0.769230769230769 0.775193798449612 0.78125 0.78740157480315
## 13 8 3 3
## 0.8 0.806451612903226 0.808625336927224 0.813008130081301
## 3 1 2 7
## 0.819672131147541 0.823045267489712 0.826446280991736 0.833333333333333
## 5 1 1 26
## 0.840336134453782 0.847457627118644 0.854700854700855 0.862068965517241
## 9 7 1 9
## 0.873362445414847 0.87719298245614 0.884955752212389 0.892857142857143
## 1 9 7 1
## 0.896860986547085 0.900900900900901 0.917431192660551 0.925925925925926
## 1 1 2 3
## 0.930232558139535 0.943396226415094 0.947867298578199 0.952380952380952
## 3 2 2 9
## 0.980392156862745 0.99009900990099 1 1.01522842639594
## 2 3 7 1
## 1.02040816326531 1.03092783505155 1.04712041884817 1.05263157894737
## 6 11 3 8
## 1.06382978723404 1.0752688172043 1.08695652173913 1.09090909090909
## 8 5 1 1
## 1.09289617486339 1.09489051094891 1.0989010989011 1.11111111111111
## 3 1 10 1
## 1.12359550561798 1.12994350282486 1.13636363636364 1.14942528735632
## 14 3 12 16
## 1.16279069767442 1.16959064327485 1.17647058823529 1.19047619047619
## 5 2 2 1
## 1.20481927710843 1.20967741935484 1.21951219512195 1.22699386503067
## 5 2 1 1
## 1.23456790123457 1.25 1.26582278481013 1.28205128205128
## 4 4 10 4
## 1.29449838187702 1.2987012987013 1.31578947368421 1.33333333333333
## 1 8 4 9
## 1.34529147982063 1.35135135135135 1.36986301369863 1.37931034482759
## 2 1 5 1
## 1.38888888888889 1.4018691588785 1.40845070422535 1.41843971631206
## 1 1 1 1
## 1.42857142857143 1.43884892086331 1.44927536231884 1.45454545454545
## 6 5 4 1
## 1.45985401459854 1.46341463414634 1.47058823529412 1.4760147601476
## 2 3 1 2
## 1.48698884758364 1.49253731343284 1.49812734082397 1.50375939849624
## 2 1 1 11
## 1.50753768844221 1.51515151515152 1.52671755725191 1.53846153846154
## 1 8 1 4
## 1.55038759689922 1.5625 1.5748031496063 1.58730158730159
## 1 6 2 3
## 1.6 1.61290322580645 1.6260162601626 1.6304347826087
## 1 4 2 1
## 1.63934426229508 1.64609053497942 1.66666666666667 1.68067226890756
## 3 1 7 3
## 1.69491525423729 1.72413793103448 1.73410404624277 1.74418604651163
## 4 7 1 1
## 1.74672489082969 1.75438596491228 1.76470588235294 1.76991150442478
## 1 15 1 6
## 1.78571428571429 1.8018018018018 1.85185185185185 1.86915887850467
## 2 1 17 2
## 1.88679245283019 1.8957345971564 1.89873417721519 1.9047619047619
## 10 1 1 1
## 1.92307692307692 1.94805194805195 1.95121951219512 1.96078431372549
## 15 1 1 1
## 1.97368421052632 1.98019801980198 2 2.01005025125628
## 1 2 4 3
## 2.01342281879195 2.02020202020202 2.04081632653061 2.05479452054794
## 1 2 1 2
## 2.06185567010309 2.06896551724138 2.08333333333333 2.10526315789474
## 4 1 2 6
## 2.12765957446809 2.1505376344086 2.15827338129496 2.18579234972678
## 6 1 2 1
## 2.1978021978022 2.22222222222222 2.24719101123596 2.25563909774436
## 9 3 8 2
## 2.25988700564972 2.27272727272727 2.29007633587786 2.29885057471264
## 3 2 1 5
## 2.30769230769231 2.3121387283237 2.32558139534884 2.34375
## 1 3 8 1
## 2.35294117647059 2.38095238095238 2.40963855421687 2.4390243902439
## 2 1 6 5
## 2.45901639344262 2.46913580246914 2.5 2.52100840336134
## 1 3 6 1
## 2.53164556962025 2.54237288135593 2.58899676375405 2.5974025974026
## 7 1 1 8
## 2.63157894736842 2.65486725663717 2.66666666666667 2.67857142857143
## 2 1 5 1
## 2.68456375838926 2.73972602739726 2.75229357798165 2.77777777777778
## 3 1 1 2
## 2.8169014084507 2.83018867924528 2.85714285714286 2.87769784172662
## 1 2 4 5
## 2.89855072463768 2.90909090909091 2.91970802919708 2.94117647058824
## 2 2 1 2
## 2.9520295202952 2.97029702970297 2.97397769516729 2.98507462686567
## 4 2 2 4
## 3.00751879699248 3.03030303030303 3.05343511450382 3.06122448979592
## 4 4 3 2
## 3.07692307692308 3.09278350515464 3.10077519379845 3.125
## 2 1 2 6
## 3.1496062992126 3.15789473684211 3.19148936170213 3.2
## 1 3 1 3
## 3.2258064516129 3.2520325203252 3.27868852459016 3.29218106995885
## 7 1 5 1
## 3.2967032967033 3.33333333333333 3.36134453781513 3.38983050847458
## 3 9 4 4
## 3.41880341880342 3.44827586206897 3.48837209302326 3.50877192982456
## 4 6 2 8
## 3.53982300884956 3.58744394618834 3.6036036036036 3.6144578313253
## 5 2 1 1
## 3.6697247706422 3.7037037037037 3.73831775700935 3.77358490566038
## 1 3 3 4
## 3.79746835443038 3.80952380952381 3.84615384615385 3.90243902439024
## 1 4 11 1
## 3.96039603960396 4 4.02010050251256 4.04040404040404
## 2 4 1 1
## 4.06091370558376 4.08163265306122 4.12371134020619 4.18848167539267
## 1 2 4 2
## 4.21052631578947 4.22163588390501 4.25531914893617 4.28571428571429
## 1 1 5 2
## 4.34782608695652 4.36363636363636 4.37158469945355 4.37956204379562
## 1 1 1 1
## 4.3956043956044 4.41176470588235 4.44444444444444 4.46096654275093
## 4 1 3 2
## 4.49438202247191 4.54545454545455 4.59770114942529 4.65116279069767
## 5 6 2 6
## 4.67836257309941 4.6875 4.70588235294118 4.76190476190476
## 2 1 1 2
## 4.81927710843374 4.8780487804878 4.9079754601227 4.91803278688525
## 2 3 1 1
## 4.93827160493827 5 5.06329113924051 5.12820512820513
## 1 4 2 1
## 5.17799352750809 5.19480519480519 5.24017467248908 5.26315789473684
## 2 6 1 6
## 5.33333333333333 5.35714285714286 5.36912751677852 5.38116591928251
## 2 1 2 1
## 5.39083557951483 5.40540540540541 5.47945205479452 5.51724137931035
## 1 1 1 6
## 5.55555555555556 5.63380281690141 5.67375886524823 5.71428571428571
## 3 2 1 3
## 5.75539568345324 5.76923076923077 5.81818181818182 5.83941605839416
## 4 6 1 4
## 5.84795321637427 6.01503759398496 6.06060606060606 6.10687022900763
## 1 5 3 4
## 6.15384615384615 6.2015503875969 6.25 6.282722513089
## 4 2 3 2
## 6.2992125984252 6.34920634920635 6.38297872340426 6.4
## 1 2 1 1
## 6.45161290322581 6.52173913043478 6.55737704918033 6.5843621399177
## 2 1 10 1
## 6.59340659340659 6.66666666666667 6.72268907563025 6.77966101694915
## 1 6 3 5
## 6.83760683760684 6.89655172413793 7.01754385964912 7.05882352941176
## 1 6 7 1
## 7.07964601769912 7.14285714285714 7.31707317073171 7.3394495412844
## 1 4 2 1
## 7.36196319018405 7.38007380073801 7.40740740740741 7.44186046511628
## 1 2 1 1
## 7.47663551401869 7.5 7.54716981132075 7.58293838862559
## 1 1 2 1
## 7.59493670886076 7.61904761904762 7.69230769230769 7.79220779220779
## 1 2 7 3
## 7.89473684210526 7.92079207920792 8 8.04020100502512
## 2 3 9 1
## 8.06451612903226 8.16326530612245 8.24742268041237 8.27586206896552
## 1 2 4 2
## 8.33333333333333 8.42105263157895 8.51063829787234 8.57142857142857
## 1 5 4 2
## 8.60215053763441 8.63309352517986 8.73362445414847 8.75912408759124
## 1 2 1 1
## 8.79120879120879 8.88888888888889 9.00900900900901 9.02255639097744
## 6 2 1 2
## 9.09090909090909 9.19540229885057 9.23076923076923 9.25925925925926
## 3 4 1 1
## 9.30232558139535 9.34579439252336 9.41176470588235 9.63855421686747
## 7 1 2 5
## 9.67741935483871 9.75609756097561 9.83606557377049 10
## 1 2 3 4
## 10.0840336134454 10.1010101010101 10.126582278481 10.1449275362319
## 1 2 4 1
## 10.1694915254237 10.2564102564103 10.3448275862069 10.3896103896104
## 1 3 3 5
## 10.5263157894737 10.6666666666667 10.7142857142857 10.762331838565
## 1 1 2 1
## 11.0091743119266 11.1111111111111 11.2676056338028 11.2994350282486
## 1 2 2 1
## 11.3207547169811 11.4285714285714 11.5107913669065 11.5606936416185
## 1 4 1 2
## 11.6279069767442 11.7073170731707 11.7647058823529 11.9402985074627
## 1 1 2 2
## 12.0300751879699 12.0481927710843 12.1212121212121 12.2137404580153
## 1 2 2 1
## 12.2270742358079 12.2448979591837 12.3076923076923 12.3711340206186
## 1 1 9 2
## 12.4031007751938 12.5 12.6315789473684 12.6582278481013
## 1 3 2 2
## 12.7659574468085 12.8 12.9032258064516 13.0081300813008
## 2 2 5 2
## 13.1147540983607 13.1868131868132 13.3333333333333 13.4615384615385
## 1 4 4 3
## 13.4831460674157 13.6363636363636 13.6986301369863 13.7931034482759
## 1 1 1 5
## 13.953488372093 14.0350877192982 14.1843971631206 14.2857142857143
## 2 1 1 5
## 14.3884892086331 14.4578313253012 14.4927536231884 14.6341463414634
## 2 2 1 1
## 14.8148148148148 14.8698884758364 15 15.0943396226415
## 3 1 2 3
## 15.1898734177215 15.2671755725191 15.3846153846154 15.5038759689922
## 1 1 3 4
## 15.5844155844156 15.6862745098039 15.7894736842105 15.8415841584158
## 1 1 2 1
## 16 16.1616161616162 16.260162601626 16.2790697674419
## 2 1 1 1
## 16.4383561643836 16.4948453608247 16.551724137931 16.6666666666667
## 1 2 1 2
## 16.8067226890756 16.8421052631579 16.8674698795181 16.9014084507042
## 1 2 1 1
## 16.9491525423729 17.0212765957447 17.4672489082969 17.5182481751825
## 2 3 2 1
## 17.5438596491228 17.5824175824176 17.6470588235294 17.7215189873418
## 1 2 1 2
## 17.7777777777778 17.8571428571429 17.910447761194 18.018018018018
## 4 1 1 1
## 18.0451127819549 18.1818181818182 18.3908045977011 18.4615384615385
## 2 2 2 1
## 18.4971098265896 18.6046511627907 18.75 18.8679245283019
## 2 1 1 1
## 18.8976377952756 18.957345971564 18.978102189781 19.047619047619
## 2 1 2 1
## 19.2307692307692 19.2771084337349 19.5121951219512 19.5652173913043
## 1 1 3 1
## 19.6078431372549 19.672131147541 19.7530864197531 19.8830409356725
## 2 1 1 1
## 20 20.1438848920863 20.1680672268908 20.253164556962
## 5 2 2 4
## 20.4379562043796 20.6185567010309 20.6896551724138 21.0526315789474
## 1 1 1 6
## 21.1538461538462 21.2389380530973 21.2765957446809 21.505376344086
## 1 1 1 1
## 21.5384615384615 21.7054263565891 21.9178082191781 21.978021978022
## 2 2 1 1
## 22.0472440944882 22.2222222222222 22.5352112676056 22.6415094339623
## 1 2 2 1
## 22.9885057471264 23.0769230769231 23.1884057971014 23.2558139534884
## 2 1 2 2
## 23.3333333333333 23.5294117647059 23.728813559322 23.8805970149254
## 3 2 1 2
## 23.9316239316239 24.0601503759398 24.4274809160305 24.6153846153846
## 1 1 1 1
## 24.6913580246914 25 25.1968503937008 25.2631578947368
## 2 5 1 1
## 25.3164556962025 25.3807106598985 25.3968253968254 25.4237288135593
## 3 1 1 1
## 25.531914893617 25.6410256410256 25.8064516129032 25.8899676375405
## 1 1 1 1
## 25.8992805755396 25.974025974026 26.0162601626016 26.2295081967213
## 1 1 1 2
## 26.3736263736264 26.5682656826568 26.6666666666667 27.027027027027
## 2 1 4 1
## 27.0676691729323 27.2727272727273 27.3972602739726 27.5862068965517
## 1 1 2 1
## 27.7456647398844 28.0373831775701 28.0701754385965 28.8461538461538
## 1 1 1 1
## 28.9855072463768 29.1970802919708 29.2682926829268 29.6296296296296
## 1 1 1 1
## 29.7397769516729 30 30.0751879699248 30.188679245283
## 1 2 1 2
## 30.379746835443 30.5343511450382 30.7692307692308 31.25
## 1 1 1 2
## 31.3725490196078 31.4606741573034 31.5789473684211 31.8181818181818
## 1 1 1 1
## 32 32.2147651006711 32.4324324324324 32.7868852459016
## 1 1 1 2
## 32.9411764705882 33.0578512396694 33.0827067669173 33.1034482758621
## 1 1 1 1
## 33.3333333333333 33.4883720930233 33.587786259542 33.6134453781513
## 1 1 1 1
## 33.6842105263158 33.8983050847458 34.1880341880342 34.2857142857143
## 2 1 1 1
## 34.4827586206897 34.6820809248555 34.9344978165939 35
## 1 1 1 1
## 35.0877192982456 35.2941176470588 35.3982300884956 35.8620689655172
## 2 1 1 1
## 36 36.0655737704918 36.3636363636364 36.8098159509202
## 1 1 2 1
## 37.037037037037 37.2093023255814 37.3831775700935 37.4531835205993
## 1 1 1 1
## 37.5 37.696335078534 37.9310344827586 37.9746835443038
## 2 1 1 1
## 38.0952380952381 38.4615384615385 38.7096774193548 38.9380530973451
## 1 1 3 1
## 39.6039603960396 40 40.4040404040404 41.6666666666667
## 1 8 1 1
## 42.3529411764706 42.5531914893617 43.1654676258993 43.3734939759036
## 1 1 1 1
## 43.9024390243902 44.7761194029851 45.1127819548872 45.2830188679245
## 1 1 1 2
## 45.4545454545455 45.6375838926174 45.7142857142857 45.8015267175573
## 1 1 2 1
## 46.1538461538462 46.5116279069767 46.7836257309941 47.0588235294118
## 2 1 1 1
## 47.2222222222222 47.4934036939314 48.1927710843374 48.2269503546099
## 1 2 1 1
## 48.9795918367347 49.079754601227 49.1803278688525 49.2307692307692
## 1 1 1 2
## 49.4845360824742 49.6350364963504 50 50.4201680672269
## 1 1 1 1
## 50.5263157894737 50.7462686567164 50.8474576271186 50.9803921568627
## 1 1 1 1
## 51.6605166051661 51.7241379310345 52.3560209424084 52.7472527472528
## 1 1 1 1
## 54.4 55.5555555555556 55.8139534883721 55.9139784946236
## 1 1 2 1
## 58.0645161290323 58.252427184466 58.3333333333333 58.5365853658537
## 1 1 1 2
## 58.8235294117647 59.0163934426229 59.4795539033457 59.9250936329588
## 1 1 1 1
## 60.1769911504425 60.2409638554217 60.6896551724138 62.3376623376623
## 1 1 1 1
## 62.5 63.1578947368421 65.1162790697674 65.2173913043478
## 1 1 1 1
## 65.9340659340659 65.989847715736 66.1157024793389 66.3507109004739
## 1 1 1 1
## 67.0520231213873 67.7966101694915 68.2926829268293 68.4931506849315
## 1 2 1 1
## 70.1754385964912 71.7488789237668 72.289156626506 73.394495412844
## 1 1 1 1
## 74.3494423791822 74.468085106383 75 77.6978417266187
## 1 1 1 1
## 78.6885245901639 80 80.4020100502513 80.6451612903226
## 1 2 1 1
## 82.3045267489712 83.3333333333333 83.7696335078534 83.8095238095238
## 1 2 1 1
## 86.2068965517241 86.9565217391304 87.431693989071 88.5608856088561
## 1 1 1 1
## 91.644204851752 94.3396226415094 96.7741935483871
## 1 1 1barplot(ab, las=1, xlab="Abundance class", ylab="Frequency", col=grey(5:0/5))
site.pres <- rowSums(abd.sp.allsp>0) # compute the number of species at ecah site
hist(site.pres, main="Species richness", las=1, xlab="Frequency of sites", ylab="Number of species", breaks=seq(0,30, by=5), col="grey")
### Compute diversity indices
(H <- diversity(abd.sp.allsp, index="shannon")) # Shannon diversity index## EA1 EB1 EC1 ED1 EE1 EF1 EG1
## 1.2048412 2.0194462 2.0880260 2.2337312 2.5862055 1.0511491 2.1772548
## EH1 EI1 EJ1 EK1 EA2 EB2 EC2
## 0.7827005 1.7160952 1.7173970 2.0143625 1.7921832 1.6136763 2.0966989
## ED2 EE2 EF2 EG2 EH2 EI2 EJ2
## 3.0679521 2.3792741 2.6691212 2.1706686 2.1678487 1.9418621 2.2600867
## EK2 EA3 EB3 EC3 ED3 EE3 EF3
## 2.3460001 2.0196523 1.7518429 1.9299621 2.6503201 2.1144059 0.7666278
## EG3 EH3 EI3 EJ3 EK3 EA4 EB4
## 1.8505194 1.3756792 2.2353452 1.6772132 1.3364631 1.1050686 1.7012615
## EC4 ED4 EE4 EF4 EG4 EH4 EI4
## 0.8550337 1.8658336 1.3543548 1.7293336 2.3456181 1.7015216 1.8767573
## EJ4 EK4 EA5 EB5 EC5 ED5 EE5
## 2.1278660 1.8537836 1.5122313 1.7840672 2.0597890 1.9188033 2.0040142
## EF5 EG5 EH5 EI5 EJ5 EK5 EA6
## 2.1565272 1.9072354 1.2748139 2.2187995 1.2660371 1.2993489 1.8271855
## EB6 EC6 ED6 EE6 EF6 EG6 EH6
## 1.2485789 1.6990426 1.3125481 1.0406879 0.8247360 1.0869647 1.4741033
## EI6 EJ6 EK6 EA7 EB7 EC7 ED7
## 1.4143971 2.1453494 1.7397021 1.9445374 0.9678841 2.0183105 1.5877918
## EE7 EF7 EG7 EH7 EI7 EJ7 EK7
## 1.5458600 0.6700832 1.5418020 1.6197730 1.4088413 1.1502788 1.6733470
## EA8 EB8 EC8 ED8 EE8 EF8 EG8
## 1.7003039 0.8061176 1.8966491 1.6853347 1.2873204 2.4065626 1.8178338
## EH8 EI8 EJ8 EK8 E600A1 E600B2 E600C3
## 1.3922753 1.8983297 1.6416593 2.0196531 1.2241626 1.9622443 1.6498877
## E600D4 E600E5 E600F6 E600G7 E600H8 E600I9 E600J10
## 1.5278353 1.0808064 1.6889408 1.3722696 1.7722603 1.2756613 1.5950154
## E600K11 E615A1 E615B2 E615C3 E615D4 E615E5 E615F6
## 1.5852776 1.7191991 0.4763957 1.5715383 1.1136193 0.3875756 1.5789451
## E615G7 E615H8 E615I9 E615J10 E615K11 E645A1 E645B2
## 1.6000640 0.8238527 1.5279849 1.5701319 0.9878082 2.0616083 2.2585279
## E645C3 E645D4 E645E5 E645F6 E645G7 E645H8 E645I9
## 0.9924535 0.6791186 1.3335541 1.5379765 0.9387963 0.7938075 1.1424403
## E645J10 E645K11 E675A1 E675B2 E675C3 E675D4 E675E5
## 1.9484553 1.6241402 1.7797897 1.5399455 0.7300541 1.8620807 1.0417379
## E675F6 E675G7 E675H8 E675I9 E675J10 E675K11 E710A1
## 0.5386819 0.8819266 0.9032957 1.2059287 0.8060881 1.6995865 1.3787517
## E710B2 E710C3 E710D4 E710E5 E710F6 E710G7 E710H8
## 1.7846425 0.8878637 0.8757581 1.0692016 1.5819251 1.5886517 1.2001664
## E710I9 E710J10 E710K11 E745A1 E745B2 E745C3 E745D4
## 0.9914079 1.1833184 0.6102335 0.8789877 1.2664527 0.6998334 1.7416032
## E745E5 E745F6 E745G7 E745H8 E745I9 E745J10 E745K11
## 0.1425059 1.6643777 1.2880711 0.8411219 0.7880507 0.6705051 1.0549202
## E775A1 E775B2 E775C3 E775D4 E775E5 E775F6 E775G7
## 1.0748166 1.5110819 1.9487442 1.9241164 1.1240652 1.8386347 0.2535477
## E775H8 E775I9 E775J10 E775K11 E800A1 E800B2 E800C3
## 0.9091322 1.4030559 0.9743148 2.0736902 0.9464717 1.6133466 1.6281480
## E800D4 E800E5 E800F6 E800G7 E800H8 E800I9 E800J10
## 2.0198831 1.4444538 1.5783258 1.4513036 1.7131399 1.5657638 1.7154207
## E800K11
## 1.4155451(N <- diversity(abd.sp.allsp, index="simpson")) # Simpson diversity index## EA1 EB1 EC1 ED1 EE1 EF1
## 0.50150122 0.77027778 0.80640000 0.84236111 0.89026063 0.57947973
## EG1 EH1 EI1 EJ1 EK1 EA2
## 0.82197585 0.29369615 0.78523419 0.62416791 0.83191222 0.76216263
## EB2 EC2 ED2 EE2 EF2 EG2
## 0.74273484 0.81295328 0.94748521 0.88043363 0.86706224 0.84699915
## EH2 EI2 EJ2 EK2 EA3 EB3
## 0.82459834 0.75232438 0.84368817 0.83241506 0.82552663 0.78497558
## EC3 ED3 EE3 EF3 EG3 EH3
## 0.82430700 0.90427824 0.85511688 0.30009921 0.72553103 0.68696473
## EI3 EJ3 EK3 EA4 EB4 EC4
## 0.88313138 0.69477162 0.58323495 0.46765469 0.73076923 0.34114854
## ED4 EE4 EF4 EG4 EH4 EI4
## 0.78552319 0.61867936 0.71355079 0.86887574 0.70932086 0.82245489
## EJ4 EK4 EA5 EB5 EC5 ED5
## 0.84793236 0.79394531 0.73898414 0.78625134 0.81752217 0.81224030
## EE5 EF5 EG5 EH5 EI5 EJ5
## 0.79516774 0.84697965 0.81329066 0.61265432 0.86939792 0.59072533
## EK5 EA6 EB6 EC6 ED6 EE6
## 0.60330756 0.77293133 0.67726525 0.72173997 0.55110871 0.57051379
## EF6 EG6 EH6 EI6 EJ6 EK6
## 0.34968889 0.57403924 0.67951894 0.63059313 0.80300000 0.78251821
## EA7 EB7 EC7 ED7 EE7 EF7
## 0.81885916 0.44154532 0.79325556 0.75520000 0.66368000 0.25360434
## EG7 EH7 EI7 EJ7 EK7 EA8
## 0.70439909 0.68876338 0.67523546 0.56505102 0.77739612 0.72359016
## EB8 EC8 ED8 EE8 EF8 EG8
## 0.36871809 0.75224490 0.77398549 0.52066775 0.87884793 0.78000000
## EH8 EI8 EJ8 EK8 E600A1 E600B2
## 0.60291769 0.76631644 0.76844291 0.83806304 0.63893491 0.83220660
## E600C3 E600D4 E600E5 E600F6 E600G7 E600H8
## 0.77950835 0.67600531 0.43509507 0.77110583 0.67085658 0.75482654
## E600I9 E600J10 E600K11 E615A1 E615B2 E615C3
## 0.67497330 0.75156250 0.70700669 0.77635744 0.23314430 0.71583045
## E615D4 E615E5 E615F6 E615G7 E615H8 E615I9
## 0.52977316 0.15703170 0.74527589 0.74765869 0.38051861 0.71978271
## E615J10 E615K11 E645A1 E645B2 E645C3 E645D4
## 0.72160911 0.54579861 0.84530343 0.86254006 0.49819629 0.45352093
## E645E5 E645F6 E645G7 E645H8 E645I9 E645J10
## 0.68265000 0.72645833 0.46168052 0.51196670 0.61560465 0.81673469
## E645K11 E675A1 E675B2 E675C3 E675D4 E675E5
## 0.75976562 0.78476331 0.77588757 0.31438297 0.79538315 0.57689350
## E675F6 E675G7 E675H8 E675I9 E675J10 E675K11
## 0.21279667 0.54098908 0.42188472 0.58734198 0.34403172 0.77303047
## E710A1 E710B2 E710C3 E710D4 E710E5 E710F6
## 0.65039964 0.79117484 0.54707221 0.41190972 0.55455287 0.70828376
## E710G7 E710H8 E710I9 E710J10 E710K11 E745A1
## 0.75371713 0.63652244 0.45608942 0.56128809 0.23249425 0.35263471
## E745B2 E745C3 E745D4 E745E5 E745F6 E745G7
## 0.53985026 0.29599623 0.77197266 0.06243496 0.75402778 0.65384410
## E745H8 E745I9 E745J10 E745K11 E775A1 E775B2
## 0.47342718 0.50027353 0.29072668 0.64000000 0.61668589 0.74484457
## E775C3 E775D4 E775E5 E775F6 E775G7 E775H8
## 0.83713549 0.84071006 0.51737382 0.81083762 0.10822357 0.48561570
## E775I9 E775J10 E775K11 E800A1 E800B2 E800C3
## 0.71947874 0.59375000 0.82235671 0.50225534 0.78375000 0.72120065
## E800D4 E800E5 E800F6 E800G7 E800H8 E800I9
## 0.85333333 0.69680473 0.65765279 0.72932813 0.73841851 0.70447074
## E800J10 E800K11
## 0.77815083 0.68159170Prepare environmental data
#Look at environmental data
env<-site.env
## 1.2 Environmental data ####
names(env)## [1] "Elevation..m." "Sky.visible...." "Slope..Degrees." "site.soil"
## [5] "site.moist"dim(env)## [1] 176 5str(env)## 'data.frame': 176 obs. of 5 variables:
## $ Elevation..m. : int 523 522 524 532 522 531 533 528 530 530 ...
## $ Sky.visible....: num 95 100 100 80 100 80 100 100 100 100 ...
## $ Slope..Degrees.: num 0 0 0 0 0 0 1 0 0 0 ...
## $ site.soil : num 22.2 22.5 14.5 18.1 26.4 ...
## $ site.moist : num 2 2 2 2 1 2 2 2 1 2 ...head(env)## Elevation..m. Sky.visible.... Slope..Degrees. site.soil site.moist
## EA1 523 95 0 22.250 2
## EB1 522 100 0 22.500 2
## EC1 524 100 0 14.500 2
## ED1 532 80 0 18.125 2
## EE1 522 100 0 26.375 1
## EF1 531 80 0 30.000 2summary(env)## Elevation..m. Sky.visible.... Slope..Degrees. site.soil
## Min. :522.0 Min. : 9.50 Min. : 0.000 Min. : 0.00
## 1st Qu.:550.8 1st Qu.: 90.00 1st Qu.: 0.000 1st Qu.: 7.75
## Median :600.0 Median :100.00 Median : 4.000 Median :14.94
## Mean :625.3 Mean : 93.97 Mean : 6.733 Mean :16.17
## 3rd Qu.:686.8 3rd Qu.:100.00 3rd Qu.:12.000 3rd Qu.:23.75
## Max. :806.0 Max. :100.00 Max. :27.000 Max. :30.00
## site.moist
## Min. :1.000
## 1st Qu.:3.000
## Median :3.000
## Mean :3.062
## 3rd Qu.:3.000
## Max. :5.000pairs(env, main="Bivariate Plots of the Environmental Data" )
Dependance between environmental data (R mode)
env.pearson<-cor(env) # Pearson r linear correlation
round(env.pearson, 2)## Elevation..m. Sky.visible.... Slope..Degrees. site.soil
## Elevation..m. 1.00 0.11 0.63 -0.73
## Sky.visible.... 0.11 1.00 -0.04 -0.06
## Slope..Degrees. 0.63 -0.04 1.00 -0.66
## site.soil -0.73 -0.06 -0.66 1.00
## site.moist 0.79 0.12 0.50 -0.66
## site.moist
## Elevation..m. 0.79
## Sky.visible.... 0.12
## Slope..Degrees. 0.50
## site.soil -0.66
## site.moist 1.00env.ken<-cor(env, method="kendall")# Kendall tau rank correlation
round(env.ken, 2)## Elevation..m. Sky.visible.... Slope..Degrees. site.soil
## Elevation..m. 1.00 0.12 0.56 -0.50
## Sky.visible.... 0.12 1.00 -0.01 -0.17
## Slope..Degrees. 0.56 -0.01 1.00 -0.48
## site.soil -0.50 -0.17 -0.48 1.00
## site.moist 0.64 0.17 0.45 -0.54
## site.moist
## Elevation..m. 0.64
## Sky.visible.... 0.17
## Slope..Degrees. 0.45
## site.soil -0.54
## site.moist 1.00Unconstrained Ordination - Principal components analysis
### PCA on hellinger-transformed species data
#?rda
#### Run the PCA
spe.h.pca <- rda(spe.hel)
# Extract the results
#summary(spe.h.pca)
#### Extract specific parts of the results
summary(spe.h.pca) # overall results##
## Call:
## rda(X = spe.hel)
##
## Partitioning of variance:
## Inertia Proportion
## Total 0.7612 1
## Unconstrained 0.7612 1
##
## Eigenvalues, and their contribution to the variance
##
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Eigenvalue 0.1191 0.1026 0.08465 0.05173 0.04275 0.04028
## Proportion Explained 0.1565 0.1348 0.11122 0.06795 0.05617 0.05291
## Cumulative Proportion 0.1565 0.2913 0.40251 0.47047 0.52663 0.57955
## PC7 PC8 PC9 PC10 PC11 PC12
## Eigenvalue 0.03001 0.02717 0.02467 0.02201 0.01684 0.01542
## Proportion Explained 0.03943 0.03570 0.03241 0.02891 0.02212 0.02026
## Cumulative Proportion 0.61898 0.65468 0.68709 0.71600 0.73813 0.75839
## PC13 PC14 PC15 PC16 PC17 PC18
## Eigenvalue 0.01385 0.01352 0.01241 0.01072 0.009377 0.00871
## Proportion Explained 0.01820 0.01776 0.01631 0.01408 0.012320 0.01144
## Cumulative Proportion 0.77659 0.79435 0.81065 0.82473 0.837050 0.84850
## PC19 PC20 PC21 PC22 PC23 PC24
## Eigenvalue 0.008192 0.00725 0.006565 0.006141 0.005546 0.005409
## Proportion Explained 0.010760 0.00953 0.008620 0.008070 0.007290 0.007110
## Cumulative Proportion 0.859260 0.86878 0.877410 0.885480 0.892760 0.899870
## PC25 PC26 PC27 PC28 PC29
## Eigenvalue 0.004977 0.004467 0.004388 0.004203 0.003913
## Proportion Explained 0.006540 0.005870 0.005770 0.005520 0.005140
## Cumulative Proportion 0.906410 0.912270 0.918040 0.923560 0.928700
## PC30 PC31 PC32 PC33 PC34
## Eigenvalue 0.003603 0.003295 0.003001 0.002728 0.002608
## Proportion Explained 0.004730 0.004330 0.003940 0.003580 0.003430
## Cumulative Proportion 0.933430 0.937760 0.941710 0.945290 0.948720
## PC35 PC36 PC37 PC38 PC39
## Eigenvalue 0.002444 0.002325 0.002186 0.002048 0.001967
## Proportion Explained 0.003210 0.003050 0.002870 0.002690 0.002580
## Cumulative Proportion 0.951930 0.954980 0.957850 0.960540 0.963130
## PC40 PC41 PC42 PC43 PC44
## Eigenvalue 0.001728 0.001698 0.001541 0.001405 0.001351
## Proportion Explained 0.002270 0.002230 0.002020 0.001850 0.001780
## Cumulative Proportion 0.965400 0.967630 0.969660 0.971500 0.973280
## PC45 PC46 PC47 PC48 PC49
## Eigenvalue 0.001322 0.001208 0.001129 0.001049 0.0009811
## Proportion Explained 0.001740 0.001590 0.001480 0.001380 0.0012900
## Cumulative Proportion 0.975010 0.976600 0.978080 0.979460 0.9807500
## PC50 PC51 PC52 PC53 PC54
## Eigenvalue 0.000956 0.0009067 0.000874 0.0008178 0.0007714
## Proportion Explained 0.001260 0.0011900 0.001150 0.0010700 0.0010100
## Cumulative Proportion 0.982000 0.9832000 0.984340 0.9854200 0.9864300
## PC55 PC56 PC57 PC58 PC59
## Eigenvalue 0.0007614 0.0006977 0.0006501 0.0006262 0.0006112
## Proportion Explained 0.0010000 0.0009200 0.0008500 0.0008200 0.0008000
## Cumulative Proportion 0.9874300 0.9883500 0.9892000 0.9900300 0.9908300
## PC60 PC61 PC62 PC63 PC64
## Eigenvalue 0.0005987 0.0005505 0.0005004 0.0004551 0.0004476
## Proportion Explained 0.0007900 0.0007200 0.0006600 0.0006000 0.0005900
## Cumulative Proportion 0.9916200 0.9923400 0.9930000 0.9935900 0.9941800
## PC65 PC66 PC67 PC68 PC69
## Eigenvalue 0.0004135 0.0003739 0.0003603 0.000313 0.0002893
## Proportion Explained 0.0005400 0.0004900 0.0004700 0.000410 0.0003800
## Cumulative Proportion 0.9947300 0.9952200 0.9956900 0.996100 0.9964800
## PC70 PC71 PC72 PC73 PC74
## Eigenvalue 0.0002502 0.0002385 0.0002084 0.0002039 0.0001892
## Proportion Explained 0.0003300 0.0003100 0.0002700 0.0002700 0.0002500
## Cumulative Proportion 0.9968100 0.9971200 0.9974000 0.9976600 0.9979100
## PC75 PC76 PC77 PC78 PC79
## Eigenvalue 0.0001673 0.0001426 0.0001352 0.000109 0.0001045
## Proportion Explained 0.0002200 0.0001900 0.0001800 0.000140 0.0001400
## Cumulative Proportion 0.9981300 0.9983200 0.9985000 0.998640 0.9987800
## PC80 PC81 PC82 PC83 PC84
## Eigenvalue 9.456e-05 9.032e-05 8.768e-05 8.002e-05 7.623e-05
## Proportion Explained 1.200e-04 1.200e-04 1.200e-04 1.100e-04 1.000e-04
## Cumulative Proportion 9.989e-01 9.990e-01 9.991e-01 9.992e-01 9.993e-01
## PC85 PC86 PC87 PC88 PC89
## Eigenvalue 6.637e-05 6.213e-05 5.594e-05 4.927e-05 4.227e-05
## Proportion Explained 9.000e-05 8.000e-05 7.000e-05 6.000e-05 6.000e-05
## Cumulative Proportion 9.994e-01 9.995e-01 9.996e-01 9.997e-01 9.997e-01
## PC90 PC91 PC92 PC93 PC94
## Eigenvalue 3.793e-05 3.296e-05 2.921e-05 2.782e-05 2.243e-05
## Proportion Explained 5.000e-05 4.000e-05 4.000e-05 4.000e-05 3.000e-05
## Cumulative Proportion 9.998e-01 9.998e-01 9.998e-01 9.999e-01 9.999e-01
## PC95 PC96 PC97 PC98 PC99
## Eigenvalue 1.758e-05 1.247e-05 1.068e-05 8.531e-06 7.656e-06
## Proportion Explained 2.000e-05 2.000e-05 1.000e-05 1.000e-05 1.000e-05
## Cumulative Proportion 9.999e-01 9.999e-01 1.000e+00 1.000e+00 1.000e+00
## PC100 PC101 PC102 PC103 PC104
## Eigenvalue 6.146e-06 5.762e-06 2.969e-06 1.561e-06 1.276e-06
## Proportion Explained 1.000e-05 1.000e-05 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
##
## 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: 3.397273
##
##
## Species scores
##
## PC1 PC2 PC3 PC4 PC5 PC6
## AchMil -0.0070213 6.494e-03 -0.0032606 0.0010939 -0.0007588 0.0077826
## AgrMer -0.0012887 -8.293e-05 0.0005490 -0.0041206 -0.0087532 0.0032192
## AlnVir 0.0408125 3.781e-02 -0.0722188 -0.2323961 -0.1280853 0.0198144
## AmeBar 0.0029580 4.700e-04 -0.0027757 0.0009714 -0.0014984 -0.0017895
## AndPol -0.0073620 -3.070e-03 0.0054822 -0.0008872 -0.0161417 0.0171260
## AnePar -0.0174201 2.626e-02 -0.0032773 0.0006065 0.0016949 0.0256357
## AntAlp -0.0003494 4.416e-03 0.0031047 0.0004479 0.0017799 -0.0009589
## AntMon -0.0002471 3.123e-03 0.0021953 0.0003167 0.0012586 -0.0006780
## ArcAlp 0.0348475 3.894e-02 0.0984755 0.0209945 -0.0321034 0.0066517
## ArnAng -0.0002471 3.123e-03 0.0021953 0.0003167 0.0012586 -0.0006780
## BarAlp -0.0038025 1.364e-02 0.0071070 -0.0037161 -0.0074120 0.0108688
## BetGla 0.8192326 6.383e-02 -0.5836491 0.3668907 -0.0225551 -0.1986668
## BisViv -0.0005453 3.552e-02 0.0270180 -0.0021520 -0.0125899 0.0031879
## CalCan 0.0011739 1.229e-02 -0.0354523 -0.0125542 -0.0358521 0.0064451
## CarAqu -0.0210399 5.312e-03 -0.0130835 0.0116049 -0.0142898 0.0445873
## CarBig 0.0409427 4.612e-02 0.0644952 0.0101647 -0.0119870 -0.0070467
## CarBru 0.0030096 3.287e-04 -0.0068822 0.0001651 -0.0088680 -0.0076441
## CarCap 0.0042078 3.346e-02 0.0448834 -0.0202606 -0.0090574 0.0036027
## CarCat -0.0004904 6.915e-03 0.0048414 -0.0009678 0.0005209 -0.0007891
## CarDef 0.0081765 -1.755e-03 0.0039217 0.0039383 0.0018423 -0.0023041
## CarDis -0.0082165 1.974e-02 -0.0009490 0.0001602 0.0027969 -0.0071560
## CarGyn -0.0482684 1.842e-02 -0.0188156 0.0264077 -0.0286480 0.0214975
## CarLep 0.0009315 3.996e-03 -0.0027907 0.0005955 -0.0020295 -0.0011901
## CarLim -0.0035976 -3.155e-03 -0.0025661 0.0011882 -0.0356168 0.0192217
## CarMag 0.0056194 -2.752e-03 -0.0081773 0.0063333 -0.0013628 0.0109439
## CarSci 0.0295113 2.217e-01 0.2246483 -0.0187630 -0.0140589 0.0066056
## CarTri 0.0005545 -4.329e-03 -0.0070322 0.0072288 -0.0009444 0.0038081
## CarUtr -0.0013183 3.634e-04 -0.0033927 -0.0081558 -0.0038061 0.0177324
## CarVag -0.2905954 1.553e-01 -0.0929405 0.1382196 -0.0176416 0.0984784
## CasSep -0.0031936 2.907e-03 0.0001294 -0.0025273 -0.0032087 0.0008900
## CerAlp -0.0002103 3.028e-03 0.0007999 0.0004029 0.0010796 -0.0008635
## ChaAng 0.0151844 -4.467e-03 -0.0020074 -0.0033196 0.0083605 -0.0059421
## CopTri -0.0235913 -4.135e-02 -0.0259630 -0.0549125 -0.0317180 0.0225175
## CorCan -0.0318838 -1.375e-01 -0.0965232 -0.0828000 0.0546787 0.0077917
## CysMon -0.0105081 7.560e-03 -0.0014559 0.0020611 0.0020980 -0.0044877
## DasFru 0.0011036 3.236e-03 -0.0020339 -0.0117192 -0.0164579 0.0085097
## AveFle 0.0052655 -1.953e-02 -0.0229655 -0.0657581 0.0141583 -0.0006445
## DiaLap 0.0111855 4.424e-03 0.0294758 -0.0089086 -0.0112961 0.0010584
## DipCom 0.0211884 -3.845e-03 0.0032610 0.0165954 -0.0001736 0.0004701
## DryExp 0.0043839 1.133e-03 -0.0043524 -0.0041197 -0.0048403 -0.0017071
## DryInt 0.0093297 9.328e-02 0.1012610 -0.0347696 -0.0183230 -0.0052616
## ElyTra 0.0075692 1.715e-02 -0.0034808 -0.0037686 -0.0033667 -0.0019326
## EmpNig -0.1768362 -2.996e-01 0.2059141 0.1199681 -0.2043569 0.1555607
## EpiHor -0.0025824 -1.640e-03 -0.0013080 0.0009254 -0.0004621 -0.0005627
## EquArv -0.0414357 4.823e-02 -0.0206802 0.0131856 0.0025623 0.0117202
## EquSci -0.0086025 4.014e-03 -0.0029584 0.0020662 0.0031823 -0.0022616
## EquSyl -0.1513167 4.165e-02 -0.0460685 0.0516678 -0.0499630 -0.0216178
## EquVar -0.0087393 8.949e-03 -0.0019396 0.0021823 -0.0003477 0.0093137
## EriVir -0.0039035 -3.154e-03 0.0028611 0.0024341 -0.0074475 0.0094327
## EurRad -0.0080198 -8.113e-04 -0.0003190 -0.0012825 -0.0394944 0.0280646
## FraVir -0.0051418 1.236e-02 -0.0065701 -0.0026783 0.0005633 0.0057887
## GauHis -0.0872529 -6.820e-02 0.0074221 0.0203432 -0.0762886 0.0069166
## GeoLiv -0.0605556 -7.674e-02 -0.0145522 -0.0301016 0.0735362 0.0106602
## HupApr -0.0003323 5.392e-03 0.0069413 -0.0007161 -0.0023630 0.0055034
## JunCom 0.0298695 1.473e-02 -0.0176247 -0.0149420 -0.0475285 0.0776285
## JunTri 0.0038641 9.864e-03 0.0054100 0.0051733 0.0015852 -0.0040037
## KalPol -0.0151548 -3.186e-02 0.0200746 0.0125437 -0.0479188 0.0360065
## LinBor -0.1201887 3.051e-03 -0.1290830 -0.0075510 0.0500574 0.0657199
## LisCor -0.0105575 -9.032e-03 -0.0041033 -0.0021102 -0.0121449 -0.0025178
## LonVil -0.0049403 4.589e-03 -0.0055954 -0.0001111 -0.0235607 0.0069680
## LuzPar -0.0119458 -7.527e-03 -0.0046480 0.0033335 -0.0039942 -0.0027720
## LycAno 0.1389051 -8.466e-02 -0.1066549 -0.1348848 -0.0918850 0.0679900
## MaiTri -0.0072448 6.687e-04 0.0024845 0.0052613 -0.0071033 0.0151891
## MinBif -0.0002103 3.028e-03 0.0007999 0.0004029 0.0010796 -0.0008635
## MitNud -0.1151545 9.670e-02 -0.0700393 0.0513760 0.0207975 0.0108263
## MoeMac 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## MonUni -0.0049820 -2.225e-03 -0.0011786 0.0018473 -0.0034965 0.0035119
## MyrGal -0.0019418 1.052e-02 -0.0123232 -0.0160301 -0.0300787 0.0403969
## OrtSec -0.0725594 -1.917e-02 -0.0163213 0.0269213 -0.0180850 -0.0258470
## PacAur -0.0019313 -1.055e-03 0.0008515 0.0010919 -0.0026497 0.0023010
## ParKot 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## PetFri -0.0284365 1.810e-02 -0.0102724 0.0052347 -0.0103084 0.0056610
## PhyCae 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## PoaArc 0.0009759 1.801e-03 0.0009621 0.0017446 -0.0009957 -0.0004377
## PyrAsa -0.0168430 1.867e-02 -0.0063040 -0.0024762 0.0063346 0.0058883
## PyrGra 0.0027736 7.881e-03 0.0046147 0.0015748 0.0014626 -0.0031491
## RhiMin -0.0017295 -5.407e-04 0.0014352 -0.0037654 -0.0081873 0.0015224
## RhoGro -0.2690178 -3.703e-01 -0.1873847 0.4078937 0.3267524 0.3242916
## RhoLap 0.0091259 5.917e-02 0.0719146 -0.0296868 -0.0123269 -0.0058217
## RibGla 0.0481060 8.183e-03 -0.0499937 -0.0455092 -0.0441599 -0.0039904
## RubArc -0.0273704 3.132e-02 -0.0197233 0.0254944 -0.0354780 0.0287479
## RubCha -0.0344208 7.098e-03 -0.0124079 0.0240123 -0.0252084 0.0093339
## RubIda 0.0269926 8.663e-03 -0.0266955 -0.0252722 -0.0277438 -0.0110245
## SalArc -0.0391834 -3.140e-02 0.0139480 0.0207462 -0.0429141 0.0612463
## SalArg -0.0082224 -1.172e-02 -0.0014281 -0.0068429 -0.0060967 -0.0071355
## SalGla -0.0152890 3.576e-02 -0.0311270 0.0109986 0.0112602 0.0240932
## SalHum 0.0097719 -2.513e-03 -0.0025056 0.0096054 0.0018143 0.0046438
## SalPed -0.0004661 1.285e-04 -0.0011995 -0.0028835 -0.0013457 0.0062694
## SalPla -0.0438209 3.051e-02 -0.0244432 -0.0009350 -0.0082231 -0.0231176
## SalUva 0.0212769 9.226e-03 0.0645130 -0.0128292 -0.0234795 0.0037264
## SalVes -0.3455932 9.161e-01 0.0687005 0.1219039 0.2670856 -0.1131331
## SchPur -0.0036117 6.863e-03 -0.0010719 -0.0064498 -0.0029387 0.0040771
## SelSel -0.0001931 -1.238e-04 0.0008726 -0.0011384 -0.0027258 0.0044546
## SolMac 0.1069544 4.663e-02 -0.1378656 -0.1988209 -0.0531017 0.0072046
## SolMul -0.0077250 2.473e-02 0.0290467 -0.0050358 -0.0303895 0.0212694
## SteBor -0.0013437 7.576e-03 -0.0005646 -0.0001127 0.0010710 -0.0052352
## SteLon 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## TofPus -0.0091845 3.317e-02 0.0357348 -0.0104053 -0.0216039 0.0108504
## TriAlp -0.0027313 -1.492e-03 0.0012043 0.0015441 -0.0037472 0.0032541
## TriBor 0.0503586 -2.239e-02 -0.0761828 -0.0642320 0.0247420 0.0241713
## TriCes -0.0360761 3.168e-02 0.0990550 -0.0752284 -0.2186683 0.1144556
## TriSpi -0.0002761 -1.399e-04 0.0001901 -0.0138712 -0.0072406 0.0014350
## VacCes 0.0695193 -1.684e-01 -0.0781768 -0.2762751 0.1961701 -0.0328316
## VacMyr 0.1277321 -2.997e-01 0.1059792 -0.2933343 0.4841707 -0.1354046
## VacOxy -0.0222647 -8.277e-03 -0.0097867 0.0248751 -0.0267783 0.0159077
## VacUli 0.4833546 -1.340e-01 0.7756458 0.2974321 0.0795106 -0.0299729
## VacVit -0.0751003 -1.397e-01 -0.0196882 0.0276122 0.0795086 -0.0087208
## VibEdu 0.0018694 2.063e-02 -0.0178973 -0.0138951 -0.0024587 0.0049775
## VioAdu -0.0238806 3.197e-02 0.0084307 -0.0066019 -0.0278489 0.0385384
## VioRen -0.0138164 1.835e-02 -0.0191517 0.0015365 -0.0072524 -0.0011862
## AbiBal -0.0349415 -4.402e-02 0.0166622 0.0046459 -0.0516524 -0.0063513
## LarLar -0.0282307 2.022e-02 -0.0270662 0.0348298 -0.0326071 0.0269357
## PicGla -0.0772446 3.700e-02 -0.2009061 -0.0382234 0.0801777 0.3107243
## PicMar -0.6560188 -4.048e-01 -0.0740443 0.1593563 -0.0974446 -0.5026995
## AreHum 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## BetMin 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## BetPum 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## CarBel 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## CarGla 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## CopLap 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## CorTri 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## LuzSpi 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## PoaAlp 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## SalHer 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
## SalMyr 0.0000000 0.000e+00 0.0000000 0.0000000 0.0000000 0.0000000
##
##
## Site scores (weighted sums of species scores)
##
## PC1 PC2 PC3 PC4 PC5 PC6
## EA1 -0.415982 -0.2375947 -0.084989 0.057645 -0.265864 -0.4327770
## EB1 -0.024410 -0.0156492 0.110326 -0.143927 -0.344623 0.5631986
## EC1 0.024664 0.0723245 -0.045457 -0.261923 -0.367833 0.1901909
## ED1 -0.287722 -0.2047784 0.034613 0.140693 -0.192284 0.2369743
## EE1 -0.099422 -0.1410162 0.140520 0.075481 -0.313831 0.5240257
## EF1 -0.346944 -0.3747661 -0.090459 0.270502 0.048008 -0.0191039
## EG1 -0.119052 -0.1039279 -0.254541 0.203734 0.102205 0.6881157
## EH1 -0.076137 0.0034968 0.085790 -0.319874 -0.544030 0.0699670
## EI1 -0.031596 0.0087090 -0.081316 -0.195475 -0.091223 0.4250043
## EJ1 -0.133202 -0.0699686 0.087083 -0.130136 -0.440110 0.1141973
## EK1 -0.237873 -0.3267671 0.188960 0.327581 -0.157710 0.0120033
## EA2 -0.341060 -0.0797058 -0.194039 0.295800 0.146426 -0.2539958
## EB2 -0.138698 -0.2166226 -0.185055 -0.046068 0.273605 0.7177036
## EC2 0.066710 0.2861341 -0.199850 0.042644 -0.145342 -0.0852286
## ED2 -0.115622 0.0048945 0.166743 -0.043645 0.152156 0.3202079
## EE2 -0.060878 0.1704884 -0.206130 0.232067 0.033205 0.2377470
## EF2 -0.210282 -0.1148388 0.092717 0.118885 -0.288504 0.2505338
## EG2 -0.233738 -0.2206981 0.176674 0.143625 -0.362885 0.0403683
## EH2 0.001556 -0.1714989 0.213716 -0.074183 -0.543148 0.1910570
## EI2 0.278714 0.0605503 -0.222347 0.268733 -0.131450 -0.0504859
## EJ2 0.197955 -0.0945912 -0.243880 0.278593 -0.013686 0.2166497
## EK2 -0.195561 -0.2052129 0.178720 0.085370 -0.458362 0.2907055
## EA3 -0.160469 0.0550980 -0.312492 0.418791 0.181288 -0.2274330
## EB3 -0.187270 -0.3969860 -0.021136 -0.036241 0.247918 0.2096055
## EC3 -0.128100 0.1559568 -0.307736 0.391820 0.092387 -0.3311941
## ED3 -0.306966 -0.1370661 -0.072618 0.113823 -0.215438 0.2163814
## EE3 -0.395071 0.1603574 -0.144635 0.158600 0.076409 0.0528140
## EF3 -0.197266 0.5789923 0.044931 -0.088845 0.191027 -0.1219302
## EG3 -0.250776 -0.1580662 -0.252065 0.212316 -0.200049 -0.4738925
## EH3 -0.082649 -0.2007295 -0.012375 -0.074729 -0.243288 0.3871958
## EI3 0.046506 0.0046434 -0.208145 0.016458 -0.333107 -0.2900212
## EJ3 0.031193 0.0550731 -0.006802 -0.259646 -0.439108 0.1815657
## EK3 -0.005962 -0.2891557 0.289794 0.066341 -0.152382 0.3932536
## EA4 -0.251345 0.4688687 -0.052893 0.047720 0.374456 0.1106961
## EB4 -0.332029 -0.1594239 -0.103276 -0.084803 -0.183548 -0.4407714
## EC4 0.070001 0.0399196 -0.160198 -0.209835 -0.173922 0.2636204
## ED4 -0.417940 -0.0688637 -0.144137 0.179505 0.133433 -0.0505122
## EE4 -0.361909 -0.3131803 -0.112259 0.085817 -0.032076 -0.4040886
## EF4 -0.339388 0.3829333 -0.079334 0.023610 0.185193 0.0397160
## EG4 -0.389615 -0.0385205 -0.145945 0.109137 0.031712 0.1618775
## EH4 -0.448159 0.0073665 -0.020712 0.168463 -0.110631 -0.3952421
## EI4 -0.309342 -0.2533057 -0.021218 0.215648 -0.213956 0.1396465
## EJ4 -0.277996 -0.1765472 -0.140808 0.099617 -0.049751 -0.0605727
## EK4 -0.288483 -0.2800093 0.023045 -0.033528 -0.490733 -0.2265012
## EA5 -0.321932 -0.3095533 -0.150093 0.103586 0.077840 -0.1675870
## EB5 0.111316 -0.1887965 -0.377865 0.012792 0.431934 0.4245379
## EC5 -0.079638 -0.3771761 0.040651 -0.031538 0.389919 0.3722467
## ED5 -0.265614 -0.2711957 -0.064674 -0.101415 0.066331 0.2065365
## EE5 -0.193151 0.2982649 -0.111434 0.222548 0.231090 0.2568414
## EF5 -0.017017 0.3171291 -0.205283 0.201534 -0.175705 -0.0370518
## EG5 -0.400579 -0.0033773 -0.100097 0.229803 0.115207 -0.1499013
## EH5 -0.041599 0.3954450 -0.257004 0.301400 0.227839 -0.2727498
## EI5 -0.375050 0.1556763 -0.059822 0.132984 0.088493 0.2151533
## EJ5 -0.387189 -0.3444965 -0.099992 0.132106 -0.108309 -0.3053327
## EK5 -0.246017 -0.1920328 0.011177 -0.054974 -0.352621 -0.1893417
## EA6 -0.174360 0.2400716 -0.108503 -0.093987 0.074440 0.2003563
## EB6 -0.348115 -0.3896719 -0.043313 0.250058 -0.076561 -0.0078197
## EC6 -0.180555 0.1312690 -0.254117 0.213195 0.397484 0.5265169
## ED6 -0.228523 0.5461723 0.039332 -0.020708 0.264769 0.1271968
## EE6 -0.332365 -0.3488690 -0.134062 0.252415 0.155221 -0.0205503
## EF6 0.133635 -0.2242758 -0.082537 -0.380027 0.663801 -0.0718874
## EG6 -0.237631 -0.3295483 0.194696 -0.013085 -0.325166 -0.4977477
## EH6 -0.280671 0.4435417 -0.010615 -0.012115 0.016898 -0.1934258
## EI6 -0.044411 -0.1822693 0.363559 0.188987 -0.093218 -0.2657606
## EJ6 -0.391314 -0.2450876 -0.117261 0.085568 -0.177154 -0.0950216
## EK6 -0.079299 -0.1714857 -0.002684 0.162315 0.235600 0.3906813
## EA7 -0.112546 0.2886555 -0.184735 0.194277 -0.084437 -0.3638347
## EB7 -0.371372 -0.3101127 -0.122875 0.015629 -0.031133 -0.4764749
## EC7 -0.243198 -0.0873045 -0.152183 0.085958 0.003043 0.3696814
## ED7 -0.323413 -0.3226478 -0.108599 0.081777 0.001065 -0.2417741
## EE7 -0.251517 -0.3438374 0.096896 -0.134238 -0.176404 -0.5259823
## EF7 -0.212104 0.6185172 0.050406 -0.083422 0.216549 -0.0694084
## EG7 -0.241857 0.4881788 -0.025789 -0.049010 0.069461 0.0044830
## EH7 -0.249470 0.5010697 -0.063409 -0.069772 0.169473 0.1362002
## EI7 0.062261 -0.3309165 0.418833 0.086020 0.396998 -0.1285808
## EJ7 -0.208121 -0.2146228 0.042104 -0.128672 -0.390772 -0.1701965
## EK7 0.061809 -0.2147503 0.391904 0.169891 -0.159137 0.2748849
## EA8 -0.354042 0.3605760 -0.078045 -0.041568 0.093645 -0.2510489
## EB8 -0.357395 -0.2884467 -0.030265 -0.051759 -0.323104 -0.6101201
## EC8 -0.194133 0.0436837 -0.164165 -0.042179 0.107441 0.6305336
## ED8 -0.123621 0.3723937 -0.053166 -0.179321 0.078608 0.1914103
## EE8 -0.331732 0.4380363 0.015559 -0.009568 0.068937 -0.3446782
## EF8 -0.047014 -0.1144633 0.149508 0.181918 -0.064093 0.5802079
## EG8 -0.176066 0.3245507 -0.113086 -0.136321 0.034670 0.3626584
## EH8 -0.314806 0.4467076 -0.011786 -0.025858 0.093207 -0.3449864
## EI8 -0.394583 0.2414512 -0.054140 0.181674 0.172693 -0.1265528
## EJ8 -0.051173 -0.3794242 0.029801 0.090259 0.454876 -0.3828370
## EK8 -0.226319 -0.3225898 -0.039308 -0.188348 -0.167810 -0.1964019
## E600A1 0.052462 0.0001359 -0.131249 -0.615090 -0.347870 0.1665578
## E600B2 -0.158828 0.3657194 -0.096182 -0.200420 0.088913 0.1865258
## E600C3 0.264581 -0.0284503 -0.375796 -0.358219 -0.079596 0.1932679
## E600D4 0.018471 -0.1034535 -0.120484 -0.611932 0.126394 0.0490700
## E600E5 0.412533 -0.0401912 -0.466626 -0.045978 0.136950 -0.1142331
## E600F6 0.034238 -0.2483698 -0.074539 -0.647888 0.588085 0.0341514
## E600G7 0.024321 -0.3402338 0.273863 -0.278080 0.524735 -0.3928458
## E600H8 0.288683 -0.1451288 -0.337455 0.118496 0.312083 0.1708658
## E600I9 0.039400 -0.3130656 0.426800 -0.176445 0.268988 -0.3956370
## E600J10 0.266557 -0.2341682 0.020131 -0.357685 0.412296 -0.4337423
## E600K11 0.113436 -0.2895432 -0.126535 -0.006495 0.076009 0.2193837
## E615A1 -0.398751 0.1414503 -0.108645 0.224908 0.299449 -0.0757224
## E615B2 0.102413 -0.0198422 -0.097714 -0.556907 -0.367656 0.1494211
## E615C3 0.109468 -0.1325610 -0.087110 -0.837401 0.256246 -0.0419529
## E615D4 0.083144 -0.2284537 0.012108 -0.775289 0.615130 -0.1434278
## E615E5 0.464979 0.0738814 -0.436313 0.152700 -0.235542 -0.2812961
## E615F6 0.127195 -0.2530664 -0.154604 -0.365799 0.661385 0.0345013
## E615G7 0.197691 -0.2837731 -0.093543 -0.129772 0.713281 0.0204153
## E615H8 0.031084 -0.2824584 0.268788 -0.400544 0.470941 -0.3879919
## E615I9 -0.138505 -0.3692454 0.232986 -0.052299 0.259870 -0.4636241
## E615J10 0.128697 -0.3222222 0.418425 0.055461 0.320212 0.2662428
## E615K11 0.069092 0.0441514 -0.111007 -0.675908 -0.366242 0.0674424
## E645A1 -0.178285 -0.1686624 -0.227363 -0.385073 -0.133554 0.1152721
## E645B2 -0.157584 0.2740646 -0.129855 -0.109061 0.132543 0.4407630
## E645C3 0.158454 0.0045669 -0.185907 -0.549410 -0.334448 0.0572224
## E645D4 0.146684 -0.1848486 0.425690 0.351653 0.227846 0.2964192
## E645E5 0.497147 -0.0916859 0.141002 0.074586 0.192263 -0.2683437
## E645F6 0.414504 -0.0454825 -0.041817 0.328036 -0.023671 0.0146770
## E645G7 0.332575 -0.1817797 0.445927 -0.002542 0.346675 -0.0784807
## E645H8 0.122283 -0.1996439 0.386550 0.359945 0.256252 0.3227310
## E645I9 0.357435 -0.1835143 0.298052 -0.256676 0.500643 -0.2501844
## E645J10 0.375687 -0.1383187 -0.184345 -0.186965 0.311365 -0.1646962
## E645K11 0.121608 -0.2872022 0.291010 -0.492576 0.433369 -0.0558614
## E675A1 0.002016 0.0147260 -0.203422 -0.497845 -0.075096 0.2967825
## E675B2 0.271351 0.0791471 -0.280138 -0.361098 -0.371347 -0.0979734
## E675C3 0.456540 -0.0294898 -0.330363 0.345576 -0.052293 -0.1007761
## E675D4 0.291624 -0.0477364 -0.424995 -0.318103 0.126577 0.0937860
## E675E5 0.088714 0.0649112 -0.111077 -0.618887 -0.350284 0.0564788
## E675F6 0.423469 0.0007559 -0.479055 0.210507 -0.119155 -0.1425503
## E675G7 0.203520 -0.1347550 -0.411589 0.408547 0.194780 0.2031761
## E675H8 0.388117 0.0521752 -0.484857 0.078922 -0.132590 -0.0127093
## E675I9 0.392107 0.0448708 -0.418394 -0.043815 -0.234203 -0.1883014
## E675J10 0.457614 0.0113773 -0.383218 0.134435 -0.142583 -0.1679556
## E675K11 0.369780 -0.0950870 -0.094814 0.363479 0.068653 0.1757262
## E710A1 0.398384 0.0278827 -0.432728 -0.285614 -0.213144 -0.1659709
## E710B2 0.354066 0.0365713 -0.362592 -0.237588 -0.275103 -0.1079694
## E710C3 0.391269 0.0213160 -0.383084 -0.116668 -0.305547 -0.1046464
## E710D4 0.431513 -0.0429251 0.350186 0.222650 -0.078422 -0.1154075
## E710E5 0.296315 -0.0614526 -0.376204 0.436596 0.068068 0.1617254
## E710F6 0.091999 0.3708385 0.186466 0.295651 0.290793 0.0608468
## E710G7 0.233630 0.0652892 -0.070170 0.508505 0.245311 0.0993852
## E710H8 0.304141 -0.0871402 -0.262685 0.449770 0.170713 0.2549267
## E710I9 0.402155 -0.0694503 0.404766 0.183297 -0.157407 -0.0483277
## E710J10 0.389286 -0.0966211 0.271669 0.331231 0.017758 0.0021088
## E710K11 0.508210 0.0355353 -0.323402 0.191930 -0.189918 -0.2506358
## E745A1 -0.040259 0.5795732 0.153104 0.077104 0.206629 -0.1652592
## E745B2 0.367175 0.2970189 -0.237265 0.189453 -0.046119 -0.2904403
## E745C3 0.404493 0.2546792 -0.282109 0.274733 -0.057821 -0.3269398
## E745D4 0.298934 0.3366722 0.124018 0.275226 0.073960 -0.2407184
## E745E5 0.363239 -0.0471815 0.532457 0.198155 -0.058432 -0.0743922
## E745F6 0.208647 0.4206691 -0.057209 0.016840 0.023333 -0.2470699
## E745G7 0.402103 0.0338992 -0.193955 0.120129 -0.143405 -0.1897736
## E745H8 -0.056356 0.3569810 -0.048260 -0.480182 -0.120099 0.0614723
## E745I9 0.486876 -0.0444745 0.227189 0.343379 -0.124772 -0.1750975
## E745J10 0.480281 0.0531614 -0.324458 0.215595 -0.164115 -0.1318711
## E745K11 -0.005039 -0.0025528 0.003470 -0.253131 -0.132131 0.0261867
## E775A1 0.328570 -0.1355052 0.358747 0.287725 -0.258443 0.0091056
## E775B2 -0.075738 0.4382614 0.199647 -0.204123 0.046827 -0.0718429
## E775C3 0.046610 0.3706456 0.411249 -0.118446 -0.007989 -0.0602098
## E775D4 0.036164 0.3380042 0.364334 -0.156345 -0.055977 -0.0376103
## E775E5 -0.041418 0.5235283 0.368049 0.053095 0.211002 -0.1136742
## E775F6 0.126931 0.2342515 0.125140 0.226909 -0.129508 -0.0569276
## E775G7 0.282462 -0.0254024 0.643750 0.103207 -0.060317 -0.0130152
## E775H8 0.217862 -0.0922219 0.608986 0.118338 -0.185839 0.0735205
## E775I9 0.233699 -0.1037599 0.380369 0.182061 -0.317003 0.0767450
## E775J10 0.183124 -0.0115388 0.610852 0.048659 -0.210848 0.0942927
## E775K11 0.122832 0.0428850 0.206272 -0.136977 -0.482538 0.2225228
## E800A1 0.199309 -0.1241751 0.611069 0.118579 -0.218507 0.1043235
## E800B2 0.180645 0.0407585 0.466156 -0.070647 -0.125180 -0.0005566
## E800C3 -0.029834 0.5152702 0.394055 0.006373 0.115455 -0.0768178
## E800D4 0.097360 0.1344241 0.327503 -0.234724 -0.208311 0.0253100
## E800E5 0.128695 0.0777423 0.358824 -0.166743 -0.174003 0.0199577
## E800F6 -0.037117 0.5233563 0.366408 -0.073242 0.039426 -0.0597183
## E800G7 0.087512 0.3765585 0.520891 0.005459 0.066078 -0.0800164
## E800H8 0.106157 -0.2327713 -0.033729 0.395081 0.067261 0.3966586
## E800I9 -0.048764 0.4941045 0.333703 -0.130402 -0.067820 -0.0038752
## E800J10 -0.029992 0.4492086 0.347423 -0.165767 -0.127265 0.0205810
## E800K11 0.028252 0.3678315 0.528474 0.086848 0.035108 -0.0178033summary(spe.h.pca, display=NULL) # only eigenvalues and their contribution to the variance##
## Call:
## rda(X = spe.hel)
##
## Partitioning of variance:
## Inertia Proportion
## Total 0.7612 1
## Unconstrained 0.7612 1
##
## Eigenvalues, and their contribution to the variance
##
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Eigenvalue 0.1191 0.1026 0.08465 0.05173 0.04275 0.04028
## Proportion Explained 0.1565 0.1348 0.11122 0.06795 0.05617 0.05291
## Cumulative Proportion 0.1565 0.2913 0.40251 0.47047 0.52663 0.57955
## PC7 PC8 PC9 PC10 PC11 PC12
## Eigenvalue 0.03001 0.02717 0.02467 0.02201 0.01684 0.01542
## Proportion Explained 0.03943 0.03570 0.03241 0.02891 0.02212 0.02026
## Cumulative Proportion 0.61898 0.65468 0.68709 0.71600 0.73813 0.75839
## PC13 PC14 PC15 PC16 PC17 PC18
## Eigenvalue 0.01385 0.01352 0.01241 0.01072 0.009377 0.00871
## Proportion Explained 0.01820 0.01776 0.01631 0.01408 0.012320 0.01144
## Cumulative Proportion 0.77659 0.79435 0.81065 0.82473 0.837050 0.84850
## PC19 PC20 PC21 PC22 PC23 PC24
## Eigenvalue 0.008192 0.00725 0.006565 0.006141 0.005546 0.005409
## Proportion Explained 0.010760 0.00953 0.008620 0.008070 0.007290 0.007110
## Cumulative Proportion 0.859260 0.86878 0.877410 0.885480 0.892760 0.899870
## PC25 PC26 PC27 PC28 PC29
## Eigenvalue 0.004977 0.004467 0.004388 0.004203 0.003913
## Proportion Explained 0.006540 0.005870 0.005770 0.005520 0.005140
## Cumulative Proportion 0.906410 0.912270 0.918040 0.923560 0.928700
## PC30 PC31 PC32 PC33 PC34
## Eigenvalue 0.003603 0.003295 0.003001 0.002728 0.002608
## Proportion Explained 0.004730 0.004330 0.003940 0.003580 0.003430
## Cumulative Proportion 0.933430 0.937760 0.941710 0.945290 0.948720
## PC35 PC36 PC37 PC38 PC39
## Eigenvalue 0.002444 0.002325 0.002186 0.002048 0.001967
## Proportion Explained 0.003210 0.003050 0.002870 0.002690 0.002580
## Cumulative Proportion 0.951930 0.954980 0.957850 0.960540 0.963130
## PC40 PC41 PC42 PC43 PC44
## Eigenvalue 0.001728 0.001698 0.001541 0.001405 0.001351
## Proportion Explained 0.002270 0.002230 0.002020 0.001850 0.001780
## Cumulative Proportion 0.965400 0.967630 0.969660 0.971500 0.973280
## PC45 PC46 PC47 PC48 PC49
## Eigenvalue 0.001322 0.001208 0.001129 0.001049 0.0009811
## Proportion Explained 0.001740 0.001590 0.001480 0.001380 0.0012900
## Cumulative Proportion 0.975010 0.976600 0.978080 0.979460 0.9807500
## PC50 PC51 PC52 PC53 PC54
## Eigenvalue 0.000956 0.0009067 0.000874 0.0008178 0.0007714
## Proportion Explained 0.001260 0.0011900 0.001150 0.0010700 0.0010100
## Cumulative Proportion 0.982000 0.9832000 0.984340 0.9854200 0.9864300
## PC55 PC56 PC57 PC58 PC59
## Eigenvalue 0.0007614 0.0006977 0.0006501 0.0006262 0.0006112
## Proportion Explained 0.0010000 0.0009200 0.0008500 0.0008200 0.0008000
## Cumulative Proportion 0.9874300 0.9883500 0.9892000 0.9900300 0.9908300
## PC60 PC61 PC62 PC63 PC64
## Eigenvalue 0.0005987 0.0005505 0.0005004 0.0004551 0.0004476
## Proportion Explained 0.0007900 0.0007200 0.0006600 0.0006000 0.0005900
## Cumulative Proportion 0.9916200 0.9923400 0.9930000 0.9935900 0.9941800
## PC65 PC66 PC67 PC68 PC69
## Eigenvalue 0.0004135 0.0003739 0.0003603 0.000313 0.0002893
## Proportion Explained 0.0005400 0.0004900 0.0004700 0.000410 0.0003800
## Cumulative Proportion 0.9947300 0.9952200 0.9956900 0.996100 0.9964800
## PC70 PC71 PC72 PC73 PC74
## Eigenvalue 0.0002502 0.0002385 0.0002084 0.0002039 0.0001892
## Proportion Explained 0.0003300 0.0003100 0.0002700 0.0002700 0.0002500
## Cumulative Proportion 0.9968100 0.9971200 0.9974000 0.9976600 0.9979100
## PC75 PC76 PC77 PC78 PC79
## Eigenvalue 0.0001673 0.0001426 0.0001352 0.000109 0.0001045
## Proportion Explained 0.0002200 0.0001900 0.0001800 0.000140 0.0001400
## Cumulative Proportion 0.9981300 0.9983200 0.9985000 0.998640 0.9987800
## PC80 PC81 PC82 PC83 PC84
## Eigenvalue 9.456e-05 9.032e-05 8.768e-05 8.002e-05 7.623e-05
## Proportion Explained 1.200e-04 1.200e-04 1.200e-04 1.100e-04 1.000e-04
## Cumulative Proportion 9.989e-01 9.990e-01 9.991e-01 9.992e-01 9.993e-01
## PC85 PC86 PC87 PC88 PC89
## Eigenvalue 6.637e-05 6.213e-05 5.594e-05 4.927e-05 4.227e-05
## Proportion Explained 9.000e-05 8.000e-05 7.000e-05 6.000e-05 6.000e-05
## Cumulative Proportion 9.994e-01 9.995e-01 9.996e-01 9.997e-01 9.997e-01
## PC90 PC91 PC92 PC93 PC94
## Eigenvalue 3.793e-05 3.296e-05 2.921e-05 2.782e-05 2.243e-05
## Proportion Explained 5.000e-05 4.000e-05 4.000e-05 4.000e-05 3.000e-05
## Cumulative Proportion 9.998e-01 9.998e-01 9.998e-01 9.999e-01 9.999e-01
## PC95 PC96 PC97 PC98 PC99
## Eigenvalue 1.758e-05 1.247e-05 1.068e-05 8.531e-06 7.656e-06
## Proportion Explained 2.000e-05 2.000e-05 1.000e-05 1.000e-05 1.000e-05
## Cumulative Proportion 9.999e-01 9.999e-01 1.000e+00 1.000e+00 1.000e+00
## PC100 PC101 PC102 PC103 PC104
## Eigenvalue 6.146e-06 5.762e-06 2.969e-06 1.561e-06 1.276e-06
## Proportion Explained 1.000e-05 1.000e-05 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
##
## 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:eigen(cov(spe.hel)) # also compute the eigenvalues## $values
## [1] 1.191117e-01 1.026150e-01 8.465447e-02 5.172552e-02 4.275334e-02
## [6] 4.027692e-02 3.001343e-02 2.717138e-02 2.467329e-02 2.200627e-02
## [11] 1.684011e-02 1.542256e-02 1.385387e-02 1.351686e-02 1.241396e-02
## [16] 1.071673e-02 9.377003e-03 8.710015e-03 8.191751e-03 7.250343e-03
## [21] 6.564948e-03 6.141461e-03 5.546072e-03 5.408781e-03 4.976573e-03
## [26] 4.466721e-03 4.388460e-03 4.202945e-03 3.912596e-03 3.602691e-03
## [31] 3.294647e-03 3.001131e-03 2.728219e-03 2.607523e-03 2.443996e-03
## [36] 2.324839e-03 2.186346e-03 2.047948e-03 1.967186e-03 1.728210e-03
## [41] 1.698443e-03 1.541342e-03 1.404781e-03 1.351337e-03 1.321536e-03
## [46] 1.207786e-03 1.129064e-03 1.048737e-03 9.810682e-04 9.560275e-04
## [51] 9.066534e-04 8.739844e-04 8.178441e-04 7.713656e-04 7.614423e-04
## [56] 6.976690e-04 6.501368e-04 6.261739e-04 6.112167e-04 5.986583e-04
## [61] 5.504852e-04 5.004073e-04 4.551005e-04 4.475810e-04 4.134940e-04
## [66] 3.738820e-04 3.602827e-04 3.130093e-04 2.892666e-04 2.501797e-04
## [71] 2.385485e-04 2.084259e-04 2.039327e-04 1.892429e-04 1.673445e-04
## [76] 1.426289e-04 1.351856e-04 1.089837e-04 1.044609e-04 9.456492e-05
## [81] 9.032066e-05 8.767543e-05 8.002499e-05 7.623374e-05 6.636881e-05
## [86] 6.212913e-05 5.593568e-05 4.927185e-05 4.226972e-05 3.792656e-05
## [91] 3.296031e-05 2.920827e-05 2.782477e-05 2.243080e-05 1.757837e-05
## [96] 1.247141e-05 1.067525e-05 8.530759e-06 7.655770e-06 6.146403e-06
## [101] 5.761735e-06 2.968729e-06 1.561038e-06 1.276035e-06 5.859312e-21
## [106] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [111] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [116] 0.000000e+00 -5.260653e-20 -6.807033e-20 -1.090728e-19 -1.531352e-19
## [121] -2.147588e-19 -3.162159e-19 -3.430523e-19 -6.843726e-19 -3.964251e-18
##
## $vectors
## [,1] [,2] [,3] [,4]
## [1,] 5.224582e-03 5.205995e-03 0.0028779536 -0.0012352247
## [2,] 9.588912e-04 -6.648639e-05 -0.0004845802 0.0046528051
## [3,] -3.036877e-02 3.030844e-02 0.0637436174 0.2624144662
## [4,] -2.201074e-03 3.767977e-04 0.0024499206 -0.0010968938
## [5,] 5.478078e-03 -2.460876e-03 -0.0048388318 0.0010017548
## [6,] 1.296237e-02 2.105050e-02 0.0028926861 -0.0006848784
## [7,] 2.599779e-04 3.540454e-03 -0.0027403408 -0.0005057366
## [8,] 1.838321e-04 2.503479e-03 -0.0019377136 -0.0003576098
## [9,] -2.593017e-02 3.121928e-02 -0.0869189736 -0.0237062862
## [10,] 1.838321e-04 2.503479e-03 -0.0019377136 -0.0003576098
## [11,] 2.829485e-03 1.093815e-02 -0.0062729429 0.0041961506
## [12,] -6.095950e-01 5.116837e-02 0.5151554123 -0.4142815500
## [13,] 4.057476e-04 2.847594e-02 -0.0238473625 0.0024299242
## [14,] -8.735279e-04 9.851398e-03 0.0312918253 0.0141758692
## [15,] 1.565593e-02 4.258304e-03 0.0115480547 -0.0131038406
## [16,] -3.046563e-02 3.697025e-02 -0.0569264293 -0.0114776212
## [17,] -2.239470e-03 2.635111e-04 0.0060745552 -0.0001864790
## [18,] -3.131066e-03 2.682726e-02 -0.0396161321 0.0228776032
## [19,] 3.649293e-04 5.543809e-03 -0.0042732366 0.0010927564
## [20,] -6.084179e-03 -1.406723e-03 -0.0034615156 -0.0044469710
## [21,] 6.113936e-03 1.582864e-02 0.0008375960 -0.0001808406
## [22,] 3.591676e-02 1.476593e-02 0.0166075500 -0.0298187506
## [23,] -6.931595e-04 3.203202e-03 0.0024631988 -0.0006723900
## [24,] 2.676992e-03 -2.529659e-03 0.0022649647 -0.0013416230
## [25,] -4.181394e-03 -2.206098e-03 0.0072176336 -0.0071513911
## [26,] -2.195948e-02 1.777614e-01 -0.1982848647 0.0211865685
## [27,] -4.126091e-04 -3.470793e-03 0.0062069743 -0.0081624898
## [28,] 9.809424e-04 2.913067e-04 0.0029945750 0.0092092687
## [29,] 2.162334e-01 1.244860e-01 0.0820335631 -0.1560732473
## [30,] 2.376377e-03 2.330145e-03 -0.0001141826 0.0028537956
## [31,] 1.565185e-04 2.427655e-03 -0.0007060652 -0.0004548946
## [32,] -1.129878e-02 -3.581401e-03 0.0017717996 0.0037483580
## [33,] 1.755440e-02 -3.314873e-02 0.0229161665 0.0620054383
## [34,] 2.372490e-02 -1.102651e-01 0.0851958250 0.0934952400
## [35,] 7.819127e-03 6.060421e-03 0.0012850073 -0.0023273582
## [36,] -8.211641e-04 2.594268e-03 0.0017951991 0.0132329200
## [37,] -3.918095e-03 -1.565408e-02 0.0202703929 0.0742519729
## [38,] -8.323213e-03 3.546594e-03 -0.0260166567 0.0100593129
## [39,] -1.576637e-02 -3.082499e-03 -0.0028782656 -0.0187390099
## [40,] -3.262076e-03 9.079226e-04 0.0038416326 0.0046518619
## [41,] -6.942264e-03 7.478166e-02 -0.0893776180 0.0392608013
## [42,] -5.632262e-03 1.374942e-02 0.0030723142 0.0042553819
## [43,] 1.315847e-01 -2.402206e-01 -0.1817492314 -0.1354642384
## [44,] 1.921556e-03 -1.314759e-03 0.0011544987 -0.0010448977
## [45,] 3.083254e-02 3.866287e-02 0.0182533332 -0.0148888052
## [46,] 6.401145e-03 3.218271e-03 0.0026111892 -0.0023330620
## [47,] 1.125955e-01 3.339346e-02 0.0406621653 -0.0583416317
## [48,] 6.502988e-03 7.174005e-03 0.0017120001 -0.0024641321
## [49,] 2.904629e-03 -2.528747e-03 -0.0025253329 -0.0027485387
## [50,] 5.967572e-03 -6.503830e-04 0.0002815551 0.0014481536
## [51,] 3.826048e-03 9.907112e-03 0.0057990803 0.0030242600
## [52,] 6.492534e-02 -5.467666e-02 -0.0065511288 -0.0229708850
## [53,] 4.505974e-02 -6.152052e-02 0.0128444180 0.0339897807
## [54,] 2.473013e-04 4.322755e-03 -0.0061266967 0.0008085874
## [55,] -2.222606e-02 1.180645e-02 0.0155563719 0.0168720579
## [56,] -2.875308e-03 7.907541e-03 -0.0047751115 -0.0058415220
## [57,] 1.127674e-02 -2.553831e-02 -0.0177187468 -0.0141639291
## [58,] 8.943297e-02 2.446096e-03 0.1139345310 0.0085263763
## [59,] 7.855894e-03 -7.240966e-03 0.0036217800 0.0023828208
## [60,] 3.676134e-03 3.679253e-03 0.0049387571 0.0001254062
## [61,] 8.888901e-03 -6.034357e-03 0.0041025263 -0.0037641187
## [62,] -1.033599e-01 -6.787099e-02 0.0941385017 0.1523077402
## [63,] 5.390871e-03 5.361255e-04 -0.0021929176 -0.0059409335
## [64,] 1.565185e-04 2.427655e-03 -0.0007060652 -0.0004548946
## [65,] 8.568706e-02 7.752408e-02 0.0618199193 -0.0580122181
## [66,] -1.210185e-122 0.000000e+00 0.0000000000 0.0000000000
## [67,] 3.707153e-03 -1.783416e-03 0.0010402670 -0.0020859554
## [68,] 1.444885e-03 8.430891e-03 0.0108770465 0.0181007184
## [69,] 5.399184e-02 -1.536506e-02 0.0144059603 -0.0303987521
## [70,] 1.437082e-03 -8.455492e-04 -0.0007516082 -0.0012329110
## [71,] 0.000000e+00 0.000000e+00 0.0000000000 0.0000000000
## [72,] 2.115974e-02 1.450864e-02 0.0090668879 -0.0059108802
## [73,] 2.099336e-140 0.000000e+00 0.0000000000 0.0000000000
## [74,] -7.261687e-04 1.443862e-03 -0.0008492219 -0.0019699165
## [75,] 1.253294e-02 1.496809e-02 0.0055642237 0.0027960182
## [76,] -2.063851e-03 6.318075e-03 -0.0040731701 -0.0017782035
## [77,] 1.286921e-03 -4.334987e-04 -0.0012667706 0.0042518155
## [78,] 2.001774e-01 -2.968643e-01 0.1653942839 -0.4605808746
## [79,] -6.790613e-03 4.743870e-02 -0.0634751157 0.0335214397
## [80,] -3.579591e-02 6.560087e-03 0.0441267480 0.0513875956
## [81,] 2.036647e-02 2.511113e-02 0.0174086900 -0.0287874833
## [82,] 2.561272e-02 5.690170e-03 0.0109517858 -0.0271139072
## [83,] -2.008529e-02 6.945073e-03 0.0235626723 0.0285366081
## [84,] 2.915652e-02 -2.517650e-02 -0.0123111370 -0.0234260092
## [85,] 6.118339e-03 -9.395825e-03 0.0012605163 0.0077267978
## [86,] 1.137658e-02 2.866656e-02 0.0274741156 -0.0124193305
## [87,] -7.271308e-03 -2.014475e-03 0.0022115435 -0.0108460796
## [88,] 3.468155e-04 1.029925e-04 0.0010587421 0.0032559682
## [89,] 3.260735e-02 2.446299e-02 0.0215746767 0.0010557391
## [90,] -1.583227e-02 7.396738e-03 -0.0569420938 0.0144863235
## [91,] 2.571576e-01 7.344545e-01 -0.0606382127 -0.1376500757
## [92,] 2.687468e-03 5.502358e-03 0.0009460866 0.0072829261
## [93,] 1.436644e-04 -9.923067e-05 -0.0007702142 0.0012854337
## [94,] -7.958526e-02 3.738019e-02 0.1216864709 0.2245023446
## [95,] 5.748176e-03 1.982477e-02 -0.0256379811 0.0056862798
## [96,] 9.998182e-04 6.073323e-03 0.0004983242 0.0001272786
## [97,] 0.000000e+00 0.000000e+00 0.0000000000 0.0000000000
## [98,] 6.834239e-03 2.659381e-02 -0.0315411454 0.0117493783
## [99,] 2.032340e-03 -1.195787e-03 -0.0010629345 -0.0017435995
## [100,] -3.747208e-02 -1.794745e-02 0.0672424388 0.0725287505
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## [,9] [,10] [,11] [,12]
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## [125,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,45] [,46] [,47] [,48]
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## [124,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [125,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,53] [,54] [,55] [,56]
## [1,] -4.814089e-02 5.125680e-02 1.166292e-02 -1.005636e-02
## [2,] 2.987756e-02 6.077559e-03 7.357334e-02 -3.034533e-02
## [3,] -4.554941e-02 7.269173e-02 5.003206e-02 -4.290470e-03
## [4,] -1.405323e-03 -6.208304e-03 2.830113e-03 6.398524e-03
## [5,] -1.163345e-01 -6.452006e-02 1.244182e-01 1.210390e-01
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## [,65] [,66] [,67] [,68]
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## [115,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
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## [124,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [125,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,73] [,74] [,75] [,76]
## [1,] -1.176862e-01 -9.004833e-02 4.587599e-01 5.843296e-02
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## [3,] -1.096260e-02 1.015423e-03 3.140809e-03 -2.779864e-03
## [4,] 6.034568e-04 4.121758e-02 -6.183639e-03 -2.228679e-02
## [5,] -7.705155e-02 -8.662287e-03 1.291415e-01 1.415152e-01
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## [125,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,85] [,86] [,87] [,88]
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## [111,] 8.842746e-03 1.088480e-02 2.665939e-02 2.086114e-02
## [112,] 3.957332e-02 1.632786e-02 -1.276973e-02 7.552330e-02
## [113,] 1.186467e-03 -2.712129e-03 -4.298373e-03 1.914894e-03
## [114,] 4.900068e-03 -5.687799e-03 6.926783e-03 3.780610e-03
## [115,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
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## [117,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [118,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [119,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [120,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
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## [122,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
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## [124,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [125,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,89] [,90] [,91] [,92]
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## [5,] -1.277930e-01 3.453819e-02 1.233433e-01 -1.012443e-01
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## [8,] 2.273585e-03 2.502090e-02 9.238578e-02 -3.526835e-02
## [9,] -1.252254e-02 4.775608e-03 3.754902e-04 -1.221892e-03
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## [13,] -7.400867e-02 9.872485e-02 1.341032e-02 2.740584e-03
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## [27,] 6.355311e-02 1.881877e-01 3.071019e-02 -2.855401e-01
## [28,] -1.179003e-01 1.368917e-01 9.051079e-02 6.628311e-03
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## [33,] -1.403082e-02 -4.685285e-02 4.868125e-02 -3.076464e-03
## [34,] -2.388337e-03 7.642637e-03 1.711215e-02 -5.690716e-04
## [35,] -1.140656e-01 -4.407929e-02 4.380292e-02 7.742583e-02
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## [73,] -4.141652e-16 1.665335e-15 2.012279e-15 -1.339207e-15
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## [76,] -1.950897e-02 -1.996894e-02 -1.236229e-01 4.573407e-01
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## [79,] -2.543914e-03 2.049238e-03 -9.748452e-03 7.810206e-02
## [80,] -1.300646e-02 2.463532e-02 2.118892e-02 1.777204e-02
## [81,] 8.265484e-03 -1.363105e-02 -4.911941e-02 -2.794029e-02
## [82,] -1.624037e-02 7.954388e-02 8.432409e-02 -1.752250e-02
## [83,] 1.176906e-02 1.918856e-02 -1.563592e-02 -4.993804e-03
## [84,] 6.901764e-02 -3.409041e-02 2.048460e-02 9.583925e-03
## [85,] 4.898450e-03 9.267356e-03 -2.659567e-02 1.410015e-02
## [86,] 3.229220e-03 5.596876e-03 2.702668e-03 5.368288e-03
## [87,] -9.290812e-02 -1.147028e-01 1.018755e-01 -4.601991e-02
## [88,] -4.168404e-02 4.839852e-02 3.200040e-02 2.343462e-03
## [89,] -3.102526e-02 1.869187e-02 8.259287e-05 1.259266e-02
## [90,] -1.351488e-03 4.895041e-03 3.908199e-03 -3.886527e-02
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## [96,] -1.965281e-01 4.852391e-02 -1.290082e-01 3.227166e-01
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## [101,] 2.657210e-02 -1.366600e-04 8.062183e-04 1.585054e-02
## [102,] 4.124837e-02 -7.348632e-03 -1.096414e-02 -6.188238e-02
## [103,] 3.857807e-04 -4.290155e-03 1.291994e-02 -7.545202e-03
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## [105,] -2.103942e-02 -8.457613e-02 1.361196e-02 1.384991e-01
## [106,] 6.722066e-03 5.437616e-03 -3.124408e-03 4.051219e-03
## [107,] -8.721350e-03 2.884457e-02 -1.788490e-02 -1.371764e-02
## [108,] 1.814235e-03 -6.377819e-02 8.215136e-04 3.226552e-02
## [109,] -5.180889e-03 2.863893e-02 5.512005e-02 1.028311e-01
## [110,] -2.426756e-02 1.280491e-03 1.654906e-02 6.698723e-02
## [111,] -1.048782e-03 1.168785e-02 -4.809941e-03 7.086412e-03
## [112,] -2.949649e-02 5.713834e-02 4.812616e-02 6.063732e-02
## [113,] 1.940996e-03 -2.090347e-04 -2.438326e-03 9.638331e-03
## [114,] 5.678784e-03 6.705653e-03 -1.268003e-03 -3.270041e-04
## [115,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [116,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
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## [118,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [119,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [120,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [121,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [122,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [123,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [124,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [125,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,93] [,94] [,95] [,96]
## [1,] 2.027570e-01 2.166342e-01 -2.724150e-02 -1.847851e-01
## [2,] 2.096284e-01 9.026023e-02 -2.959233e-01 2.337736e-01
## [3,] -2.473651e-03 -1.414133e-02 4.426492e-03 1.569046e-03
## [4,] 1.089189e-02 5.085848e-02 -3.745137e-02 -1.340700e-01
## [5,] -1.427189e-01 -3.027916e-01 9.199070e-02 -1.748057e-01
## [6,] -2.065266e-02 -9.071450e-02 -1.601670e-02 9.638609e-03
## [7,] 2.605073e-01 -3.445913e-02 1.970185e-02 6.768628e-02
## [8,] 1.842065e-01 -2.436629e-02 1.393131e-02 4.786143e-02
## [9,] 1.675529e-02 -2.089485e-02 1.005724e-02 -3.765782e-03
## [10,] 1.842065e-01 -2.436629e-02 1.393131e-02 4.786143e-02
## [11,] 4.175112e-02 8.203563e-03 2.547452e-02 1.420464e-01
## [12,] -1.150424e-03 -8.460834e-03 -8.022842e-04 3.640832e-03
## [13,] 9.607578e-02 -1.124900e-01 1.306111e-02 -2.341614e-02
## [14,] -5.434304e-03 2.044250e-03 -6.585166e-02 -1.779273e-02
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## [115,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
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## [,97] [,98] [,99] [,100]
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## [106,] -4.523834e-16 6.342583e-18 2.211230e-16 -5.181402e-16
## [107,] 1.474732e-15 -2.816757e-16 -2.927346e-16 2.226518e-15
## [108,] -6.352341e-16 -2.101943e-15 1.867972e-15 -1.107751e-14
## [109,] 4.341688e-15 1.830242e-15 -6.035320e-15 1.325329e-15
## [110,] -5.586894e-16 2.425252e-15 -4.380719e-16 -1.815822e-15
## [111,] 2.954993e-16 4.494831e-16 -1.665606e-16 3.686287e-18
## [112,] 5.291123e-15 1.026739e-15 -3.162455e-15 1.412499e-15
## [113,] -1.310800e-16 1.816039e-16 -2.459513e-16 -4.484260e-16
## [114,] -4.234894e-16 -5.074066e-17 3.005408e-16 -1.684850e-16
## [115,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [116,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [117,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [118,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [119,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [120,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [121,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [122,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [123,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [124,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [125,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,123] [,124] [,125]
## [1,] 0.000000e+00 0.000000e+00 0.000000e+00
## [2,] -1.286905e-14 1.649407e-13 3.685453e-13
## [3,] -5.263522e-16 -8.280941e-16 -1.377138e-15
## [4,] -1.028995e-13 -4.179360e-13 -4.726104e-13
## [5,] -7.402751e-14 1.457036e-13 3.223608e-13
## [6,] 2.894469e-16 6.274607e-14 1.264507e-13
## [7,] -1.636404e-01 -3.743318e-01 -4.760267e-01
## [8,] 1.179305e-01 1.832606e-01 2.705861e-02
## [9,] -1.211631e-15 -1.573403e-15 8.146419e-16
## [10,] 1.134920e-01 3.461245e-01 6.461449e-01
## [11,] 3.207803e-16 -2.482203e-14 -2.396367e-14
## [12,] 1.670480e-16 2.010464e-15 2.892690e-15
## [13,] 1.131337e-15 1.169591e-14 2.745483e-14
## [14,] 9.341194e-15 5.039533e-14 5.771704e-14
## [15,] -7.866235e-15 8.357106e-15 9.630761e-15
## [16,] -2.920131e-15 -6.069231e-15 -1.367129e-14
## [17,] -6.137030e-14 -3.298082e-14 -5.456483e-14
## [18,] 2.826522e-15 1.424313e-14 1.612717e-14
## [19,] 2.868173e-15 3.315525e-14 6.699479e-14
## [20,] -1.654314e-14 -6.780460e-15 -1.291504e-15
## [21,] -7.565090e-15 4.663166e-15 1.421600e-14
## [22,] -1.345433e-14 -2.040274e-14 -1.712488e-14
## [23,] -9.180823e-14 -3.367818e-14 1.835375e-13
## [24,] 1.728352e-14 2.443827e-14 9.723649e-14
## [25,] -2.919524e-01 9.003887e-02 6.403407e-02
## [26,] -1.700685e-15 -4.082981e-15 -8.056631e-15
## [27,] 4.128831e-01 -1.273342e-01 -9.055785e-02
## [28,] 5.864071e-02 2.101452e-01 -1.952948e-01
## [29,] 3.630833e-15 2.546240e-15 1.347622e-15
## [30,] -2.391833e-14 3.626600e-15 5.401586e-14
## [31,] 2.102032e-01 1.255328e-01 -5.563390e-02
## [32,] 3.259897e-15 2.896078e-15 -8.203739e-17
## [33,] 2.484991e-16 5.775111e-15 1.368892e-14
## [34,] 1.604619e-15 2.874220e-15 4.391669e-15
## [35,] -2.303583e-14 -7.736636e-15 1.116368e-14
## [36,] -1.510684e-14 -2.944010e-14 -3.780505e-14
## [37,] 5.068056e-15 1.514583e-15 -9.105120e-15
## [38,] 2.101834e-15 1.486766e-15 6.889454e-15
## [39,] 4.808694e-15 -2.789442e-15 -7.203886e-15
## [40,] 3.274781e-14 1.984028e-13 2.195297e-13
## [41,] -3.582854e-15 -1.087672e-15 -3.044657e-15
## [42,] 1.398103e-14 2.728435e-15 -6.484966e-15
## [43,] -1.960238e-16 -7.766140e-16 -1.161831e-15
## [44,] -5.839048e-01 1.800777e-01 1.280681e-01
## [45,] 7.176876e-16 1.436191e-14 3.059217e-14
## [46,] 7.283128e-17 3.449132e-15 -8.041162e-15
## [47,] -2.995380e-16 3.468600e-15 3.180961e-15
## [48,] -6.674457e-15 1.280215e-14 -1.306409e-15
## [49,] -5.909314e-14 -5.538522e-14 2.661142e-14
## [50,] 4.895151e-14 -1.209592e-13 -3.273897e-13
## [51,] 6.882082e-15 3.454875e-14 4.285613e-14
## [52,] -3.747003e-16 -1.834036e-15 -4.145555e-15
## [53,] -2.604850e-15 -4.894089e-15 -6.163256e-15
## [54,] 1.766512e-14 2.089369e-13 4.047828e-13
## [55,] -7.574236e-16 2.914661e-15 6.080341e-15
## [56,] 2.464690e-14 1.108362e-13 2.187680e-13
## [57,] -1.910686e-15 1.332318e-14 2.530866e-14
## [58,] -2.785099e-15 -5.048154e-15 -7.110740e-15
## [59,] -5.947825e-15 5.260007e-16 -1.533712e-15
## [60,] -1.395810e-14 -3.213661e-14 -4.216352e-14
## [61,] -4.947865e-15 2.455935e-15 8.844488e-15
## [62,] 4.445229e-17 1.469636e-15 3.014516e-15
## [63,] 2.121407e-14 -3.279003e-14 -8.021297e-14
## [64,] -2.102032e-01 -1.255328e-01 5.563390e-02
## [65,] 2.560601e-15 7.471796e-15 2.148746e-14
## [66,] 4.572778e-01 4.073222e-02 -2.361509e-02
## [67,] 7.049645e-15 1.056758e-14 1.950203e-14
## [68,] -1.064513e-14 1.611189e-14 3.064064e-14
## [69,] -3.097674e-15 1.899251e-15 3.154215e-15
## [70,] 1.134671e-01 7.878722e-02 -1.166044e-02
## [71,] 3.098297e-02 3.391465e-01 -1.470574e-01
## [72,] -8.904986e-15 -7.061734e-15 3.734751e-15
## [73,] -1.018645e-01 1.028774e-01 -4.127845e-02
## [74,] -2.753696e-14 -1.264282e-13 -2.457100e-13
## [75,] 7.835685e-15 -3.021255e-15 -1.527844e-16
## [76,] 2.491876e-14 4.447424e-14 9.069796e-14
## [77,] 1.198748e-14 -5.445232e-14 -1.226948e-14
## [78,] -6.960578e-16 -3.345848e-16 6.534486e-16
## [79,] 3.639450e-15 1.076580e-14 2.631543e-14
## [80,] 4.267094e-15 -1.020413e-14 -1.395607e-14
## [81,] -5.852815e-15 -1.024317e-14 -2.087251e-14
## [82,] -5.102255e-16 -7.349373e-15 1.105778e-15
## [83,] 2.823371e-15 2.113587e-14 2.556240e-14
## [84,] 3.030996e-15 1.509318e-15 -6.970390e-15
## [85,] -7.428953e-16 -3.659074e-15 -6.273736e-15
## [86,] -1.310773e-15 -3.394447e-15 -2.543037e-15
## [87,] -3.703499e-15 -2.613767e-15 -5.691655e-16
## [88,] 4.058056e-02 -6.580474e-01 5.070982e-01
## [89,] 1.056848e-14 -3.197746e-15 -2.485224e-14
## [90,] -1.425509e-15 -2.500604e-15 -6.595635e-15
## [91,] 1.333569e-17 3.467279e-16 -7.702714e-16
## [92,] -6.435716e-15 9.847255e-14 1.552802e-13
## [93,] -7.478869e-14 -1.972712e-13 -2.673773e-13
## [94,] -4.460679e-15 -8.469489e-15 -6.167321e-15
## [95,] -3.190590e-15 -4.562084e-14 -8.057162e-14
## [96,] -3.838986e-14 -5.834688e-15 2.897530e-14
## [97,] 1.287343e-01 -6.679240e-02 2.983868e-02
## [98,] 1.979970e-15 -5.261053e-14 -7.750663e-14
## [99,] -8.023335e-02 -5.571098e-02 8.245177e-03
## [100,] -2.024639e-15 -1.130118e-15 2.802121e-15
## [101,] 1.928904e-15 1.261209e-14 1.889423e-14
## [102,] 9.948639e-16 1.195203e-14 2.216998e-14
## [103,] -3.428247e-16 7.936360e-16 1.686260e-15
## [104,] -3.712308e-16 -8.539176e-16 -1.266348e-15
## [105,] 2.077982e-15 1.155217e-14 1.397005e-14
## [106,] -5.450284e-16 -6.819632e-17 7.993281e-16
## [107,] 2.205701e-15 2.671908e-15 1.825146e-15
## [108,] -7.985149e-15 -5.418279e-14 -6.987379e-14
## [109,] 2.384377e-15 -1.867831e-14 -5.688982e-14
## [110,] -3.608442e-15 -1.390424e-14 -2.232351e-14
## [111,] 6.841316e-17 -3.295947e-15 -5.839621e-15
## [112,] 7.169612e-15 -2.044133e-14 -4.436187e-14
## [113,] -6.910705e-16 -2.623227e-15 -5.008580e-15
## [114,] -4.941794e-16 4.818194e-16 1.989945e-15
## [115,] 0.000000e+00 0.000000e+00 0.000000e+00
## [116,] 0.000000e+00 0.000000e+00 0.000000e+00
## [117,] 0.000000e+00 0.000000e+00 0.000000e+00
## [118,] 0.000000e+00 0.000000e+00 0.000000e+00
## [119,] 0.000000e+00 0.000000e+00 0.000000e+00
## [120,] 0.000000e+00 0.000000e+00 0.000000e+00
## [121,] 0.000000e+00 0.000000e+00 0.000000e+00
## [122,] 0.000000e+00 0.000000e+00 0.000000e+00
## [123,] 0.000000e+00 0.000000e+00 0.000000e+00
## [124,] 0.000000e+00 0.000000e+00 0.000000e+00
## [125,] 0.000000e+00 0.000000e+00 0.000000e+00#spe.scores <- scores(spe.h.pca, display="species", choices=c(1,2)) # species scores on the first two PCA axes
#site.scores <- scores(spe.h.pca, display="sites", choices=c(1,2)) # sites scores on the first two PCA axes
#Note: if you don’t specify the number of principal components to extract (e.g. choices=c(1,2) or choices=c(1:2) then all of the scores will be extracted for all of the principal components.
# Identify the significant axis using the Kaiser-Guttman criterion
ev <- spe.h.pca$CA$eig
ev[ev>mean(ev)]## PC1 PC2 PC3 PC4 PC5 PC6
## 0.119111710 0.102615035 0.084654467 0.051725524 0.042753340 0.040276919
## PC7 PC8 PC9 PC10 PC11 PC12
## 0.030013433 0.027171385 0.024673291 0.022006266 0.016840108 0.015422556
## PC13 PC14 PC15 PC16 PC17 PC18
## 0.013853868 0.013516857 0.012413964 0.010716728 0.009377003 0.008710015
## PC19
## 0.008191751n <- length(ev)
#dev.new(width=11.8, height=8)
barplot(ev, main="Eigenvalues", col="grey", las=2)
abline(h=mean(ev), col="red")
legend("topright", "Average eigenvalue", lwd=1, col=2, bty="n")
Environmental variable PCA
### PCA on the environmental variables
#### Run the PCA
env.pca <- rda(env.z) # or rda(env, scale=TRUE)
#### Extract the results # scale default is 2
summary(env.pca)##
## Call:
## rda(X = env.z)
##
## Partitioning of variance:
## Inertia Proportion
## Total 5 1
## Unconstrained 5 1
##
## Eigenvalues, and their contribution to the variance
##
## Importance of components:
## PC1 PC2 PC3 PC4 PC5
## Eigenvalue 2.9979 1.0238 0.5029 0.29028 0.18511
## Proportion Explained 0.5996 0.2048 0.1006 0.05806 0.03702
## Cumulative Proportion 0.5996 0.8043 0.9049 0.96298 1.00000
##
## 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: 5.438787
##
##
## Species scores
##
## PC1 PC2 PC3 PC4 PC5
## Elevation..m. 2.231 -0.1062 0.4106 0.30977 0.81394
## Sky.visible.... 0.271 -2.3799 -0.4207 0.02587 -0.03019
## Slope..Degrees. 1.926 0.5582 -1.2422 0.55306 -0.21639
## site.soil -2.147 -0.1326 0.2457 1.10818 0.04565
## site.moist 2.090 -0.2286 1.0132 0.29457 -0.61873
##
##
## Site scores (weighted sums of species scores)
##
## PC1 PC2 PC3 PC4 PC5
## EA1 -0.453655 -0.074995 -0.076294 -0.245078 -0.072946
## EB1 -0.452341 -0.234505 -0.132775 -0.222740 -0.091430
## EC1 -0.339603 -0.215037 -0.204556 -0.804330 -0.112256
## ED1 -0.402614 0.410715 0.071004 -0.546811 0.017563
## EE1 -0.620375 -0.207354 -0.428284 -0.106171 0.477412
## EF1 -0.567128 0.381422 0.180663 0.320550 0.065216
## EG1 -0.452240 -0.229426 -0.152648 0.009679 -0.014856
## EH1 -0.373327 -0.222980 -0.171310 -0.585583 -0.064647
## EI1 -0.614011 -0.209891 -0.412142 -0.062206 0.547210
## EJ1 -0.370448 -0.223381 -0.168153 -0.581456 -0.047641
## EK1 -0.410826 -0.130321 0.335347 0.422719 -0.490689
## EA2 -0.326971 0.049202 0.308126 -0.151062 -0.591521
## EB2 -0.387249 -0.283039 0.248318 0.267943 -0.570831
## EC2 -0.615121 -0.211935 -0.401143 -0.017344 0.583587
## ED2 -0.557642 -0.200157 -0.448033 -0.353002 0.536798
## EE2 -0.437357 -0.019115 -0.471938 -1.013905 0.522406
## EF2 -0.355502 -0.224366 -0.157864 -0.583251 0.019201
## EG2 -0.530409 -0.177274 -0.549747 -0.197801 0.527659
## EH2 -0.292873 -0.211656 -0.208267 -0.946363 -0.029362
## EI2 -0.329021 -0.062133 -0.107542 -0.705093 0.073107
## EJ2 -0.316808 -0.200332 -0.262276 -0.469681 0.024113
## EK2 -0.326597 -0.219599 -0.175021 -0.727616 0.018246
## EA3 -0.413033 -0.233388 -0.126302 -0.305734 0.012017
## EB3 -0.143859 -0.302554 0.525711 -0.123809 -1.048641
## EC3 -0.536626 -0.255741 -0.041995 0.353198 0.054577
## ED3 -0.314456 -0.058116 -0.125158 -0.811954 0.041095
## EE3 -0.440121 -0.199141 -0.296204 0.201280 -0.128965
## EF3 -0.570940 -0.210397 -0.395433 -0.116579 0.694355
## EG3 -0.509465 0.066824 0.060887 0.188650 0.117281
## EH3 -0.208014 -0.257998 0.167024 -0.531856 -0.488574
## EI3 -0.664677 0.415790 -0.132200 0.178175 0.717771
## EJ3 -0.487580 -0.232601 -0.138105 0.469997 0.109916
## EK3 -0.051119 -0.267363 0.376752 -0.327594 -1.089336
## EA4 -0.517466 -0.251815 -0.057625 0.241312 0.038981
## EB4 -0.290912 -0.276678 0.244055 -0.011996 -0.388038
## EC4 -0.365898 0.676544 0.582621 0.036472 -0.416004
## ED4 -0.523756 0.073909 0.025226 0.400433 0.108824
## EE4 -0.309337 -0.099996 0.212086 0.138570 -0.496213
## EF4 -0.483315 -0.230446 -0.148696 0.418047 0.081452
## EG4 -0.282138 0.067432 0.237935 0.075828 -0.453743
## EH4 -0.226113 0.121776 -0.012646 0.202655 -0.634534
## EI4 -0.366995 -0.291360 0.301075 0.413116 -0.343840
## EJ4 -0.491093 -0.197339 -0.442218 -0.513069 0.693855
## EK4 -0.294199 0.046832 0.331860 -0.150524 -0.440830
## EA5 -0.262051 0.560900 0.340454 -0.003176 -0.437942
## EB5 -0.181158 -0.079584 0.144195 -0.316358 -0.398563
## EC5 -0.298542 -0.267918 0.192929 -0.185522 -0.583381
## ED5 -0.423985 1.299960 0.872745 0.335893 -0.224890
## EE5 -0.217658 -0.253760 0.148676 -0.266957 -0.426642
## EF5 -0.500646 -0.260757 -0.002526 0.404789 0.267154
## EG5 -0.328308 0.215603 0.342936 0.360794 -0.356822
## EH5 -0.312946 0.098696 0.087553 0.821391 -0.460653
## EI5 -0.127523 -0.207065 -0.056719 -0.369947 -0.524812
## EJ5 -0.218918 0.754233 0.248310 0.212446 -0.411909
## EK5 -0.181906 0.438665 0.127258 0.132228 -0.406724
## EA6 -0.367703 -0.223821 -0.152363 -0.066524 0.232802
## EB6 -0.330554 -0.264959 0.174476 0.140210 -0.567739
## EC6 -0.371967 -0.135738 0.377974 0.478438 -0.261106
## ED6 -0.260854 -0.146933 -0.499327 0.017062 0.036938
## EE6 -0.149975 0.294823 0.001923 0.117185 -0.458129
## EF6 -0.346854 -0.272987 0.222121 0.674281 -0.287546
## EG6 0.045500 -0.271081 0.420267 -0.734884 -0.884262
## EH6 -0.615978 0.265762 -0.217764 0.268469 0.840567
## EI6 -0.227005 0.087524 0.160717 0.247808 -0.319511
## EJ6 -0.317011 0.189549 0.474699 0.214386 -0.162979
## EK6 -0.197977 -0.210147 -0.045708 0.481332 -0.338335
## EA7 -0.575706 -0.055208 -0.307754 0.297444 0.961611
## EB7 -0.282476 0.034203 0.405799 0.098550 -0.156909
## EC7 -0.471715 0.059362 0.114512 0.289231 0.383242
## ED7 -0.436017 0.754543 0.077767 0.630274 0.349185
## EE7 -0.316835 -0.115646 0.300756 0.650417 -0.126874
## EF7 -0.268064 -0.264729 0.201662 0.380794 -0.197695
## EG7 -0.193375 -0.231420 0.057334 0.244033 -0.259171
## EH7 -0.325865 -0.295445 0.337031 0.437252 -0.133036
## EI7 -0.064909 -0.208647 -0.027736 -0.431139 -0.294411
## EJ7 -0.230178 -0.087998 0.183433 0.275316 -0.215087
## EK7 -0.179042 -0.209488 -0.043262 0.438803 -0.290863
## EA8 -0.260317 -0.059374 0.043778 0.905701 -0.256033
## EB8 -0.136702 -0.184990 0.014597 0.186501 -0.182274
## EC8 -0.422563 -0.094722 0.043323 0.124674 0.411275
## ED8 -0.456009 -0.102154 0.073820 0.332206 0.449789
## EE8 -0.299232 -0.292011 0.326545 0.324469 -0.115211
## EF8 -0.458908 -0.266575 0.043257 0.464635 0.513744
## EG8 -0.439749 -0.262649 0.027627 0.352749 0.498147
## EH8 -0.328920 -0.290476 0.316749 0.676759 -0.064374
## EI8 -0.307206 -0.201380 -0.236742 0.217672 0.425987
## EJ8 0.024825 -0.160652 -0.232177 -0.221138 -0.243845
## EK8 -0.052614 -0.044841 0.017580 -0.224916 -0.141014
## E600A1 -0.133757 0.438145 0.153984 0.410316 -0.067737
## E600B2 -0.131147 0.172081 -0.211617 1.035677 -0.261578
## E600C3 0.055681 0.205409 -0.336499 0.049342 -0.316916
## E600D4 0.043205 -0.161015 -0.224231 -0.241236 -0.178185
## E600E5 -0.009019 0.585000 0.288195 -0.894583 -0.102138
## E600F6 0.140150 -0.099732 -0.500164 -0.322838 -0.364068
## E600G7 0.147470 -0.263711 0.420521 -0.704793 -0.527814
## E600H8 -0.021515 -0.190217 -0.099506 -0.206312 -0.165135
## E600I9 -0.025166 -0.215287 0.021969 -0.350926 -0.038136
## E600J10 0.015739 -0.165982 -0.205496 -0.094807 -0.168727
## E600K11 -0.009755 -0.252101 0.198216 -0.955981 0.028069
## E615A1 -0.096359 0.106986 0.111365 0.319027 0.067676
## E615B2 -0.091017 1.106968 0.245164 0.447873 -0.003282
## E615C3 0.135112 -0.127357 -0.364941 -0.411374 -0.191598
## E615D4 0.079312 -0.178434 -0.132437 -0.607558 -0.073875
## E615E5 0.164687 0.531262 -0.233793 -0.648200 -0.233022
## E615F6 0.096396 2.775091 0.575785 -0.776715 -0.028154
## E615G7 0.116987 -0.119592 -0.397308 0.131703 -0.050137
## E615H8 0.144143 -0.142303 -0.291465 -0.619091 -0.134146
## E615I9 0.083304 -0.187382 -0.089750 -0.764429 -0.061871
## E615J10 -0.017134 -0.225348 0.072142 -0.490391 0.008472
## E615K11 0.003878 2.081240 0.517438 -0.374940 0.011427
## E645A1 0.005945 0.158176 -0.106773 0.442534 0.095915
## E645B2 0.055261 -0.186481 -0.087187 -0.061374 0.181991
## E645C3 0.014790 0.446574 0.155075 0.007815 0.241057
## E645D4 0.424809 -0.078643 -0.393475 0.064653 -0.626025
## E645E5 0.509863 0.139777 -0.603153 0.026840 -0.780784
## E645F6 0.331805 0.637916 -0.697586 -0.094924 -0.204008
## E645G7 0.236420 -0.104906 -0.440370 -0.358997 0.043716
## E645H8 0.467101 -0.026783 -0.634688 0.264695 -0.802087
## E645I9 0.239695 -0.096017 -0.488693 -0.551724 -0.119389
## E645J10 0.221743 -0.082228 -0.554464 -0.136144 -0.094970
## E645K11 0.150175 -0.165627 -0.172414 -0.645297 0.077317
## E675A1 0.146814 0.328652 -0.065345 -0.026270 0.353395
## E675B2 0.178675 1.335730 0.041743 0.082539 0.316109
## E675C3 0.245570 0.416507 -0.463379 0.347669 0.180744
## E675D4 0.264151 -0.124310 -0.331941 -0.330858 0.335503
## E675E5 0.249892 0.867062 -0.160786 -0.160442 0.282484
## E675F6 0.290902 0.059616 -0.385424 -0.231642 0.317566
## E675G7 0.633426 -0.132083 0.044547 -0.237622 -0.903126
## E675H8 0.217095 0.253453 -0.509781 0.489878 0.136524
## E675I9 0.290156 0.406153 -0.408094 -0.180694 0.174150
## E675J10 0.370192 0.300021 -0.702473 -0.045436 0.066045
## E675K11 0.354533 0.007625 -0.944310 0.484032 -0.022758
## E710A1 0.319526 0.235584 -0.394096 0.032846 0.460959
## E710B2 0.331744 0.548542 -0.250974 -0.246044 0.488195
## E710C3 0.268040 0.194497 -0.207384 -0.041009 0.572816
## E710D4 0.205305 -0.225223 0.147351 -0.659189 0.802556
## E710E5 0.481373 -0.094224 -0.288672 0.308344 -0.141576
## E710F6 0.435595 -0.143949 -0.060443 0.068465 -0.018306
## E710G7 0.190094 -0.144627 -0.234657 0.550086 0.671580
## E710H8 0.509984 0.056904 -1.134688 0.567611 0.212147
## E710I9 0.536861 -0.093859 -0.281113 -0.123083 -0.147306
## E710J10 0.490570 -0.115588 -0.183642 0.066021 -0.045997
## E710K11 0.605168 -0.005057 -0.694224 0.276876 -0.435453
## E745A1 0.258804 -0.147406 -0.201210 0.335046 0.857079
## E745B2 0.550395 -0.079917 -0.329275 0.581532 0.149849
## E745C3 0.487027 -0.052254 -0.610482 -0.150577 0.691408
## E745D4 0.615460 -0.095325 -0.239310 0.128986 0.307178
## E745E5 0.801139 -0.052046 -0.279505 0.537148 -0.527986
## E745F6 0.828067 0.127312 -0.315864 0.392729 -0.631592
## E745G7 0.789403 0.040209 -0.853027 0.401729 -0.030486
## E745H8 0.346739 1.188853 -0.022824 -0.074087 0.757747
## E745I9 0.610464 -0.037277 -0.521842 0.609628 0.035036
## E745J10 0.790754 -0.101352 -0.050493 -0.104908 -0.475515
## E745K11 0.777801 -0.099547 -0.064702 -0.123481 -0.552042
## E775A1 0.643593 -0.220538 0.497664 -0.083737 -0.020853
## E775B2 0.412893 -0.245705 0.439342 -0.126744 0.668076
## E775C3 0.289596 -0.320503 0.773539 -0.059711 0.858416
## E775D4 0.766751 -0.101564 -0.040443 0.615554 -0.197049
## E775E5 0.658911 -0.194750 0.384272 0.367946 0.050719
## E775F6 0.628742 -0.099375 -0.212524 0.194484 0.428585
## E775G7 0.776230 -0.133008 0.112364 0.245879 -0.079190
## E775H8 0.721146 -0.145265 0.154381 0.248177 -0.190821
## E775I9 0.638168 -0.128063 -0.075043 -0.233332 0.492471
## E775J10 0.891222 -0.059252 -0.218728 0.213390 -0.275668
## E775K11 0.482445 -0.349609 1.079608 -0.512330 0.231416
## E800A1 0.606611 -0.290326 0.831874 -0.252947 0.346732
## E800B2 0.560275 -0.330482 1.015073 -0.354258 0.456816
## E800C3 0.486998 -0.185345 0.177786 0.525395 0.778255
## E800D4 0.655324 -0.254350 0.672659 -0.066937 0.325817
## E800E5 0.661913 -0.253619 0.670725 -0.092329 0.332547
## E800F6 0.304844 -0.400167 1.303175 0.824018 0.652522
## E800G7 0.486519 -0.357179 1.131279 -0.018725 0.567583
## E800H8 0.471905 -0.369031 1.184096 -0.086142 0.576995
## E800I9 0.490510 -0.366127 1.173965 -0.175596 0.579587
## E800J10 0.505127 -0.364866 1.171676 -0.224317 0.601550
## E800K11 0.738585 -0.187715 0.370892 0.098954 0.167262summary(env.pca, scaling=2)##
## Call:
## rda(X = env.z)
##
## Partitioning of variance:
## Inertia Proportion
## Total 5 1
## Unconstrained 5 1
##
## Eigenvalues, and their contribution to the variance
##
## Importance of components:
## PC1 PC2 PC3 PC4 PC5
## Eigenvalue 2.9979 1.0238 0.5029 0.29028 0.18511
## Proportion Explained 0.5996 0.2048 0.1006 0.05806 0.03702
## Cumulative Proportion 0.5996 0.8043 0.9049 0.96298 1.00000
##
## 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: 5.438787
##
##
## Species scores
##
## PC1 PC2 PC3 PC4 PC5
## Elevation..m. 2.231 -0.1062 0.4106 0.30977 0.81394
## Sky.visible.... 0.271 -2.3799 -0.4207 0.02587 -0.03019
## Slope..Degrees. 1.926 0.5582 -1.2422 0.55306 -0.21639
## site.soil -2.147 -0.1326 0.2457 1.10818 0.04565
## site.moist 2.090 -0.2286 1.0132 0.29457 -0.61873
##
##
## Site scores (weighted sums of species scores)
##
## PC1 PC2 PC3 PC4 PC5
## EA1 -0.453655 -0.074995 -0.076294 -0.245078 -0.072946
## EB1 -0.452341 -0.234505 -0.132775 -0.222740 -0.091430
## EC1 -0.339603 -0.215037 -0.204556 -0.804330 -0.112256
## ED1 -0.402614 0.410715 0.071004 -0.546811 0.017563
## EE1 -0.620375 -0.207354 -0.428284 -0.106171 0.477412
## EF1 -0.567128 0.381422 0.180663 0.320550 0.065216
## EG1 -0.452240 -0.229426 -0.152648 0.009679 -0.014856
## EH1 -0.373327 -0.222980 -0.171310 -0.585583 -0.064647
## EI1 -0.614011 -0.209891 -0.412142 -0.062206 0.547210
## EJ1 -0.370448 -0.223381 -0.168153 -0.581456 -0.047641
## EK1 -0.410826 -0.130321 0.335347 0.422719 -0.490689
## EA2 -0.326971 0.049202 0.308126 -0.151062 -0.591521
## EB2 -0.387249 -0.283039 0.248318 0.267943 -0.570831
## EC2 -0.615121 -0.211935 -0.401143 -0.017344 0.583587
## ED2 -0.557642 -0.200157 -0.448033 -0.353002 0.536798
## EE2 -0.437357 -0.019115 -0.471938 -1.013905 0.522406
## EF2 -0.355502 -0.224366 -0.157864 -0.583251 0.019201
## EG2 -0.530409 -0.177274 -0.549747 -0.197801 0.527659
## EH2 -0.292873 -0.211656 -0.208267 -0.946363 -0.029362
## EI2 -0.329021 -0.062133 -0.107542 -0.705093 0.073107
## EJ2 -0.316808 -0.200332 -0.262276 -0.469681 0.024113
## EK2 -0.326597 -0.219599 -0.175021 -0.727616 0.018246
## EA3 -0.413033 -0.233388 -0.126302 -0.305734 0.012017
## EB3 -0.143859 -0.302554 0.525711 -0.123809 -1.048641
## EC3 -0.536626 -0.255741 -0.041995 0.353198 0.054577
## ED3 -0.314456 -0.058116 -0.125158 -0.811954 0.041095
## EE3 -0.440121 -0.199141 -0.296204 0.201280 -0.128965
## EF3 -0.570940 -0.210397 -0.395433 -0.116579 0.694355
## EG3 -0.509465 0.066824 0.060887 0.188650 0.117281
## EH3 -0.208014 -0.257998 0.167024 -0.531856 -0.488574
## EI3 -0.664677 0.415790 -0.132200 0.178175 0.717771
## EJ3 -0.487580 -0.232601 -0.138105 0.469997 0.109916
## EK3 -0.051119 -0.267363 0.376752 -0.327594 -1.089336
## EA4 -0.517466 -0.251815 -0.057625 0.241312 0.038981
## EB4 -0.290912 -0.276678 0.244055 -0.011996 -0.388038
## EC4 -0.365898 0.676544 0.582621 0.036472 -0.416004
## ED4 -0.523756 0.073909 0.025226 0.400433 0.108824
## EE4 -0.309337 -0.099996 0.212086 0.138570 -0.496213
## EF4 -0.483315 -0.230446 -0.148696 0.418047 0.081452
## EG4 -0.282138 0.067432 0.237935 0.075828 -0.453743
## EH4 -0.226113 0.121776 -0.012646 0.202655 -0.634534
## EI4 -0.366995 -0.291360 0.301075 0.413116 -0.343840
## EJ4 -0.491093 -0.197339 -0.442218 -0.513069 0.693855
## EK4 -0.294199 0.046832 0.331860 -0.150524 -0.440830
## EA5 -0.262051 0.560900 0.340454 -0.003176 -0.437942
## EB5 -0.181158 -0.079584 0.144195 -0.316358 -0.398563
## EC5 -0.298542 -0.267918 0.192929 -0.185522 -0.583381
## ED5 -0.423985 1.299960 0.872745 0.335893 -0.224890
## EE5 -0.217658 -0.253760 0.148676 -0.266957 -0.426642
## EF5 -0.500646 -0.260757 -0.002526 0.404789 0.267154
## EG5 -0.328308 0.215603 0.342936 0.360794 -0.356822
## EH5 -0.312946 0.098696 0.087553 0.821391 -0.460653
## EI5 -0.127523 -0.207065 -0.056719 -0.369947 -0.524812
## EJ5 -0.218918 0.754233 0.248310 0.212446 -0.411909
## EK5 -0.181906 0.438665 0.127258 0.132228 -0.406724
## EA6 -0.367703 -0.223821 -0.152363 -0.066524 0.232802
## EB6 -0.330554 -0.264959 0.174476 0.140210 -0.567739
## EC6 -0.371967 -0.135738 0.377974 0.478438 -0.261106
## ED6 -0.260854 -0.146933 -0.499327 0.017062 0.036938
## EE6 -0.149975 0.294823 0.001923 0.117185 -0.458129
## EF6 -0.346854 -0.272987 0.222121 0.674281 -0.287546
## EG6 0.045500 -0.271081 0.420267 -0.734884 -0.884262
## EH6 -0.615978 0.265762 -0.217764 0.268469 0.840567
## EI6 -0.227005 0.087524 0.160717 0.247808 -0.319511
## EJ6 -0.317011 0.189549 0.474699 0.214386 -0.162979
## EK6 -0.197977 -0.210147 -0.045708 0.481332 -0.338335
## EA7 -0.575706 -0.055208 -0.307754 0.297444 0.961611
## EB7 -0.282476 0.034203 0.405799 0.098550 -0.156909
## EC7 -0.471715 0.059362 0.114512 0.289231 0.383242
## ED7 -0.436017 0.754543 0.077767 0.630274 0.349185
## EE7 -0.316835 -0.115646 0.300756 0.650417 -0.126874
## EF7 -0.268064 -0.264729 0.201662 0.380794 -0.197695
## EG7 -0.193375 -0.231420 0.057334 0.244033 -0.259171
## EH7 -0.325865 -0.295445 0.337031 0.437252 -0.133036
## EI7 -0.064909 -0.208647 -0.027736 -0.431139 -0.294411
## EJ7 -0.230178 -0.087998 0.183433 0.275316 -0.215087
## EK7 -0.179042 -0.209488 -0.043262 0.438803 -0.290863
## EA8 -0.260317 -0.059374 0.043778 0.905701 -0.256033
## EB8 -0.136702 -0.184990 0.014597 0.186501 -0.182274
## EC8 -0.422563 -0.094722 0.043323 0.124674 0.411275
## ED8 -0.456009 -0.102154 0.073820 0.332206 0.449789
## EE8 -0.299232 -0.292011 0.326545 0.324469 -0.115211
## EF8 -0.458908 -0.266575 0.043257 0.464635 0.513744
## EG8 -0.439749 -0.262649 0.027627 0.352749 0.498147
## EH8 -0.328920 -0.290476 0.316749 0.676759 -0.064374
## EI8 -0.307206 -0.201380 -0.236742 0.217672 0.425987
## EJ8 0.024825 -0.160652 -0.232177 -0.221138 -0.243845
## EK8 -0.052614 -0.044841 0.017580 -0.224916 -0.141014
## E600A1 -0.133757 0.438145 0.153984 0.410316 -0.067737
## E600B2 -0.131147 0.172081 -0.211617 1.035677 -0.261578
## E600C3 0.055681 0.205409 -0.336499 0.049342 -0.316916
## E600D4 0.043205 -0.161015 -0.224231 -0.241236 -0.178185
## E600E5 -0.009019 0.585000 0.288195 -0.894583 -0.102138
## E600F6 0.140150 -0.099732 -0.500164 -0.322838 -0.364068
## E600G7 0.147470 -0.263711 0.420521 -0.704793 -0.527814
## E600H8 -0.021515 -0.190217 -0.099506 -0.206312 -0.165135
## E600I9 -0.025166 -0.215287 0.021969 -0.350926 -0.038136
## E600J10 0.015739 -0.165982 -0.205496 -0.094807 -0.168727
## E600K11 -0.009755 -0.252101 0.198216 -0.955981 0.028069
## E615A1 -0.096359 0.106986 0.111365 0.319027 0.067676
## E615B2 -0.091017 1.106968 0.245164 0.447873 -0.003282
## E615C3 0.135112 -0.127357 -0.364941 -0.411374 -0.191598
## E615D4 0.079312 -0.178434 -0.132437 -0.607558 -0.073875
## E615E5 0.164687 0.531262 -0.233793 -0.648200 -0.233022
## E615F6 0.096396 2.775091 0.575785 -0.776715 -0.028154
## E615G7 0.116987 -0.119592 -0.397308 0.131703 -0.050137
## E615H8 0.144143 -0.142303 -0.291465 -0.619091 -0.134146
## E615I9 0.083304 -0.187382 -0.089750 -0.764429 -0.061871
## E615J10 -0.017134 -0.225348 0.072142 -0.490391 0.008472
## E615K11 0.003878 2.081240 0.517438 -0.374940 0.011427
## E645A1 0.005945 0.158176 -0.106773 0.442534 0.095915
## E645B2 0.055261 -0.186481 -0.087187 -0.061374 0.181991
## E645C3 0.014790 0.446574 0.155075 0.007815 0.241057
## E645D4 0.424809 -0.078643 -0.393475 0.064653 -0.626025
## E645E5 0.509863 0.139777 -0.603153 0.026840 -0.780784
## E645F6 0.331805 0.637916 -0.697586 -0.094924 -0.204008
## E645G7 0.236420 -0.104906 -0.440370 -0.358997 0.043716
## E645H8 0.467101 -0.026783 -0.634688 0.264695 -0.802087
## E645I9 0.239695 -0.096017 -0.488693 -0.551724 -0.119389
## E645J10 0.221743 -0.082228 -0.554464 -0.136144 -0.094970
## E645K11 0.150175 -0.165627 -0.172414 -0.645297 0.077317
## E675A1 0.146814 0.328652 -0.065345 -0.026270 0.353395
## E675B2 0.178675 1.335730 0.041743 0.082539 0.316109
## E675C3 0.245570 0.416507 -0.463379 0.347669 0.180744
## E675D4 0.264151 -0.124310 -0.331941 -0.330858 0.335503
## E675E5 0.249892 0.867062 -0.160786 -0.160442 0.282484
## E675F6 0.290902 0.059616 -0.385424 -0.231642 0.317566
## E675G7 0.633426 -0.132083 0.044547 -0.237622 -0.903126
## E675H8 0.217095 0.253453 -0.509781 0.489878 0.136524
## E675I9 0.290156 0.406153 -0.408094 -0.180694 0.174150
## E675J10 0.370192 0.300021 -0.702473 -0.045436 0.066045
## E675K11 0.354533 0.007625 -0.944310 0.484032 -0.022758
## E710A1 0.319526 0.235584 -0.394096 0.032846 0.460959
## E710B2 0.331744 0.548542 -0.250974 -0.246044 0.488195
## E710C3 0.268040 0.194497 -0.207384 -0.041009 0.572816
## E710D4 0.205305 -0.225223 0.147351 -0.659189 0.802556
## E710E5 0.481373 -0.094224 -0.288672 0.308344 -0.141576
## E710F6 0.435595 -0.143949 -0.060443 0.068465 -0.018306
## E710G7 0.190094 -0.144627 -0.234657 0.550086 0.671580
## E710H8 0.509984 0.056904 -1.134688 0.567611 0.212147
## E710I9 0.536861 -0.093859 -0.281113 -0.123083 -0.147306
## E710J10 0.490570 -0.115588 -0.183642 0.066021 -0.045997
## E710K11 0.605168 -0.005057 -0.694224 0.276876 -0.435453
## E745A1 0.258804 -0.147406 -0.201210 0.335046 0.857079
## E745B2 0.550395 -0.079917 -0.329275 0.581532 0.149849
## E745C3 0.487027 -0.052254 -0.610482 -0.150577 0.691408
## E745D4 0.615460 -0.095325 -0.239310 0.128986 0.307178
## E745E5 0.801139 -0.052046 -0.279505 0.537148 -0.527986
## E745F6 0.828067 0.127312 -0.315864 0.392729 -0.631592
## E745G7 0.789403 0.040209 -0.853027 0.401729 -0.030486
## E745H8 0.346739 1.188853 -0.022824 -0.074087 0.757747
## E745I9 0.610464 -0.037277 -0.521842 0.609628 0.035036
## E745J10 0.790754 -0.101352 -0.050493 -0.104908 -0.475515
## E745K11 0.777801 -0.099547 -0.064702 -0.123481 -0.552042
## E775A1 0.643593 -0.220538 0.497664 -0.083737 -0.020853
## E775B2 0.412893 -0.245705 0.439342 -0.126744 0.668076
## E775C3 0.289596 -0.320503 0.773539 -0.059711 0.858416
## E775D4 0.766751 -0.101564 -0.040443 0.615554 -0.197049
## E775E5 0.658911 -0.194750 0.384272 0.367946 0.050719
## E775F6 0.628742 -0.099375 -0.212524 0.194484 0.428585
## E775G7 0.776230 -0.133008 0.112364 0.245879 -0.079190
## E775H8 0.721146 -0.145265 0.154381 0.248177 -0.190821
## E775I9 0.638168 -0.128063 -0.075043 -0.233332 0.492471
## E775J10 0.891222 -0.059252 -0.218728 0.213390 -0.275668
## E775K11 0.482445 -0.349609 1.079608 -0.512330 0.231416
## E800A1 0.606611 -0.290326 0.831874 -0.252947 0.346732
## E800B2 0.560275 -0.330482 1.015073 -0.354258 0.456816
## E800C3 0.486998 -0.185345 0.177786 0.525395 0.778255
## E800D4 0.655324 -0.254350 0.672659 -0.066937 0.325817
## E800E5 0.661913 -0.253619 0.670725 -0.092329 0.332547
## E800F6 0.304844 -0.400167 1.303175 0.824018 0.652522
## E800G7 0.486519 -0.357179 1.131279 -0.018725 0.567583
## E800H8 0.471905 -0.369031 1.184096 -0.086142 0.576995
## E800I9 0.490510 -0.366127 1.173965 -0.175596 0.579587
## E800J10 0.505127 -0.364866 1.171676 -0.224317 0.601550
## E800K11 0.738585 -0.187715 0.370892 0.098954 0.167262# Identify the significant axis using the Kaiser-Guttman criterion
ev <- env.pca$CA$eig
ev[ev>mean(ev)]## PC1 PC2
## 2.997882 1.023789n <- length(ev)
barplot(ev, main="Eigenvalues", col="grey", las=2)
abline(h=mean(ev), col="red")
legend("topright", "Average eigenvalue", lwd=1, col=2, bty="n")
### Construct a biplot
#### Biplot of the PCA on transformed species data (scaling 1)
#dev.new(width=11.8, height=8)
plot(spe.h.pca)
#?biplot
#biplot(spe.h.pca)
#plot(spe.h.pca, scaling=1, type="none", # scaling 1 = distance biplot :
# distances among abjects in the biplot approximate their Euclidean distances
# but angles among descriptor vectors DO NOT reflect their correlation
#xlab=c("PC1 (%)", round((spe.h.pca$CA$eig[1]/sum(spe.h.pca$CA$eig))*100,2)),
#ylab=c("PC2 (%)", round((spe.h.pca$CA$eig[2]/sum(spe.h.pca$CA$eig))*100,2)))
#points(scores(spe.h.pca, display="sites", choices=c(1,2), scaling=1),
# pch=21, col="black", bg="steelblue", cex=1.2)
#text(scores(spe.h.pca, display="species", choices=c(1), scaling=1),
# scores(spe.h.pca, display="species", choices=c(2), scaling=1),
#labels=rownames(scores(spe.h.pca, display="species", scaling=1)),
#col="red", cex=0.8)
#### Biplot on the environmental variables (scaling 2)
#dev.new(width=11.8, height=8)
plot(env.pca)
plot(env.pca, scaling=2, type="none", # scaling 2 = correlation biplot :
# distances among abjects in the biplot DO NOT approximate their Euclidean distances
# but angles among descriptor vectors reflect their correlation
xlab=c("PC1 (%)", round((env.pca$CA$eig[1]/sum(env.pca$CA$eig))*100,2)),
ylab=c("PC2 (%)", round((env.pca$CA$eig[2]/sum(env.pca$CA$eig))*100,2)),
xlim=c(-3,3), ylim=c(-3,3))
points(scores(env.pca, display="sites", choices=c(1,2), scaling=2),
pch=21, col="black", bg="gray50", cex=1.2)
text(scores(env.pca, display="species", choices=c(1), scaling=2),
scores(env.pca, display="species", choices=c(2), scaling=2),
labels=rownames(scores(env.pca, display="species", scaling=2)),
col="black", cex=0.8)
Redundancy Analysis (RDA)
### Prepare the data
### Run the RDA of all explanatory variables of env2 on species abundances
#?rda
spe.rda <- rda(spe.hel~., data=env)
# the "env" variables do not need to be starndardized as the PCA is computed on fited values (which are identicl whether
#or not the initial table of centered or standardized)### Extract the results
summary(spe.rda, display=NULL)##
## Call:
## rda(formula = spe.hel ~ Elevation..m. + Sky.visible.... + Slope..Degrees. + site.soil + site.moist, data = env)
##
## Partitioning of variance:
## Inertia Proportion
## Total 0.7612 1.0000
## Constrained 0.1652 0.2171
## Unconstrained 0.5959 0.7829
##
## Eigenvalues, and their contribution to the variance
##
## Importance of components:
## RDA1 RDA2 RDA3 RDA4 RDA5 PC1
## Eigenvalue 0.07989 0.03969 0.02542 0.01083 0.00942 0.07483
## Proportion Explained 0.10496 0.05214 0.03340 0.01422 0.01238 0.09830
## Cumulative Proportion 0.10496 0.15710 0.19049 0.20471 0.21709 0.31539
## PC2 PC3 PC4 PC5 PC6 PC7
## Eigenvalue 0.06580 0.04732 0.04411 0.03984 0.03659 0.02662
## Proportion Explained 0.08644 0.06217 0.05795 0.05234 0.04807 0.03497
## Cumulative Proportion 0.40183 0.46400 0.52196 0.57429 0.62236 0.65733
## PC8 PC9 PC10 PC11 PC12 PC13
## Eigenvalue 0.02319 0.02113 0.01625 0.01428 0.01347 0.01264
## Proportion Explained 0.03047 0.02776 0.02135 0.01876 0.01770 0.01661
## Cumulative Proportion 0.68780 0.71555 0.73691 0.75567 0.77337 0.78998
## PC14 PC15 PC16 PC17 PC18 PC19
## Eigenvalue 0.01215 0.01117 0.009314 0.008821 0.008441 0.007189
## Proportion Explained 0.01596 0.01467 0.012240 0.011590 0.011090 0.009440
## Cumulative Proportion 0.80594 0.82061 0.832850 0.844430 0.855520 0.864970
## PC20 PC21 PC22 PC23 PC24
## Eigenvalue 0.006982 0.006285 0.005776 0.005436 0.005268
## Proportion Explained 0.009170 0.008260 0.007590 0.007140 0.006920
## Cumulative Proportion 0.874140 0.882400 0.889990 0.897130 0.904050
## PC25 PC26 PC27 PC28 PC29
## Eigenvalue 0.004767 0.004306 0.004148 0.003944 0.003854
## Proportion Explained 0.006260 0.005660 0.005450 0.005180 0.005060
## Cumulative Proportion 0.910310 0.915970 0.921420 0.926600 0.931660
## PC30 PC31 PC32 PC33 PC34 PC35
## Eigenvalue 0.003465 0.003224 0.00297 0.002663 0.00255 0.002347
## Proportion Explained 0.004550 0.004240 0.00390 0.003500 0.00335 0.003080
## Cumulative Proportion 0.936220 0.940450 0.94435 0.947850 0.95120 0.954280
## PC36 PC37 PC38 PC39 PC40 PC41
## Eigenvalue 0.002175 0.001976 0.00192 0.001901 0.001633 0.001605
## Proportion Explained 0.002860 0.002600 0.00252 0.002500 0.002150 0.002110
## Cumulative Proportion 0.957140 0.959740 0.96226 0.964760 0.966900 0.969010
## PC42 PC43 PC44 PC45 PC46 PC47
## Eigenvalue 0.001401 0.001389 0.00132 0.00123 0.00114 0.001116
## Proportion Explained 0.001840 0.001830 0.00173 0.00162 0.00150 0.001470
## Cumulative Proportion 0.970850 0.972680 0.97441 0.97603 0.97753 0.978990
## PC48 PC49 PC50 PC51 PC52
## Eigenvalue 0.0009995 0.0009509 0.0009352 0.000872 0.0008462
## Proportion Explained 0.0013100 0.0012500 0.0012300 0.001150 0.0011100
## Cumulative Proportion 0.9803100 0.9815500 0.9827800 0.983930 0.9850400
## PC53 PC54 PC55 PC56 PC57
## Eigenvalue 0.0007952 0.0007419 0.000736 0.0006702 0.0006403
## Proportion Explained 0.0010400 0.0009700 0.000970 0.0008800 0.0008400
## Cumulative Proportion 0.9860900 0.9870600 0.988030 0.9889100 0.9897500
## PC58 PC59 PC60 PC61 PC62
## Eigenvalue 0.0006182 0.0005908 0.0005734 0.0005221 0.0004905
## Proportion Explained 0.0008100 0.0007800 0.0007500 0.0006900 0.0006400
## Cumulative Proportion 0.9905600 0.9913400 0.9920900 0.9927800 0.9934200
## PC63 PC64 PC65 PC66 PC67
## Eigenvalue 0.0004365 0.0004214 0.0003809 0.0003513 0.0003171
## Proportion Explained 0.0005700 0.0005500 0.0005000 0.0004600 0.0004200
## Cumulative Proportion 0.9939900 0.9945500 0.9950500 0.9955100 0.9959300
## PC68 PC69 PC70 PC71 PC72
## Eigenvalue 0.0002939 0.00028 0.0002377 0.0002208 0.0002003
## Proportion Explained 0.0003900 0.00037 0.0003100 0.0002900 0.0002600
## Cumulative Proportion 0.9963100 0.99668 0.9969900 0.9972800 0.9975500
## PC73 PC74 PC75 PC76 PC77
## Eigenvalue 0.000198 0.0001827 0.0001442 0.0001355 0.0001292
## Proportion Explained 0.000260 0.0002400 0.0001900 0.0001800 0.0001700
## Cumulative Proportion 0.997810 0.9980500 0.9982300 0.9984100 0.9985800
## PC78 PC79 PC80 PC81 PC82
## Eigenvalue 0.0001051 0.0001021 9.359e-05 8.588e-05 7.826e-05
## Proportion Explained 0.0001400 0.0001300 1.200e-04 1.100e-04 1.000e-04
## Cumulative Proportion 0.9987200 0.9988500 9.990e-01 9.991e-01 9.992e-01
## PC83 PC84 PC85 PC86 PC87
## Eigenvalue 7.656e-05 7.306e-05 6.406e-05 6.007e-05 5.306e-05
## Proportion Explained 1.000e-04 1.000e-04 8.000e-05 8.000e-05 7.000e-05
## Cumulative Proportion 9.993e-01 9.994e-01 9.995e-01 9.996e-01 9.996e-01
## PC88 PC89 PC90 PC91 PC92
## Eigenvalue 3.795e-05 3.729e-05 3.398e-05 3.031e-05 0.0000282
## Proportion Explained 5.000e-05 5.000e-05 4.000e-05 4.000e-05 0.0000400
## Cumulative Proportion 9.997e-01 9.997e-01 9.998e-01 9.998e-01 0.9998400
## PC93 PC94 PC95 PC96 PC97
## Eigenvalue 2.626e-05 2.196e-05 1.618e-05 1.227e-05 1.053e-05
## Proportion Explained 3.000e-05 3.000e-05 2.000e-05 2.000e-05 1.000e-05
## Cumulative Proportion 9.999e-01 9.999e-01 9.999e-01 9.999e-01 1.000e+00
## PC98 PC99 PC100 PC101 PC102
## Eigenvalue 8.04e-06 7.121e-06 5.859e-06 5.655e-06 2.935e-06
## Proportion Explained 1.00e-05 1.000e-05 1.000e-05 1.000e-05 0.000e+00
## Cumulative Proportion 1.00e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC103 PC104
## Eigenvalue 1.375e-06 1.23e-06
## Proportion Explained 0.000e+00 0.00e+00
## Cumulative Proportion 1.000e+00 1.00e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## RDA1 RDA2 RDA3 RDA4 RDA5
## Eigenvalue 0.07989 0.03969 0.02542 0.01083 0.00942
## Proportion Explained 0.48347 0.24017 0.15383 0.06551 0.05701
## Cumulative Proportion 0.48347 0.72365 0.87748 0.94299 1.00000
##
## 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:### Select the significant explanatory variables by forward selection
#?ordiR2step
ordiR2step(rda(spe.hel~1, data=env), scope= formula(spe.rda), direction= "forward", R2scope=TRUE, pstep=1000)## Step: R2.adj= 0
## Call: spe.hel ~ 1
##
## R2.adjusted
## <All variables> 0.19406323
## + Elevation..m. 0.08551800
## + site.soil 0.08493067
## + Slope..Degrees. 0.07527487
## + site.moist 0.05073090
## + Sky.visible.... 0.01802826
## <none> 0.00000000
##
## Df AIC F N.Perm Pr(>F)
## + Elevation..m. 1 -61.775 17.365 999 0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: R2.adj= 0.085518
## Call: spe.hel ~ Elevation..m.
##
## R2.adjusted
## <All variables> 0.1940632
## + site.soil 0.1344768
## + Slope..Degrees. 0.1247353
## + site.moist 0.1064681
## + Sky.visible.... 0.1015897
## <none> 0.0855180
##
## Df AIC F N.Perm Pr(>F)
## + site.soil 1 -70.473 10.842 999 0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: R2.adj= 0.1344768
## Call: spe.hel ~ Elevation..m. + site.soil
##
## R2.adjusted
## <All variables> 0.1940632
## + Slope..Degrees. 0.1607685
## + site.moist 0.1554494
## + Sky.visible.... 0.1505137
## <none> 0.1344768
##
## Df AIC F N.Perm Pr(>F)
## + Slope..Degrees. 1 -74.923 6.4198 999 0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: R2.adj= 0.1607685
## Call: spe.hel ~ Elevation..m. + site.soil + Slope..Degrees.
##
## R2.adjusted
## <All variables> 0.1940632
## + site.moist 0.1797042
## + Sky.visible.... 0.1750973
## <none> 0.1607685
##
## Df AIC F N.Perm Pr(>F)
## + site.moist 1 -77.966 4.9705 999 0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: R2.adj= 0.1797042
## Call: spe.hel ~ Elevation..m. + site.soil + Slope..Degrees. + site.moist
##
## R2.adjusted
## + Sky.visible.... 0.1940632
## <All variables> 0.1940632
## <none> 0.1797042## Call: rda(formula = spe.hel ~ Elevation..m. + site.soil +
## Slope..Degrees. + site.moist, data = env)
##
## Inertia Proportion Rank
## Total 0.7612 1.0000
## Constrained 0.1511 0.1985 4
## Unconstrained 0.6101 0.8015 104
## Inertia is variance
##
## Eigenvalues for constrained axes:
## RDA1 RDA2 RDA3 RDA4
## 0.079510 0.037973 0.024113 0.009462
##
## Eigenvalues for unconstrained axes:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
## 0.07486 0.06734 0.05113 0.04732 0.04102 0.03705 0.02662 0.02354
## (Showed only 8 of all 104 unconstrained eigenvalues)env.signif <- subset(env)
### Re-run the RDA of significant explanatory variables on species abundances
spe.rda.signif <- rda(spe.hel~., data=env.signif)
### Extract the results
summary(spe.rda.signif, display=NULL)##
## Call:
## rda(formula = spe.hel ~ Elevation..m. + Sky.visible.... + Slope..Degrees. + site.soil + site.moist, data = env.signif)
##
## Partitioning of variance:
## Inertia Proportion
## Total 0.7612 1.0000
## Constrained 0.1652 0.2171
## Unconstrained 0.5959 0.7829
##
## Eigenvalues, and their contribution to the variance
##
## Importance of components:
## RDA1 RDA2 RDA3 RDA4 RDA5 PC1
## Eigenvalue 0.07989 0.03969 0.02542 0.01083 0.00942 0.07483
## Proportion Explained 0.10496 0.05214 0.03340 0.01422 0.01238 0.09830
## Cumulative Proportion 0.10496 0.15710 0.19049 0.20471 0.21709 0.31539
## PC2 PC3 PC4 PC5 PC6 PC7
## Eigenvalue 0.06580 0.04732 0.04411 0.03984 0.03659 0.02662
## Proportion Explained 0.08644 0.06217 0.05795 0.05234 0.04807 0.03497
## Cumulative Proportion 0.40183 0.46400 0.52196 0.57429 0.62236 0.65733
## PC8 PC9 PC10 PC11 PC12 PC13
## Eigenvalue 0.02319 0.02113 0.01625 0.01428 0.01347 0.01264
## Proportion Explained 0.03047 0.02776 0.02135 0.01876 0.01770 0.01661
## Cumulative Proportion 0.68780 0.71555 0.73691 0.75567 0.77337 0.78998
## PC14 PC15 PC16 PC17 PC18 PC19
## Eigenvalue 0.01215 0.01117 0.009314 0.008821 0.008441 0.007189
## Proportion Explained 0.01596 0.01467 0.012240 0.011590 0.011090 0.009440
## Cumulative Proportion 0.80594 0.82061 0.832850 0.844430 0.855520 0.864970
## PC20 PC21 PC22 PC23 PC24
## Eigenvalue 0.006982 0.006285 0.005776 0.005436 0.005268
## Proportion Explained 0.009170 0.008260 0.007590 0.007140 0.006920
## Cumulative Proportion 0.874140 0.882400 0.889990 0.897130 0.904050
## PC25 PC26 PC27 PC28 PC29
## Eigenvalue 0.004767 0.004306 0.004148 0.003944 0.003854
## Proportion Explained 0.006260 0.005660 0.005450 0.005180 0.005060
## Cumulative Proportion 0.910310 0.915970 0.921420 0.926600 0.931660
## PC30 PC31 PC32 PC33 PC34 PC35
## Eigenvalue 0.003465 0.003224 0.00297 0.002663 0.00255 0.002347
## Proportion Explained 0.004550 0.004240 0.00390 0.003500 0.00335 0.003080
## Cumulative Proportion 0.936220 0.940450 0.94435 0.947850 0.95120 0.954280
## PC36 PC37 PC38 PC39 PC40 PC41
## Eigenvalue 0.002175 0.001976 0.00192 0.001901 0.001633 0.001605
## Proportion Explained 0.002860 0.002600 0.00252 0.002500 0.002150 0.002110
## Cumulative Proportion 0.957140 0.959740 0.96226 0.964760 0.966900 0.969010
## PC42 PC43 PC44 PC45 PC46 PC47
## Eigenvalue 0.001401 0.001389 0.00132 0.00123 0.00114 0.001116
## Proportion Explained 0.001840 0.001830 0.00173 0.00162 0.00150 0.001470
## Cumulative Proportion 0.970850 0.972680 0.97441 0.97603 0.97753 0.978990
## PC48 PC49 PC50 PC51 PC52
## Eigenvalue 0.0009995 0.0009509 0.0009352 0.000872 0.0008462
## Proportion Explained 0.0013100 0.0012500 0.0012300 0.001150 0.0011100
## Cumulative Proportion 0.9803100 0.9815500 0.9827800 0.983930 0.9850400
## PC53 PC54 PC55 PC56 PC57
## Eigenvalue 0.0007952 0.0007419 0.000736 0.0006702 0.0006403
## Proportion Explained 0.0010400 0.0009700 0.000970 0.0008800 0.0008400
## Cumulative Proportion 0.9860900 0.9870600 0.988030 0.9889100 0.9897500
## PC58 PC59 PC60 PC61 PC62
## Eigenvalue 0.0006182 0.0005908 0.0005734 0.0005221 0.0004905
## Proportion Explained 0.0008100 0.0007800 0.0007500 0.0006900 0.0006400
## Cumulative Proportion 0.9905600 0.9913400 0.9920900 0.9927800 0.9934200
## PC63 PC64 PC65 PC66 PC67
## Eigenvalue 0.0004365 0.0004214 0.0003809 0.0003513 0.0003171
## Proportion Explained 0.0005700 0.0005500 0.0005000 0.0004600 0.0004200
## Cumulative Proportion 0.9939900 0.9945500 0.9950500 0.9955100 0.9959300
## PC68 PC69 PC70 PC71 PC72
## Eigenvalue 0.0002939 0.00028 0.0002377 0.0002208 0.0002003
## Proportion Explained 0.0003900 0.00037 0.0003100 0.0002900 0.0002600
## Cumulative Proportion 0.9963100 0.99668 0.9969900 0.9972800 0.9975500
## PC73 PC74 PC75 PC76 PC77
## Eigenvalue 0.000198 0.0001827 0.0001442 0.0001355 0.0001292
## Proportion Explained 0.000260 0.0002400 0.0001900 0.0001800 0.0001700
## Cumulative Proportion 0.997810 0.9980500 0.9982300 0.9984100 0.9985800
## PC78 PC79 PC80 PC81 PC82
## Eigenvalue 0.0001051 0.0001021 9.359e-05 8.588e-05 7.826e-05
## Proportion Explained 0.0001400 0.0001300 1.200e-04 1.100e-04 1.000e-04
## Cumulative Proportion 0.9987200 0.9988500 9.990e-01 9.991e-01 9.992e-01
## PC83 PC84 PC85 PC86 PC87
## Eigenvalue 7.656e-05 7.306e-05 6.406e-05 6.007e-05 5.306e-05
## Proportion Explained 1.000e-04 1.000e-04 8.000e-05 8.000e-05 7.000e-05
## Cumulative Proportion 9.993e-01 9.994e-01 9.995e-01 9.996e-01 9.996e-01
## PC88 PC89 PC90 PC91 PC92
## Eigenvalue 3.795e-05 3.729e-05 3.398e-05 3.031e-05 0.0000282
## Proportion Explained 5.000e-05 5.000e-05 4.000e-05 4.000e-05 0.0000400
## Cumulative Proportion 9.997e-01 9.997e-01 9.998e-01 9.998e-01 0.9998400
## PC93 PC94 PC95 PC96 PC97
## Eigenvalue 2.626e-05 2.196e-05 1.618e-05 1.227e-05 1.053e-05
## Proportion Explained 3.000e-05 3.000e-05 2.000e-05 2.000e-05 1.000e-05
## Cumulative Proportion 9.999e-01 9.999e-01 9.999e-01 9.999e-01 1.000e+00
## PC98 PC99 PC100 PC101 PC102
## Eigenvalue 8.04e-06 7.121e-06 5.859e-06 5.655e-06 2.935e-06
## Proportion Explained 1.00e-05 1.000e-05 1.000e-05 1.000e-05 0.000e+00
## Cumulative Proportion 1.00e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC103 PC104
## Eigenvalue 1.375e-06 1.23e-06
## Proportion Explained 0.000e+00 0.00e+00
## Cumulative Proportion 1.000e+00 1.00e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## RDA1 RDA2 RDA3 RDA4 RDA5
## Eigenvalue 0.07989 0.03969 0.02542 0.01083 0.00942
## Proportion Explained 0.48347 0.24017 0.15383 0.06551 0.05701
## Cumulative Proportion 0.48347 0.72365 0.87748 0.94299 1.00000
##
## 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:### Calculate the adjusted R^2 of the RDA
(R2adj <- RsquareAdj(spe.rda.signif)$adj.r.squared)## [1] 0.1940632### Test the significance of the model and the significance of axis
#?anova.cca
anova(spe.rda.signif, step=1000)## Permutation test for rda under reduced model
##
## Model: rda(formula = spe.hel ~ Elevation..m. + Sky.visible.... + Slope..Degrees. + site.soil + site.moist, data = env.signif)
## Df Var F N.Perm Pr(>F)
## Model 5 0.16524 9.4277 999 0.001 ***
## Residual 170 0.59593
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(spe.rda.signif, step=1000, by="axis")## Model: rda(formula = spe.hel ~ Elevation..m. + Sky.visible.... + Slope..Degrees. + site.soil + site.moist, data = env.signif)
## Df Var F N.Perm Pr(>F)
## RDA1 1 0.07989 22.7903 999 0.001 ***
## RDA2 1 0.03969 11.3214 999 0.001 ***
## RDA3 1 0.02542 7.2515 999 0.001 ***
## RDA4 1 0.01083 3.0881 999 0.001 ***
## RDA5 1 0.00942 2.6873 999 0.001 ***
## Residual 170 0.59593
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RDA plot with only environmental variables
### Plot the results
#dev.new(width=11.8, height=6)
par(mfrow=c(1,2))
plot(spe.rda.signif, scaling=1, main="Triplot RDA (scaling 1)")
plot(spe.rda.signif, scaling=2, main="Triplot RDA (scaling 2)")
#### advanced plots scaling 1
#dev.new(width=11.8, height=6)
par(mfrow=c(1,2))
plot(spe.rda.signif, scaling=1, main="Triplot RDA - scaling 1", type="none", xlab=c("RDA1"), ylab=c("RDA2"), xlim=c(-1,1), ylim=c(-1,1))
points(scores(spe.rda.signif, display="sites", choices=c(1,2), scaling=1),
pch=21, col="black", bg="gray59", cex=1.2)
text(scores(spe.rda.signif, display="species", choices=c(1), scaling=1),
scores(spe.rda.signif, display="species", choices=c(2), scaling=1),
labels=rownames(scores(spe.rda.signif, display="species", scaling=1)),
col="grey", cex=0.8)
arrows(0,0,
scores(spe.rda.signif, display="bp", choices=c(1), scaling=1),
scores(spe.rda.signif, display="bp", choices=c(2), scaling=1),
col="black")
text(scores(spe.rda.signif, display="bp", choices=c(1), scaling=1)+0.05,
scores(spe.rda.signif, display="bp", choices=c(2), scaling=1)+0.05,
labels=rownames(scores(spe.rda.signif, display="bp", choices=c(2), scaling=1)),
col="black", cex=0.75)
#### advanced plots scaling 2
plot(spe.rda.signif, scaling=2, main="Triplot RDA - scaling 2", type="none", xlab=c("RDA1"), ylab=c("RDA2"), xlim=c(-1,1), ylim=c(-1,1))
points(scores(spe.rda.signif, display="sites", choices=c(1,2), scaling=2),
pch=21, col="black", bg="gray50", cex=1.2)
text(scores(spe.rda.signif, display="species", choices=c(1), scaling=2),
scores(spe.rda.signif, display="species", choices=c(2), scaling=2),
labels=rownames(scores(spe.rda.signif, display="species", scaling=2)),
col="grey", cex=0.8)
arrows(0,0,
scores(spe.rda.signif, display="bp", choices=c(1), scaling=2),
scores(spe.rda.signif, display="bp", choices=c(2), scaling=2),
col="black")
text(scores(spe.rda.signif, display="bp", choices=c(1), scaling=2)+0.05,
scores(spe.rda.signif, display="bp", choices=c(2), scaling=2)+0.05,
labels=rownames(scores(spe.rda.signif, display="bp", choices=c(2), scaling=2)),
col="black", cex=0.75) 
RDA with site distance include
#distances among plots
site.lat.long<-cbind(site.lat, site.lon)
### Run the partial RDA
spe.env.dist <- rda(spe.hel, env, site.lat.long)
### Extract the results
summary(spe.env.dist, display=NULL)##
## Call:
## rda(X = spe.hel, Y = env, Z = site.lat.long)
##
## Partitioning of variance:
## Inertia Proportion
## Total 0.76117 1.0000
## Conditioned 0.07852 0.1032
## Constrained 0.11320 0.1487
## Unconstrained 0.56946 0.7481
##
## Eigenvalues, and their contribution to the variance
## after removing the contribution of conditiniong variables
##
## Importance of components:
## RDA1 RDA2 RDA3 RDA4 RDA5 PC1
## Eigenvalue 0.04361 0.02900 0.02216 0.01011 0.008326 0.07236
## Proportion Explained 0.06388 0.04248 0.03245 0.01480 0.012200 0.10600
## Cumulative Proportion 0.06388 0.10637 0.13882 0.15363 0.165820 0.27182
## PC2 PC3 PC4 PC5 PC6 PC7
## Eigenvalue 0.06527 0.04644 0.04075 0.03553 0.03266 0.02425
## Proportion Explained 0.09561 0.06804 0.05969 0.05205 0.04784 0.03552
## Cumulative Proportion 0.36742 0.43546 0.49515 0.54720 0.59503 0.63056
## PC8 PC9 PC10 PC11 PC12 PC13
## Eigenvalue 0.02268 0.01856 0.01533 0.01385 0.01299 0.01241
## Proportion Explained 0.03322 0.02718 0.02245 0.02029 0.01903 0.01818
## Cumulative Proportion 0.66378 0.69096 0.71341 0.73370 0.75273 0.77092
## PC14 PC15 PC16 PC17 PC18 PC19
## Eigenvalue 0.01127 0.01111 0.009267 0.008642 0.008204 0.007011
## Proportion Explained 0.01651 0.01627 0.013580 0.012660 0.012020 0.010270
## Cumulative Proportion 0.78743 0.80370 0.817280 0.829940 0.841950 0.852220
## PC20 PC21 PC22 PC23 PC24 PC25
## Eigenvalue 0.006861 0.006078 0.005668 0.00534 0.005257 0.004678
## Proportion Explained 0.010050 0.008900 0.008300 0.00782 0.007700 0.006850
## Cumulative Proportion 0.862270 0.871180 0.879480 0.88730 0.895000 0.901860
## PC26 PC27 PC28 PC29 PC30
## Eigenvalue 0.004303 0.004102 0.003943 0.003529 0.003454
## Proportion Explained 0.006300 0.006010 0.005780 0.005170 0.005060
## Cumulative Proportion 0.908160 0.914170 0.919950 0.925120 0.930180
## PC31 PC32 PC33 PC34 PC35
## Eigenvalue 0.003202 0.002941 0.002645 0.002531 0.002287
## Proportion Explained 0.004690 0.004310 0.003870 0.003710 0.003350
## Cumulative Proportion 0.934870 0.939170 0.943050 0.946760 0.950110
## PC36 PC37 PC38 PC39 PC40 PC41
## Eigenvalue 0.002145 0.001972 0.001919 0.001882 0.00161 0.001534
## Proportion Explained 0.003140 0.002890 0.002810 0.002760 0.00236 0.002250
## Cumulative Proportion 0.953250 0.956140 0.958950 0.961700 0.96406 0.966310
## PC42 PC43 PC44 PC45 PC46 PC47
## Eigenvalue 0.00139 0.001384 0.001228 0.001215 0.001131 0.001107
## Proportion Explained 0.00204 0.002030 0.001800 0.001780 0.001660 0.001620
## Cumulative Proportion 0.96835 0.970370 0.972170 0.973950 0.975610 0.977230
## PC48 PC49 PC50 PC51 PC52
## Eigenvalue 0.000997 0.0009419 0.000875 0.0008407 0.0008109
## Proportion Explained 0.001460 0.0013800 0.001280 0.0012300 0.0011900
## Cumulative Proportion 0.978690 0.9800700 0.981350 0.9825800 0.9837700
## PC53 PC54 PC55 PC56 PC57
## Eigenvalue 0.0007811 0.0007373 0.0006666 0.0006475 0.0006352
## Proportion Explained 0.0011400 0.0010800 0.0009800 0.0009500 0.0009300
## Cumulative Proportion 0.9849200 0.9860000 0.9869700 0.9879200 0.9888500
## PC58 PC59 PC60 PC61 PC62
## Eigenvalue 0.0006178 0.00059 0.0005409 0.0005089 0.0004515
## Proportion Explained 0.0009000 0.00086 0.0007900 0.0007500 0.0006600
## Cumulative Proportion 0.9897600 0.99062 0.9914100 0.9921600 0.9928200
## PC63 PC64 PC65 PC66 PC67
## Eigenvalue 0.000433 0.0004082 0.0003776 0.0003466 0.0003119
## Proportion Explained 0.000630 0.0006000 0.0005500 0.0005100 0.0004600
## Cumulative Proportion 0.993450 0.9940500 0.9946100 0.9951100 0.9955700
## PC68 PC69 PC70 PC71 PC72
## Eigenvalue 0.0002912 0.0002765 0.00023 0.0002182 0.0001979
## Proportion Explained 0.0004300 0.0004100 0.00034 0.0003200 0.0002900
## Cumulative Proportion 0.9960000 0.9964000 0.99674 0.9970600 0.9973500
## PC73 PC74 PC75 PC76 PC77
## Eigenvalue 0.0001931 0.000161 0.0001439 0.0001354 0.0001242
## Proportion Explained 0.0002800 0.000240 0.0002100 0.0002000 0.0001800
## Cumulative Proportion 0.9976300 0.997870 0.9980800 0.9982800 0.9984600
## PC78 PC79 PC80 PC81 PC82
## Eigenvalue 0.000105 9.729e-05 0.0000928 8.405e-05 7.749e-05
## Proportion Explained 0.000150 1.400e-04 0.0001400 1.200e-04 1.100e-04
## Cumulative Proportion 0.998610 9.988e-01 0.9988900 9.990e-01 9.991e-01
## PC83 PC84 PC85 PC86 PC87
## Eigenvalue 7.241e-05 7.039e-05 6.202e-05 5.824e-05 5.006e-05
## Proportion Explained 1.100e-04 1.000e-04 9.000e-05 9.000e-05 7.000e-05
## Cumulative Proportion 9.992e-01 9.993e-01 9.994e-01 9.995e-01 9.996e-01
## PC88 PC89 PC90 PC91 PC92
## Eigenvalue 3.777e-05 3.654e-05 3.389e-05 3.015e-05 2.771e-05
## Proportion Explained 6.000e-05 5.000e-05 5.000e-05 4.000e-05 4.000e-05
## Cumulative Proportion 9.996e-01 9.997e-01 9.997e-01 9.998e-01 9.998e-01
## PC93 PC94 PC95 PC96 PC97
## Eigenvalue 2.605e-05 2.114e-05 1.575e-05 0.000012 1.047e-05
## Proportion Explained 4.000e-05 3.000e-05 2.000e-05 0.000020 2.000e-05
## Cumulative Proportion 9.999e-01 9.999e-01 9.999e-01 0.999940 1.000e+00
## PC98 PC99 PC100 PC101 PC102
## Eigenvalue 8.017e-06 6.79e-06 5.808e-06 5.383e-06 2.717e-06
## Proportion Explained 1.000e-05 1.00e-05 1.000e-05 1.000e-05 0.000e+00
## Cumulative Proportion 1.000e+00 1.00e+00 1.000e+00 1.000e+00 1.000e+00
## PC103 PC104
## Eigenvalue 1.354e-06 1.224e-06
## Proportion Explained 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## RDA1 RDA2 RDA3 RDA4 RDA5
## Eigenvalue 0.04361 0.0290 0.02216 0.01011 0.008326
## Proportion Explained 0.38525 0.2562 0.19572 0.08928 0.073550
## Cumulative Proportion 0.38525 0.6414 0.83717 0.92645 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:### Calculate adjusted the R^2 of the partial RDA
(R2adj <- RsquareAdj(spe.env.dist)$adj.r.squared)## [1] 0.1279118Variation partitioning using RDA
The five environmental variables explain by far more variance based on the Venn diagram
#?varpart
#vegandocs("partitioning.pdf")
## Variation partitioning with all explanatory variables
spe.part.all <- varpart(spe.hel, env, site.lat.long)
spe.part.all##
## Partition of variation in RDA
##
## Call: varpart(Y = spe.hel, X = env, site.lat.long)
##
## Explanatory tables:
## X1: env
## X2: site.lat.long
##
## No. of explanatory tables: 2
## Total variation (SS): 133.21
## Variance: 0.76117
## No. of observations: 176
##
## Partition table:
## Df R.squared Adj.R.squared Testable
## [a+b] = X1 5 0.21709 0.19406 TRUE
## [b+c] = X2 2 0.10316 0.09279 TRUE
## [a+b+c] = X1+X2 7 0.25187 0.22070 TRUE
## Individual fractions
## [a] = X1|X2 5 0.12791 TRUE
## [b] 0 0.06615 FALSE
## [c] = X2|X1 2 0.02664 TRUE
## [d] = Residuals 0.77930 FALSE
## ---
## Use function 'rda' to test significance of fractions of interest#dev.new(title="Variation partitioning - all variables", width=11.8, height=8)
plot(spe.part.all, digits=2) 