Chapitre 15 Analyse en coordonnées principales
La PCA, comme la CA, impose une préservation des distances entre objets: la distance euclidienne dans le cas de la PCA, et la distance de Chi2 dans la CA. Si l’objectif est d’ordonner les objets sur la base d’une autre mesure de distance plus appropriée au problème, la PCoA constitue une technique de choix. Dans une PCA, les données sont pivotées de façon à ce que la première composante principale (correspondant à une combinaison linéaire des descripteurs) explique la plus forte proportion de variation possible; la contribution de chaque descripteur (espèces ou variables environnementales) à chaque composante principale peut alors être évaluée d’après son score. La PCoA est une seconde méthode d’ordination sans contrainte dans laquelle les points sont ajoutés les uns après les autres à l’espace d’ordination en utilisant la distance euclidienne ou n’importe quelle mesure de distance (dissimilarité) métrique vous choisissez. Un premier point est ainsi placé dans l’espèce d’ordination, puis un second point placé à la valeur de distance du premier, puis un troisième et ainsi de suite en ajoutant autant d’axes (de dimensions) que nécessaire. Il est parfois difficile de choisir entre effectuer une PCA ou une PCoA. La PCA permet toutefois de réduire des données multivariables en un faible nombre de dimensions tandis que la PCoA est utile pour visualiser les distances entre sites (ou objets). La PCoA est aussi particulièrement adaptées pour les jeux de données présentant plus de colonnes que de lignes. Par exemple, si des centaines d’espèces ont été observées dans un petit nombree de quadrats, une approche basée sur une PCoA utilisant la distance de Bray-Curtis (voir ci-dessous) peut être plus adaptée.
PCoA avec DoubsSpe (transformé Hellinger):
# En utilisant la fonction cmdscale() ?cmdscale
# cmdscale(dist(spe.hel), k=(nrow(spe)-1), eig=TRUE)
# En utilisant la fonction pcoa() ?pcoa
spe.h.pcoa <- pcoa(dist(spe.hel))
# Extraction des résultats
spe.h.pcoa## $correction
## [1] "none" "1"
##
## $note
## [1] "There were no negative eigenvalues. No correction was applied"
##
## $values
## Eigenvalues Relative_eig Broken_stick Cumul_eig Cumul_br_stick
## 1 7.2247719550 4.959363e-01 0.144128028 0.4959363 0.1441280
## 2 1.9115365901 1.312153e-01 0.107090991 0.6271515 0.2512190
## 3 1.3384760670 9.187817e-02 0.088572472 0.7190297 0.3397915
## 4 1.0797364397 7.411728e-02 0.076226793 0.7931470 0.4160183
## 5 0.6161946090 4.229798e-02 0.066967534 0.8354450 0.4829858
## 6 0.4820458816 3.308949e-02 0.059560127 0.8685345 0.5425459
## 7 0.4283230637 2.940175e-02 0.053387287 0.8979362 0.5959332
## 8 0.3762159586 2.582492e-02 0.048096282 0.9237611 0.6440295
## 9 0.3056520040 2.098113e-02 0.043466652 0.9447423 0.6874962
## 10 0.1933000228 1.326886e-02 0.039351426 0.9580111 0.7268476
## 11 0.1461674552 1.003350e-02 0.035647722 0.9680446 0.7624953
## 12 0.1234859973 8.476556e-03 0.032280719 0.9765212 0.7947760
## 13 0.0802304371 5.507327e-03 0.029194299 0.9820285 0.8239703
## 14 0.0757579222 5.200317e-03 0.026345296 0.9872288 0.8503156
## 15 0.0436416031 2.995728e-03 0.023699794 0.9902245 0.8740154
## 16 0.0402292154 2.761489e-03 0.021230658 0.9929860 0.8952461
## 17 0.0300862815 2.065239e-03 0.018915843 0.9950513 0.9141619
## 18 0.0226628371 1.555665e-03 0.016737194 0.9966069 0.9308991
## 19 0.0137723152 9.453849e-04 0.014679581 0.9975523 0.9455787
## 20 0.0123632307 8.486599e-04 0.012730263 0.9984010 0.9583090
## 21 0.0081555480 5.598283e-04 0.010878411 0.9989608 0.9691874
## 22 0.0063464793 4.356469e-04 0.009114743 0.9993965 0.9783021
## 23 0.0040090171 2.751944e-04 0.007431241 0.9996717 0.9857334
## 24 0.0025405355 1.743922e-04 0.005820935 0.9998460 0.9915543
## 25 0.0015475694 1.062311e-04 0.004277725 0.9999523 0.9958320
## 26 0.0004279456 2.937584e-05 0.002796244 0.9999817 0.9986283
## 27 0.0002672735 1.834669e-05 0.001371742 1.0000000 1.0000000
##
## $vectors
## Axis.1 Axis.2 Axis.3 Axis.4 Axis.5 Axis.6
## 1 -0.510156945 0.34756659 0.603085591 -0.310543265 -0.197553521 -0.221069305
## 2 -0.697567847 0.04025083 0.104205663 -0.225612118 0.163849922 0.057118813
## 3 -0.639279415 -0.02078733 0.039889544 -0.263628398 0.130319412 0.111253367
## 4 -0.411968300 -0.13472113 -0.142902757 -0.290074579 0.003953021 0.070356253
## 5 0.005052046 -0.09541567 -0.305402114 -0.285298970 -0.319905818 -0.074116109
## 6 -0.292971968 -0.11423456 -0.318658086 -0.235971751 -0.055670665 -0.023524696
## 7 -0.606181804 0.01311371 -0.103502900 -0.166666590 0.068994249 0.046616186
## 8 -0.044277099 0.37855579 0.209803758 -0.041860959 -0.050340441 -0.224811387
## 9 -0.055398038 0.23770911 -0.554896259 0.035714264 0.245404126 -0.294269844
## 10 -0.411659370 -0.04289473 -0.334330241 -0.064890540 -0.036668552 0.163955021
## 11 -0.647448909 0.07241771 0.059230271 0.165765759 0.138217948 0.077220226
## 12 -0.660227103 0.04063431 0.069626365 0.164694182 0.151045792 0.067901571
## 13 -0.669989292 -0.02617200 0.254127895 0.296853851 0.020112254 0.039361331
## 14 -0.514123243 -0.11759191 0.124161107 0.337034089 -0.072737199 0.102923203
## 15 -0.382456316 -0.18268726 -0.044509503 0.326475994 -0.196934814 0.009434612
## 16 -0.104612763 -0.34327514 -0.060655999 0.173934966 -0.240560559 -0.196130632
## 17 0.077182346 -0.31157335 0.004924379 0.223599341 -0.025562246 -0.150291623
## 18 0.190358561 -0.28346955 -0.003617427 0.210396847 -0.002011505 -0.072026282
## 19 0.375901506 -0.23662078 -0.085630881 0.044242671 0.070944646 0.008377573
## 20 0.527629462 -0.15173319 -0.018308764 -0.019944534 0.064702813 -0.003343781
## 21 0.569870073 -0.16047375 0.065307725 -0.068096992 0.062804974 0.031580390
## 22 0.617258390 -0.11793174 0.094167103 -0.068833539 0.041405159 -0.002858822
## 23 0.336055026 0.73592106 -0.204488229 0.227831244 0.025285812 -0.134590432
## 24 0.497505046 0.55783894 0.004515865 0.162635299 0.089200208 0.187738632
## 25 0.451988375 0.40277173 -0.125327479 0.012077795 -0.406808027 0.294782035
## 26 0.614448977 -0.01805379 0.074796024 -0.072007390 0.085588501 0.080433384
## 27 0.618392379 -0.08429084 0.101059106 -0.072533377 0.073400866 0.025763345
## 28 0.620954661 -0.08172447 0.118745770 -0.079281887 0.097537821 0.019641919
## 29 0.495638840 -0.18890154 0.177201163 -0.005346842 0.048466617 0.036178632
## 30 0.650082728 -0.11422705 0.197383307 -0.110664573 0.023519205 -0.033603580
## Axis.7 Axis.8 Axis.9 Axis.10 Axis.11
## 1 0.144778497 -0.108680760 0.18105189 0.042053483 -0.0016587031
## 2 0.131675051 0.067697769 -0.06442281 0.016322950 0.0766957137
## 3 0.069666241 0.031770585 -0.18133335 0.054260234 0.1067437960
## 4 -0.047927061 -0.136480728 -0.13598284 0.106888544 -0.1645322957
## 5 -0.131095899 -0.174271395 -0.05877177 -0.073981709 0.0131279680
## 6 -0.021743286 -0.115004262 0.03097933 0.065134857 -0.0476015027
## 7 0.145272319 0.133736176 0.13596783 -0.071403704 0.0478781210
## 8 -0.249281692 0.347792146 -0.20431566 -0.019627104 -0.1000657420
## 9 -0.156249571 -0.036248842 0.08732011 0.069397576 0.0711114885
## 10 0.053941040 0.277546755 0.15097392 -0.090289879 -0.0627982226
## 11 -0.075619678 -0.113051884 0.05179123 -0.166515459 -0.0936935628
## 12 -0.082316286 -0.089474135 0.05531765 -0.101060997 -0.0354555822
## 13 -0.111861920 -0.051493606 -0.11003492 0.007324915 0.0835976123
## 14 -0.155831067 -0.084666037 -0.05268442 0.108373540 0.0413567293
## 15 -0.102805610 0.082457361 0.19458097 0.085700119 0.0295625679
## 16 0.126867264 0.110495416 0.01963519 0.097451870 0.0123631286
## 17 0.229852292 -0.022948272 -0.09446251 -0.070757727 -0.0318276098
## 18 0.171587545 -0.053114138 -0.06502363 -0.053291310 -0.1178208859
## 19 0.127081334 0.087197011 -0.11829211 0.047993991 0.0835424502
## 20 0.069016007 0.000460929 -0.04253991 -0.018492619 -0.0139967841
## 21 -0.009766216 -0.006130571 -0.03271554 -0.023218456 -0.0006656359
## 22 -0.046128905 0.013506969 0.06301853 0.004431100 -0.0278464929
## 23 0.159237588 -0.121000025 -0.06538492 -0.086608737 0.0660163262
## 24 0.131408044 0.004925476 0.04467269 0.198440168 -0.1434962817
## 25 -0.000769921 0.012976434 -0.06943344 -0.066678460 0.0711120416
## 26 -0.071425449 -0.028398595 0.05601302 0.050939982 0.0494279711
## 27 -0.076854712 0.004905405 0.06998558 0.042964922 0.0448326499
## 28 -0.085841284 0.011954160 0.08869290 -0.008741900 0.0253749009
## 29 -0.027534472 -0.052600816 0.04462036 -0.026347339 0.0190432434
## 30 -0.107330191 0.006141473 0.02077662 -0.120662852 -0.0003274070
## Axis.12 Axis.13 Axis.14 Axis.15 Axis.16
## 1 -0.016985570 -0.059356684 -0.032259029 0.017751662 -0.032551065
## 2 -0.040382483 -0.004522773 0.034175345 0.030438784 -0.003470435
## 3 0.059748365 0.030529406 -0.056369389 -0.030472273 0.023507620
## 4 0.128113024 0.005672885 0.029024190 0.037726744 -0.016192023
## 5 -0.142025015 0.027986563 0.044895706 -0.031926925 0.021644656
## 6 0.002730923 -0.012716449 0.048262228 -0.020739758 0.012986316
## 7 0.013501670 0.021247503 0.016671866 -0.052330462 0.012911167
## 8 0.006193487 -0.025282152 0.007970746 -0.025493553 0.011617612
## 9 -0.038202009 -0.020718941 -0.094846511 0.001390466 -0.054329506
## 10 0.018135140 0.002582547 0.027579884 0.012535440 -0.057093096
## 11 -0.045020205 0.026564345 -0.032588078 0.066552203 0.005309144
## 12 -0.014423939 -0.019722088 -0.073255141 -0.022081383 0.088608382
## 13 -0.113643929 0.047913574 0.086889725 -0.029669059 -0.023007366
## 14 0.085753156 -0.024981689 -0.041772099 0.018944140 -0.049571366
## 15 0.042255905 -0.081698779 0.091913004 0.009632658 0.028317188
## 16 0.009130686 0.148327119 -0.068359877 0.043569274 0.052496280
## 17 0.016739286 -0.016572914 0.002677102 -0.048014006 -0.005203501
## 18 0.014076801 -0.050636202 -0.046206632 -0.074380342 -0.035703891
## 19 -0.102061060 -0.062317049 0.012286823 0.061776992 -0.020887344
## 20 -0.043631886 -0.121847295 -0.015523233 0.039146960 0.032396504
## 21 -0.020855074 -0.020418570 0.023435950 0.064833903 0.017006933
## 22 0.013713142 0.015947853 0.012667359 0.027584750 0.038980645
## 23 0.136150259 0.026788223 0.100732248 0.026844661 0.019799830
## 24 -0.131949957 0.057983455 0.004971150 -0.020944221 0.003456220
## 25 0.012583227 -0.029467230 -0.104718995 0.001544042 -0.014342105
## 26 0.029739984 -0.047390015 0.028381466 -0.071868171 0.023492243
## 27 0.051420190 0.003944216 -0.021284610 -0.021355323 0.038782465
## 28 0.038056995 0.056857822 -0.012266161 -0.015148328 0.009103088
## 29 0.019744857 0.066405552 0.020151093 -0.027354925 -0.088766027
## 30 0.011394031 0.058897769 0.006763871 0.031506050 -0.039298567
## Axis.17 Axis.18 Axis.19 Axis.20 Axis.21
## 1 -0.002022009 -0.0114828298 0.016218432 0.001079419 -0.0005019483
## 2 0.032848263 0.0221283401 -0.033450998 -0.026019257 -0.0339142968
## 3 -0.041700683 0.0295264894 0.010334071 0.005409936 0.0035999917
## 4 0.035988011 -0.0254209339 -0.020162069 0.016483289 0.0167710090
## 5 -0.055721856 0.0037098626 -0.013022444 0.005899574 -0.0164850945
## 6 0.033956416 0.0087676376 0.050604576 -0.019181658 0.0067963329
## 7 -0.022284596 -0.0165882742 -0.040039849 0.014046393 0.0363072960
## 8 -0.010291948 0.0055408227 0.002787075 -0.004392699 0.0024537397
## 9 0.011778079 -0.0003455269 -0.013508307 -0.001331984 0.0043800067
## 10 -0.013908033 -0.0135256237 0.037445682 0.004395065 -0.0235946995
## 11 -0.009826263 0.0703357289 0.002523735 -0.010262220 0.0075908622
## 12 0.016312674 -0.0721256365 0.014210040 0.010521804 -0.0134186070
## 13 0.047335815 -0.0161922560 0.009042442 -0.003528424 0.0235887894
## 14 -0.067022434 -0.0116252988 0.001354905 0.010199583 -0.0219927886
## 15 0.009364557 0.0263486731 -0.023351454 -0.001296985 0.0094959853
## 16 0.025964781 0.0104597824 -0.006956306 0.006661384 -0.0094263976
## 17 -0.020248107 0.0067446767 0.027258460 0.026967756 -0.0015512224
## 18 0.027093364 0.0072679935 -0.028002826 -0.047328412 -0.0059261451
## 19 0.009924204 -0.0481308750 0.024850340 -0.004324904 0.0079824875
## 20 -0.015585863 0.0277501077 -0.013702681 0.047724297 0.0182074195
## 21 -0.016542963 0.0092821760 0.001480220 -0.025370160 -0.0084429859
## 22 -0.055684864 -0.0561345635 -0.024796601 -0.040797082 0.0050452392
## 23 -0.008860634 -0.0069233159 0.004266889 -0.002271375 -0.0054075510
## 24 -0.018443767 0.0075841409 -0.002515486 0.014595728 -0.0022631488
## 25 0.040923141 -0.0024101993 -0.007624906 -0.011774119 0.0140077288
## 26 0.035467099 0.0174345585 -0.010536421 0.019434700 -0.0402246854
## 27 -0.002288486 0.0406949575 0.041498383 -0.023999144 0.0203703758
## 28 0.018397048 -0.0095601545 0.008600220 0.001377984 0.0035839658
## 29 -0.038561698 -0.0001869609 -0.004530281 -0.001379115 0.0121067848
## 30 0.053640748 -0.0029234986 -0.010274840 0.038460625 -0.0091384433
## Axis.22 Axis.23 Axis.24 Axis.25 Axis.26
## 1 0.0014833225 -0.0065787897 0.0025708440 0.0006111797 -6.652485e-04
## 2 0.0097642374 0.0268452560 -0.0100620960 0.0038976796 2.137164e-03
## 3 -0.0092776871 -0.0037606885 0.0144658364 -0.0036287070 -6.821978e-03
## 4 0.0028506107 -0.0027090716 -0.0017569852 0.0057491452 -1.706076e-03
## 5 0.0136989727 0.0003475077 0.0011424898 -0.0030847372 -2.908802e-03
## 6 -0.0115349565 0.0047214339 -0.0018803323 -0.0034464820 5.217117e-03
## 7 -0.0056934775 -0.0093295061 0.0003530511 -0.0072762582 5.329989e-03
## 8 -0.0008469183 -0.0004881854 -0.0038862115 0.0017875196 -1.512602e-04
## 9 -0.0074683994 0.0047774096 0.0019637794 0.0029468259 5.485785e-04
## 10 0.0098644645 -0.0076437028 -0.0018942865 -0.0002971812 3.409468e-04
## 11 -0.0037986549 -0.0152174925 0.0080735768 0.0096867419 -7.755451e-04
## 12 -0.0033199047 0.0093492106 -0.0131126832 -0.0028589307 -4.710659e-03
## 13 0.0039517664 -0.0090423073 -0.0004737194 0.0008766611 4.745572e-03
## 14 0.0093856775 -0.0005970185 0.0010930490 -0.0090303061 6.734889e-03
## 15 -0.0063600828 0.0142798563 0.0080190556 0.0001970928 -8.014365e-03
## 16 0.0006285270 -0.0125371143 -0.0098869078 0.0012568280 7.931333e-04
## 17 -0.0176256858 0.0250253705 0.0100018862 0.0137503799 3.542893e-03
## 18 0.0143625846 -0.0098348246 0.0033598507 -0.0120505422 -2.320132e-03
## 19 0.0015468382 -0.0153852060 0.0067802235 0.0012764314 -6.401490e-03
## 20 0.0216341197 -0.0019871266 -0.0143405081 -0.0015301558 3.713579e-03
## 21 -0.0176748102 0.0008238311 -0.0027859661 -0.0083260780 3.104888e-03
## 22 -0.0158740130 0.0002140067 0.0104861271 0.0093024539 4.263876e-03
## 23 0.0081132047 -0.0063640810 -0.0031794156 -0.0034469454 -1.325333e-03
## 24 -0.0038248668 0.0081036968 0.0040210079 -0.0045838875 -9.888835e-04
## 25 -0.0080154023 0.0073904422 -0.0006747257 0.0067623375 1.688911e-03
## 26 -0.0155602791 -0.0299232051 -0.0002259646 0.0111009252 1.625749e-03
## 27 0.0039892822 0.0049533207 -0.0106345438 -0.0087416826 3.701578e-05
## 28 0.0549447863 0.0095490227 0.0166916073 0.0079819755 3.801458e-04
## 29 -0.0085946905 0.0042374550 -0.0270118328 0.0085586800 -6.625968e-03
## 30 -0.0207485655 0.0107805002 0.0127837939 -0.0174409634 -7.887060e-04
## Axis.27
## 1 -0.0002438509
## 2 -0.0016677021
## 3 0.0045375912
## 4 -0.0044881420
## 5 -0.0030365301
## 6 0.0073731251
## 7 -0.0023330313
## 8 0.0005887564
## 9 -0.0005713160
## 10 -0.0004645789
## 11 -0.0009212218
## 12 0.0005358741
## 13 0.0003558427
## 14 -0.0008856661
## 15 0.0011316764
## 16 0.0009562223
## 17 -0.0032726121
## 18 0.0011084512
## 19 -0.0028887932
## 20 0.0044727668
## 21 0.0012218169
## 22 0.0016579982
## 23 0.0005197968
## 24 -0.0001848745
## 25 0.0003261856
## 26 -0.0010766735
## 27 -0.0091910944
## 28 0.0024768505
## 29 0.0035590558
## 30 0.0004040766
##
## $trace
## [1] 14.56794
##
## attr(,"class")
## [1] "pcoa"# Représentation graphique
biplot.pcoa(spe.h.pcoa, spe.hel, dir.axis2 = -1)
Vous pouvez aussi exécuter cette PCoA avec une autre mesure de distance (ex. Bray-Curtis):
spe.bray.pcoa <- pcoa(spe.db) # il s'agit de la matrice de distances de Bray-Curtis qu'on a générée plus tôt
spe.bray.pcoa## $correction
## [1] "none" "1"
##
## $note
## [1] "No correction was applied to the negative eigenvalues"
##
## $values
## Eigenvalues Relative_eig Rel_corr_eig Broken_stick Cum_corr_eig
## 1 3.695332e+00 4.924914e-01 0.396254705 0.140256109 0.3962547
## 2 1.197352e+00 1.595758e-01 0.133291315 0.104541823 0.5295460
## 3 8.465325e-01 1.128207e-01 0.096360364 0.086684680 0.6259064
## 4 5.253896e-01 7.002074e-02 0.062553505 0.074779918 0.6884599
## 5 4.147227e-01 5.527173e-02 0.050903553 0.065851347 0.7393634
## 6 2.977969e-01 3.968856e-02 0.038594722 0.058708489 0.7779582
## 7 1.913094e-01 2.549655e-02 0.027384732 0.052756109 0.8053429
## 8 1.554757e-01 2.072086e-02 0.023612504 0.047654068 0.8289554
## 9 1.307617e-01 1.742712e-02 0.021010850 0.043189782 0.8499663
## 10 1.272105e-01 1.695385e-02 0.020637021 0.039221528 0.8706033
## 11 8.550928e-02 1.139616e-02 0.016247110 0.035650099 0.8868504
## 12 4.357746e-02 5.807740e-03 0.011832929 0.032403346 0.8986833
## 13 3.862321e-02 5.147468e-03 0.011311393 0.029427156 0.9099947
## 14 2.727686e-02 3.635295e-03 0.010116958 0.026679903 0.9201117
## 15 1.303318e-02 1.736984e-03 0.008617519 0.024128883 0.9287292
## 16 6.704839e-03 8.935804e-04 0.007951331 0.021747930 0.9366805
## 17 3.817779e-03 5.088104e-04 0.007647409 0.019515787 0.9443279
## 18 1.300463e-03 1.733178e-04 0.007382410 0.017414947 0.9517103
## 19 0.000000e+00 0.000000e+00 0.007241723 0.015430820 0.9589521
## 20 -3.597737e-05 -4.794846e-06 0.006806781 0.013551121 0.9657588
## 21 -4.167639e-03 -5.554377e-04 0.006301162 0.011765406 0.9720600
## 22 -8.970687e-03 -1.195559e-03 0.005694152 0.010064726 0.9777541
## 23 -1.473688e-02 -1.964042e-03 0.005560103 0.008441350 0.9833143
## 24 -1.601025e-02 -2.133749e-03 0.004966161 0.006888555 0.9882804
## 25 -2.165231e-02 -2.885689e-03 0.003953426 0.005400459 0.9922338
## 26 -3.127263e-02 -4.167827e-03 0.003620673 0.003971888 0.9958545
## 27 -3.443356e-02 -4.589097e-03 0.003284015 0.002598262 0.9991385
## 28 -3.763160e-02 -5.015311e-03 0.000861473 0.001275510 1.0000000
## 29 -6.064415e-02 -8.082285e-03 0.000000000 0.000000000 1.0000000
## 30 -6.882758e-02 -9.172922e-03 0.000000000 0.000000000 1.0000000
## Cumul_br_stick
## 1 0.1402561
## 2 0.2447979
## 3 0.3314826
## 4 0.4062625
## 5 0.4721139
## 6 0.5308224
## 7 0.5835785
## 8 0.6312325
## 9 0.6744223
## 10 0.7136439
## 11 0.7492940
## 12 0.7816973
## 13 0.8111245
## 14 0.8378044
## 15 0.8619332
## 16 0.8836812
## 17 0.9031970
## 18 0.9206119
## 19 0.9360427
## 20 0.9495938
## 21 0.9613593
## 22 0.9714240
## 23 0.9798653
## 24 0.9867539
## 25 0.9921543
## 26 0.9961262
## 27 0.9987245
## 28 1.0000000
## 29 1.0000000
## 30 1.0000000
##
## $vectors
## Axis.1 Axis.2 Axis.3 Axis.4 Axis.5
## 1 -0.320449823 0.23306708 0.4052011521 0.413065395 0.015467310
## 2 -0.502684922 -0.03668632 0.0997686617 0.057953534 0.131243584
## 3 -0.472042556 -0.07339838 0.0403753966 0.006212226 0.047271525
## 4 -0.316249689 -0.09691873 -0.0491347038 0.002385678 0.066184200
## 5 0.066641517 -0.13220277 -0.0390672681 -0.012811215 0.179083299
## 6 -0.241592757 -0.04199098 -0.1494561573 0.012030513 0.103395863
## 7 -0.441932409 -0.01314509 -0.0447489079 0.020783790 0.061783592
## 8 -0.001003178 0.48166769 0.4918540684 -0.484890471 -0.022190458
## 9 -0.028617328 0.08917429 -0.1852217989 -0.148928771 0.391250238
## 10 -0.293012598 -0.02300668 -0.1871502897 -0.096313161 0.118272698
## 11 -0.438723426 0.06823719 0.0580789208 0.147205049 -0.015397336
## 12 -0.472756087 -0.02746175 -0.0121736070 -0.004845316 -0.034829016
## 13 -0.475481686 -0.07544948 0.1076846382 -0.002262210 -0.152129112
## 14 -0.374686608 -0.08941462 -0.0393980393 -0.058453813 -0.201138975
## 15 -0.243653042 -0.17161666 -0.0604201374 -0.094551547 -0.124766409
## 16 -0.073434106 -0.19187100 -0.0766719854 -0.084668713 -0.153297850
## 17 0.040676259 -0.17425458 -0.0875892901 -0.055947030 -0.163426682
## 18 0.144508662 -0.14874280 -0.1071774823 -0.063043216 -0.123147241
## 19 0.229660655 -0.14844143 -0.1097826754 -0.072230936 -0.047123653
## 20 0.401052593 -0.11604102 -0.0002766332 -0.007839228 0.027044314
## 21 0.438415129 -0.10928733 0.0607616262 0.031524233 0.014274293
## 22 0.465196276 -0.10586147 0.1107737062 0.036773609 0.034947440
## 23 0.116548455 0.59487844 -0.2494981196 0.086922295 -0.075488505
## 24 0.320052060 0.35575234 -0.2002483247 0.073501208 -0.028683520
## 25 0.226020916 0.38053577 -0.2829375696 0.057844064 -0.125723103
## 26 0.434698863 -0.01620189 -0.0228296456 0.040594850 0.018358257
## 27 0.462587642 -0.07973733 0.0872440317 0.046221679 0.028473423
## 28 0.462892804 -0.08746326 0.1130809043 0.048047644 0.048644676
## 29 0.409464629 -0.14642284 0.1498949779 0.045443752 -0.017221474
## 30 0.477903756 -0.09769640 0.1790645512 0.060276109 -0.001131376
## Axis.6 Axis.7 Axis.8 Axis.9 Axis.10
## 1 -0.078285649 0.0281757686 0.152419739 0.0620214512 -0.0084554849
## 2 0.042274052 0.0647050617 -0.046966117 0.0143279884 0.0405790440
## 3 -0.092178285 0.0646661933 -0.122869623 0.0796812732 -0.0146515001
## 4 -0.126239659 0.0018330966 -0.077145856 0.0229106939 -0.0158674810
## 5 -0.147957254 -0.2144370289 0.052128944 -0.1149083302 -0.0366926489
## 6 -0.149604492 0.0187947347 0.049587848 0.0219358922 0.0065920493
## 7 -0.061421046 0.0155580388 -0.066973268 0.0493668301 0.0392205663
## 8 -0.073508675 0.0132432281 0.019726717 -0.0102409140 0.0260418495
## 9 0.212219629 -0.0213876730 0.084549171 0.0833210876 -0.0862271809
## 10 -0.042173259 0.0595019777 -0.006366994 -0.1525320721 0.1266833055
## 11 0.097100129 -0.0547434551 0.026313041 -0.1170521719 0.1003201704
## 12 0.118684341 -0.0038674809 -0.036603841 -0.0083417190 -0.0032760416
## 13 0.150478201 -0.0152858466 -0.057633010 -0.0454827223 -0.0944894934
## 14 0.040946350 0.0171424468 -0.062093588 -0.0221704722 -0.1350306736
## 15 0.034048165 -0.0516086788 0.098276062 -0.0360009400 -0.1004717412
## 16 -0.087210913 -0.0623387129 0.185188284 0.0934010593 -0.0134974136
## 17 0.065064290 0.0156944167 0.056920618 0.0397691611 0.1316850202
## 18 0.067261462 0.0089925735 0.074536919 0.0067912156 0.0997951967
## 19 -0.081932990 0.0808348609 -0.058475012 0.1289316028 0.0384049959
## 20 0.005055568 0.0522460709 0.021009409 0.0305227531 0.0251360419
## 21 -0.012210424 0.0170555064 -0.026624540 -0.0107184566 0.0473053698
## 22 0.018336154 -0.0391108664 -0.009713173 -0.0004278611 -0.0145278880
## 23 0.130741953 -0.1778339520 -0.067327702 0.1126514521 0.0477877228
## 24 0.088821183 0.2340538172 0.069625917 -0.0988142834 -0.0374512340
## 25 -0.235264361 -0.0454730098 -0.051405489 -0.0582072398 -0.0511812804
## 26 -0.046619217 0.1067385313 0.019401955 -0.0020776418 -0.0875194852
## 27 0.010207061 0.0240932023 -0.033950337 -0.0162326594 -0.0382303296
## 28 0.031303330 0.0001778202 -0.062589906 -0.0076687424 -0.0357280637
## 29 0.088986182 -0.0695883636 -0.054404092 -0.0394183353 0.0005809206
## 30 0.033078176 -0.0678322774 -0.068542079 -0.0053378990 0.0431656874
## Axis.11 Axis.12 Axis.13 Axis.14 Axis.15
## 1 -0.022513152 -0.0318331401 -0.0045374664 -0.015077925 0.0031514532
## 2 0.004346706 -0.0464769912 -0.0303066505 0.006230699 -0.0144407298
## 3 0.007605501 -0.0202944454 0.0086976933 0.001783476 -0.0241033581
## 4 0.113604692 0.0150396902 0.0625367256 -0.057056064 0.0451045108
## 5 0.085457125 -0.0373920345 -0.0011773242 0.040833799 -0.0080899983
## 6 0.012985916 0.0573687582 0.0214274380 -0.005953678 -0.0351495991
## 7 -0.087085273 0.0072777798 -0.0122808336 0.029907929 0.0252014820
## 8 0.013088057 0.0134033106 -0.0014114206 -0.002947475 0.0007884534
## 9 -0.005670494 -0.0108812935 -0.0133239372 -0.020611411 -0.0101564754
## 10 -0.097334439 -0.0219174760 0.0170523689 0.007001587 0.0027982719
## 11 0.032374573 0.1009488052 -0.0365944549 -0.009018777 0.0006566102
## 12 -0.022014126 0.0203339131 0.0157782484 0.010840871 0.0182929659
## 13 0.068391690 -0.0329503130 -0.0342092959 0.034415085 -0.0129269717
## 14 0.016999784 -0.0101130826 0.0176159540 -0.010254550 -0.0128577160
## 15 -0.117836229 0.0037692594 0.0003900737 -0.029259843 0.0294199049
## 16 -0.024101817 0.0055763715 0.0259347583 0.044524714 -0.0066274081
## 17 0.054096138 -0.0007715256 0.0698100584 0.003525640 -0.0067179644
## 18 0.035445421 -0.0269397615 -0.0745064719 -0.076763249 -0.0162243590
## 19 -0.025979200 0.0085842408 -0.0593572055 0.035387675 0.0027740422
## 20 0.053661635 -0.0609488270 -0.0272268776 -0.026509555 0.0224754279
## 21 0.061210849 0.0078654082 -0.0293185530 0.047424785 0.0158689438
## 22 -0.015952815 -0.0092570258 -0.0047907493 0.024730677 0.0553511539
## 23 0.009607789 0.0150524279 0.0166706456 0.014413980 0.0045712548
## 24 0.029482022 -0.0375430818 0.0457779315 0.034080068 0.0062274271
## 25 -0.034619949 -0.0346910621 -0.0466250483 -0.033314532 -0.0074982529
## 26 0.047801977 0.0941097564 -0.0065089702 -0.001246796 -0.0140351406
## 27 -0.063767848 0.0481306939 -0.0117106873 0.020080313 -0.0210301432
## 28 -0.047675392 0.0376833081 0.0289096828 -0.050138582 0.0078730675
## 29 -0.025499193 -0.0053410529 -0.0219190042 -0.002121161 -0.0123922727
## 30 -0.056109947 -0.0477926103 0.0852033720 -0.014907698 -0.0383045803
## Axis.16 Axis.17 Axis.18
## 1 -0.0041089733 0.001281615 -1.578001e-04
## 2 -0.0008511369 -0.010134296 6.215124e-04
## 3 -0.0191012489 0.008554064 5.435894e-03
## 4 0.0007208242 -0.009200677 2.802553e-03
## 5 0.0061478570 -0.001737084 -2.337866e-03
## 6 0.0065979265 0.011562195 1.814119e-03
## 7 0.0257149123 0.006045217 -8.690735e-03
## 8 0.0019250117 0.001207893 1.716228e-05
## 9 -0.0069122537 0.003732332 5.125124e-04
## 10 -0.0136488283 -0.003474875 -7.283457e-04
## 11 -0.0015574416 0.002778467 1.154824e-03
## 12 0.0021606023 -0.004478062 4.226975e-03
## 13 0.0179575259 -0.001803925 -7.357764e-03
## 14 -0.0238185726 -0.001882466 3.850686e-03
## 15 0.0216875991 0.002420574 2.142474e-03
## 16 -0.0216100892 -0.011978541 -5.622120e-03
## 17 0.0116958034 0.013519024 -8.567581e-05
## 18 -0.0117577436 -0.008506454 4.595190e-03
## 19 0.0007245537 0.004918996 -2.351058e-03
## 20 0.0347124084 -0.001991238 -2.245306e-03
## 21 -0.0159517282 -0.015709825 -4.490605e-03
## 22 -0.0227505122 0.015099333 1.584427e-02
## 23 0.0012299491 -0.005809954 3.671371e-04
## 24 -0.0038107317 0.002199450 -1.845175e-03
## 25 -0.0004268606 0.003758138 2.147508e-04
## 26 0.0156858166 0.011041608 7.294447e-04
## 27 0.0147261003 -0.031157037 1.393095e-02
## 28 -0.0198937624 -0.011611121 -2.269475e-02
## 29 -0.0113382328 0.033581892 -4.128149e-03
## 30 0.0158512255 -0.002225245 4.474894e-03
##
## $trace
## [1] 7.503343
##
## attr(,"class")
## [1] "pcoa"biplot.pcoa(spe.bray.pcoa, spe.hel, dir.axis2 = -1)
# Le choix d'une mesure de distance est très important car
# ça influence les résultats!Défi 5 Exécuter une PCoA sur les données d’abondance des espèces d’acariens transformées Hellinger (données mite). Quels sont les axes importants? Quels groupes de sites pouvez-vous identifier? Quelles espèces sont liées à chaque groupe de sites? Comment les résultats de cette PCoA se comparent-ils avec ceux de la PCA?
Défi 5 - Solution
mite.spe.h.pcoa <- pcoa(dist(mite.spe.hel))
mite.spe.h.pcoa## $correction
## [1] "none" "1"
##
## $note
## [1] "There were no negative eigenvalues. No correction was applied"
##
## $values
## Eigenvalues Relative_eig Broken_stick Cumul_eig Cumul_br_stick
## 1 11.602643193 0.4264887201 0.1184794691 0.4264887 0.1184795
## 2 3.526055542 0.1296103733 0.0899080405 0.5560991 0.2083875
## 3 2.186367334 0.0803662571 0.0756223263 0.6364654 0.2840098
## 4 1.570196758 0.0577171249 0.0660985167 0.6941825 0.3501084
## 5 1.171005251 0.0430436861 0.0589556596 0.7372262 0.4090640
## 6 1.006554628 0.0369988276 0.0532413739 0.7742250 0.4623054
## 7 0.844412363 0.0310388195 0.0484794691 0.8052638 0.5107849
## 8 0.653368743 0.0240164585 0.0443978365 0.8292803 0.5551827
## 9 0.548575687 0.0201644865 0.0408264079 0.8494448 0.5960091
## 10 0.529037917 0.0194463193 0.0376518047 0.8688911 0.6336609
## 11 0.385624780 0.0141747545 0.0347946619 0.8830658 0.6684556
## 12 0.380429104 0.0139837724 0.0321972593 0.8970496 0.7006528
## 13 0.340199814 0.0125050284 0.0298163069 0.9095546 0.7304691
## 14 0.284248035 0.0104483589 0.0276185047 0.9200030 0.7580876
## 15 0.276071181 0.0101477950 0.0255776884 0.9301508 0.7836653
## 16 0.240701481 0.0088476794 0.0236729265 0.9389985 0.8073383
## 17 0.225645857 0.0082942663 0.0218872122 0.9472927 0.8292255
## 18 0.186479038 0.0068545766 0.0202065399 0.9541473 0.8494320
## 19 0.162466773 0.0059719363 0.0186192383 0.9601192 0.8680512
## 20 0.149898967 0.0055099702 0.0171154789 0.9656292 0.8851667
## 21 0.147693237 0.0054288922 0.0156869075 0.9710581 0.9008536
## 22 0.128050704 0.0047068741 0.0143263633 0.9757650 0.9151800
## 23 0.114094908 0.0041938885 0.0130276620 0.9799589 0.9282077
## 24 0.085824674 0.0031547342 0.0117854259 0.9831136 0.9399931
## 25 0.081991690 0.0030138418 0.0105949498 0.9861274 0.9505880
## 26 0.076994065 0.0028301396 0.0094520926 0.9889576 0.9600401
## 27 0.056610567 0.0020808852 0.0083531915 0.9910385 0.9683933
## 28 0.055672481 0.0020464031 0.0072949905 0.9930849 0.9756883
## 29 0.047757948 0.0017554816 0.0062745823 0.9948404 0.9819629
## 30 0.042041391 0.0015453530 0.0052893606 0.9963857 0.9872522
## 31 0.036886153 0.0013558573 0.0043369797 0.9977416 0.9915892
## 32 0.023659824 0.0008696853 0.0034153207 0.9986112 0.9950045
## 33 0.019271950 0.0007083963 0.0025224635 0.9993196 0.9975270
## 34 0.013529456 0.0004973143 0.0016566627 0.9998170 0.9991837
## 35 0.004979684 0.0001830427 0.0008163265 1.0000000 1.0000000
##
## $vectors
## Axis.1 Axis.2 Axis.3 Axis.4 Axis.5 Axis.6
## 1 0.072050731 -0.404874957 0.123880209 -0.214979492 -0.009322998 0.04540086
## 2 -0.080178872 -0.475895251 -0.040770237 -0.132551999 -0.187285469 0.03404235
## 3 -0.006340714 -0.532965199 -0.071896456 -0.085631135 -0.109737585 -0.05262964
## 4 0.065918599 -0.390261954 -0.023053705 -0.061263985 -0.125083832 0.06828817
## 5 0.475151216 -0.176766735 0.005673279 0.014041251 -0.127282100 0.05785622
## 6 0.508769546 -0.137055078 -0.066473245 0.113920983 -0.061556779 0.12041210
## 7 0.615792769 -0.012727468 -0.035579920 0.025759028 0.018790021 0.12033710
## 8 0.578722079 -0.084058324 0.062705431 0.012841804 -0.143529919 0.05319677
## 9 0.197878804 -0.410753144 0.020690961 -0.194665880 -0.078958035 -0.11658023
## 10 0.608325106 -0.015468259 0.025731538 0.050448066 -0.021002061 0.12889625
## 11 0.478021945 -0.067075271 0.317222690 -0.060486992 0.141958632 0.14829596
## 12 0.587259598 0.042587053 0.079365613 0.019598754 0.066693660 0.01729548
## 13 0.558944326 0.009379685 -0.050295252 0.097753588 -0.087203405 -0.11625856
## 14 0.570349529 -0.075826157 0.015931378 0.089155654 -0.040227562 0.26254962
## 15 0.081724886 -0.327652800 0.089794988 -0.250898445 -0.041952295 -0.01567727
## 16 0.492924862 -0.063384901 0.107549414 -0.061933568 0.122444718 -0.13143314
## 17 0.605418395 -0.031177967 0.062448858 -0.043530873 0.111937022 -0.17626401
## 18 0.473400394 -0.060716576 -0.025228123 0.008950565 -0.053679152 0.17744501
## 19 0.268953127 0.072137657 -0.079958674 -0.091057728 -0.041435916 0.19671612
## 20 0.592151288 -0.134817005 -0.106682850 0.063603203 -0.061353879 0.17070630
## 21 0.543656538 0.073134587 -0.124289921 0.168830238 0.044259335 0.06728093
## 22 0.540084475 0.120592846 -0.225644134 0.135460999 -0.044740495 0.01840295
## 23 0.116027323 0.058972633 0.223538124 -0.207598692 0.099716583 -0.09291938
## 24 0.610752047 -0.066007703 -0.037653614 0.011528145 0.134979947 -0.08918350
## 25 0.426004859 0.034350409 0.194793819 -0.178435260 0.059422271 -0.10172354
## 26 0.390690776 -0.109530838 0.011995476 -0.092230045 -0.057845914 -0.24266016
## 27 0.524790071 0.044933189 -0.166240198 0.188395173 -0.038489018 0.02482370
## 28 0.196897594 0.234782188 0.110252021 -0.041060202 0.141258740 -0.32628433
## 29 0.421587994 0.118835403 0.305620715 -0.099846519 0.208524889 -0.14463319
## 30 -0.009302721 -0.058229090 0.079113402 -0.151699920 0.202495657 -0.08300807
## 31 -0.177633108 -0.031743654 -0.041439735 -0.140365559 -0.036010456 -0.18243789
## 32 0.205409152 0.191604525 -0.141474447 -0.054579730 0.008040158 0.05754339
## 33 0.008226966 0.208030587 0.149147135 -0.172134356 0.135320503 0.02130081
## 34 0.312956055 0.162088598 -0.125369421 0.013521253 -0.065070596 -0.11979025
## 35 0.264512217 0.223992775 -0.435382803 0.112936301 0.083849778 -0.04652766
## 36 -0.027824772 0.092274228 -0.327703849 -0.078961006 0.068275335 0.03289788
## 37 0.016183720 0.316431956 -0.392738667 0.051253154 0.021953563 0.11550571
## 38 -0.458017323 -0.230280095 -0.047613826 -0.053488937 0.063512513 0.03129361
## 39 -0.311094921 -0.105368514 -0.249237716 -0.067490190 0.063178838 -0.25061363
## 40 -0.414536308 0.112183606 -0.095507102 -0.165839771 -0.154670110 0.09171669
## 41 -0.477835885 -0.018642421 -0.060820510 -0.184988555 -0.081318549 0.06911550
## 42 -0.526855511 0.019085981 -0.124548101 -0.156244757 -0.072060578 0.02227910
## 43 -0.421784721 -0.347740029 -0.054249960 0.111664813 0.124847907 -0.04252694
## 44 -0.496668283 -0.472265941 -0.017533282 0.363355616 0.295294190 0.08036815
## 45 -0.411617255 0.147025739 -0.060863587 -0.106046792 0.078253378 -0.04681688
## 46 -0.147972303 0.152402083 -0.292129022 -0.037564627 -0.010626511 -0.04209114
## 47 -0.059396147 0.422482800 -0.363724173 0.032699346 -0.021440171 0.06018240
## 48 -0.540357634 -0.019577661 -0.227248515 0.068413003 -0.064988499 0.03087487
## 49 -0.103779359 0.421322375 0.011131249 -0.084039038 -0.046883869 -0.06674867
## 50 -0.374998473 0.082845872 0.096635202 -0.135005680 -0.112409494 0.10430752
## 51 -0.457882308 0.194328933 -0.002301925 -0.092323183 -0.034599072 -0.06958501
## 52 -0.520380836 0.050588718 -0.089262342 0.004906471 0.072706620 -0.04358735
## 53 -0.452455480 0.169000417 0.068782608 0.065289195 -0.132036073 -0.07522844
## 54 -0.555004826 0.067191946 0.128956265 -0.175519992 0.049194077 0.16125106
## 55 -0.379842520 0.165447433 -0.103778345 -0.174888630 -0.088650571 -0.10147860
## 56 -0.577115324 -0.040132955 0.149994387 0.006154776 -0.051880100 0.07292502
## 57 -0.535724762 -0.070762288 -0.109142545 0.170910085 0.561454633 0.10546998
## 58 -0.349421103 0.343568476 -0.221171854 -0.097188293 0.006148163 0.06623027
## 59 -0.569563891 -0.454176975 -0.002932557 0.318294201 0.184176662 -0.05703861
## 60 -0.475931334 0.062643143 0.022690473 -0.118532626 -0.051440357 0.06652905
## 61 -0.351111983 0.276409674 0.324110966 0.008842665 -0.026062892 0.16970214
## 62 -0.062102525 0.435917916 0.507168325 -0.037231831 0.244367271 0.27667297
## 63 -0.134804460 0.114873983 0.233289844 0.124305709 -0.110676437 -0.15028214
## 64 -0.417100776 0.147390907 0.227304817 0.187682188 -0.140213429 0.03178561
## 65 -0.261469224 -0.005878805 0.233424650 0.504731310 -0.169850465 -0.08177118
## 66 -0.103105531 0.340214098 0.237501878 0.199192965 -0.129160880 -0.07185010
## 67 -0.641978437 -0.473517641 -0.038747654 -0.013507009 -0.029761513 0.06843047
## 68 -0.250539755 -0.039504714 0.307659441 0.189967645 -0.300772626 -0.00219446
## 69 0.059739523 0.042395505 0.013737233 0.327360181 -0.019588367 -0.20136385
## 70 -0.327547127 0.173388449 0.130845880 0.252042971 -0.132197039 -0.10714025
## Axis.7 Axis.8 Axis.9 Axis.10 Axis.11
## 1 0.054979690 -0.1259798298 -0.038388402 0.0416029181 -0.003343086
## 2 -0.013772704 0.0424759853 -0.023242740 0.0142629726 0.053781054
## 3 0.011569809 0.0487209775 -0.026872719 0.0155367809 0.066889828
## 4 0.149518923 0.0082899082 -0.072465166 0.0027443926 0.108237651
## 5 -0.163909150 0.1002439832 -0.001393597 -0.1092631607 0.180358560
## 6 0.031834849 -0.0230837010 0.071516621 -0.0012109434 0.093347455
## 7 0.014793181 -0.1081213875 0.006970952 -0.0972433509 0.008375110
## 8 -0.146234433 0.1232853527 0.077095965 0.1271726643 0.053170849
## 9 -0.124276773 -0.0543478847 0.107500472 0.1871654922 -0.067217056
## 10 -0.002018798 0.0427695962 -0.118563815 0.0462900431 -0.055493791
## 11 -0.050546611 0.1797122146 -0.006052679 -0.0122751784 0.127062487
## 12 -0.051450504 -0.0985123481 -0.106546735 -0.0031404745 0.023612699
## 13 -0.149360160 -0.0114240488 -0.074643603 0.1139616947 0.124733237
## 14 0.137455955 0.1771412930 0.001755198 -0.0002730352 -0.117938414
## 15 -0.005111966 0.1339553719 -0.026358135 -0.0470726142 -0.139668556
## 16 -0.179283676 -0.1143665801 -0.079927663 0.1696727226 -0.061972235
## 17 -0.098459396 -0.0943549245 0.021270966 -0.0725845230 -0.090125685
## 18 0.211932781 0.0254476001 -0.024196119 -0.0860041122 -0.038021355
## 19 0.059585480 -0.0006793380 0.076005861 0.0087134149 -0.159833033
## 20 -0.033432873 0.1793374186 0.058011000 0.1186598197 -0.149502079
## 21 -0.051116783 -0.2097074081 0.088113698 -0.0324457386 -0.003899276
## 22 -0.006819811 -0.0439374076 -0.049141951 -0.0911331199 -0.007124479
## 23 0.153258923 -0.1054977932 0.153647302 0.0873371291 0.040112862
## 24 -0.090440201 -0.1245755252 -0.056912009 -0.0516696004 0.015033932
## 25 -0.145680117 -0.0336613586 0.054221475 -0.2319031504 0.007034901
## 26 -0.016058442 -0.0116438487 -0.039825838 -0.0325677863 0.095929468
## 27 -0.073027893 0.1183113984 -0.100232251 0.0374415826 -0.063618254
## 28 -0.061258900 0.0634346364 0.003413527 -0.0064311681 -0.012612001
## 29 0.168378760 0.0261114845 -0.010076647 -0.1954983867 -0.063165381
## 30 0.201627200 0.0918935222 0.006844985 0.1355824594 -0.073197434
## 31 0.105334433 -0.0413408787 -0.013162531 -0.1551350458 -0.004087350
## 32 0.048916610 -0.0274920479 0.152668370 0.1246760627 0.073120512
## 33 0.229288869 0.0983781577 -0.009600415 -0.0805465316 -0.002913514
## 34 -0.054478868 -0.0026304894 0.144344969 -0.0650447663 0.009368832
## 35 0.150479695 -0.1078446792 -0.103303802 -0.0327024027 -0.028222449
## 36 0.088755708 -0.1323677937 -0.052061228 0.0413269157 0.050078439
## 37 0.109922197 -0.1350301284 0.009319563 -0.0211761074 -0.045178157
## 38 0.196889490 0.0239558002 0.050481487 0.0734082622 0.060643762
## 39 -0.137354105 0.1229745346 -0.054003032 -0.0989478988 -0.113107163
## 40 -0.043769785 -0.0292884844 0.095585470 -0.0914004885 0.003912074
## 41 0.053564940 0.0694142397 -0.032623657 -0.0964475885 0.027341540
## 42 -0.119494712 0.0368513256 -0.052701512 0.0040413750 0.022440629
## 43 0.175127167 -0.1120364171 0.075237982 0.1333128325 0.049235854
## 44 -0.071150065 -0.0007002596 0.339956513 -0.0473190064 0.017139112
## 45 0.053744586 0.1090509070 0.024947135 0.0195849462 -0.020556711
## 46 0.111543767 -0.1338339995 -0.036350496 0.1302375527 0.046500041
## 47 -0.103466859 -0.0289057423 0.023898507 -0.0095084652 0.011134728
## 48 -0.041464580 0.1508344704 -0.019512061 -0.1239059035 -0.013651658
## 49 0.032783637 0.0568739426 0.234081670 0.0888618090 -0.034706009
## 50 -0.083648566 -0.0534891586 -0.044797312 -0.0381473572 0.041772326
## 51 -0.060893303 -0.0107780319 -0.077948348 0.1063037716 0.021821591
## 52 0.047538862 0.1001280449 -0.014901675 -0.0261195396 0.134841333
## 53 -0.014301516 -0.0081772429 -0.011935959 0.0064219620 0.045795454
## 54 -0.100444424 -0.0304592644 -0.021749289 0.0388418562 -0.058753685
## 55 -0.094205657 0.0757014184 0.129503314 0.0659212523 -0.097470701
## 56 -0.157392732 -0.1150222659 0.025971435 -0.0083061667 -0.048830224
## 57 -0.206113955 0.1206099899 -0.254283898 0.1368673802 -0.010273229
## 58 -0.117188568 0.1068084565 0.031439021 -0.0480701935 0.043925961
## 59 -0.020235949 -0.0781189775 0.076688475 -0.1240166048 -0.032437350
## 60 -0.061703906 -0.0419688609 -0.066995799 -0.0129099288 0.102440109
## 61 0.027713475 -0.0100958081 -0.115194257 -0.0544700755 -0.079657841
## 62 -0.039775488 -0.0950793695 0.033826038 0.0016214222 0.141246681
## 63 0.217789267 -0.0336927708 -0.113982235 0.1210213701 -0.084367040
## 64 -0.078221810 0.0122938516 0.007016610 0.0218941720 -0.058225073
## 65 -0.011806064 0.0026497544 0.049509607 -0.0619555495 -0.087247318
## 66 -0.071722739 0.0223785593 0.035953419 0.1017211984 -0.035936948
## 67 0.001160322 -0.1628278152 -0.115069960 -0.0881969614 -0.096911371
## 68 0.030564329 -0.1753016469 -0.104511592 0.0521954334 -0.017223454
## 69 0.214509235 0.2388983869 -0.039636129 0.0258853614 0.140137016
## 70 0.060530698 0.0174429339 -0.057632349 -0.0452460983 0.035913270
## Axis.12 Axis.13 Axis.14 Axis.15 Axis.16
## 1 -0.110681911 -0.011045953 -0.0143687288 0.0079825796 0.0241099789
## 2 0.023069872 -0.081317893 -0.0266120930 0.0226698395 0.0719038273
## 3 -0.077773222 0.033308708 -0.0283338720 0.0267315712 -0.0127746261
## 4 -0.075938167 -0.053293673 0.0244658272 -0.0326340920 0.0339536617
## 5 -0.041071137 0.164515099 -0.0594547449 -0.0207568133 -0.0826374492
## 6 -0.185673332 0.089457954 -0.0085475005 0.0542603232 -0.0409483579
## 7 -0.085801770 -0.038865240 0.0141818148 0.0423703885 -0.0080447997
## 8 -0.004066936 0.066459189 0.0262256033 0.0612070960 -0.0275915600
## 9 -0.030443746 -0.053677400 -0.0072257576 0.0366395855 -0.0397572555
## 10 -0.099515839 0.079048313 0.0416959754 0.0172507049 0.0814299884
## 11 -0.012171578 -0.014843432 -0.1379814582 -0.0312880402 -0.0413558844
## 12 -0.002046185 0.022188461 -0.0204560588 0.0551185940 0.0512186249
## 13 0.068098539 -0.056179799 0.0909004579 0.1046258321 -0.0017734530
## 14 -0.059111344 0.021867551 0.0803926922 -0.0876316722 0.0542560583
## 15 0.045801510 -0.088166986 0.0928434839 -0.2019252101 -0.0163125991
## 16 0.014300846 -0.021868864 -0.0522306660 0.0081884716 0.0812231920
## 17 0.028771164 0.071658071 0.0021089068 0.0206881839 -0.0314864586
## 18 0.030726547 0.012264276 0.0293283220 -0.0382539780 0.0439208048
## 19 -0.085603786 -0.023819321 -0.0291961284 0.0044453546 -0.0152077305
## 20 0.123535092 -0.134428794 0.0215807107 -0.0395596539 -0.0502173529
## 21 0.018151588 -0.029190820 -0.0245242151 0.0537191247 0.0596366183
## 22 0.140126583 0.005291937 0.0839636565 -0.0106682225 -0.0278820591
## 23 0.031711528 0.095810923 -0.0034786776 -0.1027400186 -0.0449714002
## 24 0.027819338 -0.181670115 0.0065002083 0.0976257454 -0.1236277050
## 25 -0.024821202 0.098264755 -0.1177909307 -0.0425812286 -0.0040741126
## 26 0.127161655 0.029268110 0.0388809399 -0.0707441743 -0.0379741011
## 27 0.052334086 -0.037429824 -0.0599071300 0.0761656200 0.1010558734
## 28 -0.092961163 -0.181967202 -0.0270398763 -0.0919897718 0.0575604444
## 29 0.093687768 0.020294764 0.0577503466 0.0838798983 -0.0017052840
## 30 -0.024713583 -0.002694932 -0.0223308284 0.0908275233 -0.0374814190
## 31 -0.100524831 -0.078004085 0.0465755459 -0.0165638415 0.0557950946
## 32 0.070699632 0.089570673 -0.0174431879 -0.2154265746 -0.0926176365
## 33 0.059226667 -0.014497544 -0.0427052434 0.0778643971 -0.0213468354
## 34 -0.018441513 -0.019694187 0.0806471630 -0.1137315673 0.0172014231
## 35 0.027638380 0.052405275 -0.1003719731 -0.0523477350 -0.0003811319
## 36 -0.097975258 -0.030667144 0.0043216189 0.0049461448 -0.1159265467
## 37 -0.028584717 -0.041617091 -0.0357896180 -0.0188914570 0.0182962223
## 38 0.127957150 -0.048227349 0.0519499617 0.0726603498 -0.0341254867
## 39 0.028102493 0.077257923 0.0310572946 0.0008312879 -0.0051799519
## 40 0.075825576 0.016032704 -0.0632337456 0.0291392535 0.0763029125
## 41 0.111756752 0.033667256 -0.0311763256 0.0441776645 0.0644633823
## 42 0.036429088 -0.033751529 -0.0363677386 0.0322966729 0.0545030717
## 43 0.129774163 -0.036491377 -0.0557499806 0.0137069233 -0.0401607946
## 44 0.070104777 -0.062094775 -0.0433794081 0.0182616684 0.0380731199
## 45 -0.126003120 0.037891873 0.0002582049 0.0226782908 0.0553078302
## 46 0.004263033 0.046322858 0.0239659977 -0.0399926660 0.0541260538
## 47 -0.001659923 0.020460426 0.0259287483 -0.0094058501 -0.0110036751
## 48 -0.032709107 -0.087265899 -0.0198575662 0.0495634437 -0.0629143634
## 49 -0.058900987 -0.012472448 -0.1098073595 0.0685156001 0.0598695786
## 50 0.115631566 -0.051108736 -0.0584228139 -0.0408385396 0.1628695158
## 51 -0.072780179 -0.007092176 0.0313132878 -0.0185868329 -0.0094136521
## 52 -0.152294360 -0.097327163 0.0426185297 -0.0081616694 0.0191540974
## 53 -0.104341064 -0.093331568 -0.1189367774 -0.0703678560 -0.0242693060
## 54 -0.014377757 0.072591511 0.0435498741 0.0597984421 -0.0900892337
## 55 0.035026367 0.184795940 0.0084732982 0.0778422349 0.0483353160
## 56 -0.032990865 0.013332000 0.0418194839 -0.0287690453 -0.0155565347
## 57 0.004194121 0.076674704 -0.0565545580 -0.1131544969 0.0163298509
## 58 0.051700255 -0.022221390 0.0554465303 0.0664377252 -0.0808606455
## 59 -0.103406549 0.081667633 0.1075354327 -0.0030932673 0.0682957346
## 60 0.075581566 -0.001611872 0.1893893068 -0.0188132653 -0.0348104271
## 61 0.017502992 -0.035358820 -0.1216866911 0.0366535888 -0.1530463112
## 62 0.015546112 -0.037291029 0.1435086796 0.0009765413 0.0994535383
## 63 -0.045037400 0.099492146 0.0596002140 0.0400234622 -0.0094934135
## 64 -0.022047639 -0.017287396 -0.0062949148 -0.0078039177 -0.0521778649
## 65 -0.003098698 0.004050166 0.0114296984 -0.0327366085 -0.0463902317
## 66 -0.039717775 -0.010170666 0.1166417496 0.0374516421 -0.0074743343
## 67 0.024153473 0.087405631 0.0009171793 0.0301721125 -0.0522177596
## 68 0.111865185 0.014185271 -0.1180893744 -0.0617751275 0.0557352790
## 69 0.073734060 0.091752652 -0.0219694431 0.0390492904 0.0446419102
## 70 -0.024722882 -0.061210264 -0.0304513591 -0.0462099789 -0.0637432588
## Axis.17 Axis.18 Axis.19 Axis.20 Axis.21
## 1 0.1456382325 -0.020901790 9.674368e-02 0.0870975056 -9.637297e-02
## 2 -0.0124733490 0.043376108 -2.727828e-02 0.0403973485 1.100675e-01
## 3 -0.0464678390 0.037778081 -7.583428e-02 -0.0642431152 5.495810e-02
## 4 -0.0519271696 0.098510329 -2.681726e-03 0.0026836134 1.733641e-02
## 5 0.0833144865 -0.025803572 -8.458268e-03 -0.0005495176 -4.575199e-02
## 6 -0.0497598527 0.050639841 1.499189e-02 -0.1004140334 -9.319535e-03
## 7 -0.0812759804 0.061605210 -2.118716e-02 -0.0542437757 5.122670e-02
## 8 -0.0163084099 -0.076890124 -1.391162e-02 -0.0646313186 5.576417e-02
## 9 -0.0233632665 -0.004852586 1.059609e-02 0.0157394381 -5.054585e-02
## 10 -0.0534031812 0.001314603 2.073294e-02 0.0275422690 6.973359e-03
## 11 0.0525447737 -0.041764439 2.956717e-05 0.0191515200 1.331754e-02
## 12 -0.0208906704 0.029038591 1.676862e-02 0.0008119271 -4.611191e-02
## 13 -0.0938237905 -0.032553245 1.287237e-01 -0.0117765005 -1.001255e-01
## 14 -0.0401989312 -0.039743814 4.465570e-02 0.0172717046 2.222420e-02
## 15 -0.0349053822 -0.025640048 3.008143e-04 0.0249648290 3.878325e-02
## 16 0.0050710435 0.033032460 -2.811728e-02 0.0718797313 -6.867173e-03
## 17 -0.0017577951 -0.056925167 -1.132138e-01 -0.0515443614 -5.719464e-02
## 18 -0.0493068893 0.030978770 -1.696447e-02 -0.0250514561 -3.551161e-02
## 19 0.1046646594 0.052207447 5.609506e-02 -0.0314716404 -1.215348e-01
## 20 0.0350952229 -0.095960338 5.680576e-03 -0.0214747161 2.500358e-02
## 21 0.0553104520 0.057755124 1.215887e-02 0.1044506490 4.004886e-02
## 22 0.0006623028 0.011511928 -7.070360e-02 0.0845345986 -6.844238e-02
## 23 -0.0746764903 0.033409411 -1.176782e-02 -0.0159792892 -7.584224e-03
## 24 -0.0627715717 0.009966023 1.587759e-02 -0.0240554811 1.011006e-01
## 25 0.0955945734 -0.008384812 2.671743e-02 -0.0084945848 5.837061e-02
## 26 -0.0087090209 -0.026850354 2.910935e-02 0.0339621716 -2.444727e-02
## 27 0.1116226136 -0.015536509 -8.273959e-02 0.0011804383 -4.410336e-03
## 28 0.0019270743 -0.005476935 2.779431e-02 -0.0504395321 5.614761e-02
## 29 -0.0555162897 -0.052117008 -5.692147e-02 -0.0196729895 -4.552761e-02
## 30 0.1083219890 0.079937991 -7.797664e-03 0.0036153124 4.241026e-03
## 31 -0.0210203153 0.021252772 1.766589e-02 0.0294281270 -2.602886e-02
## 32 -0.0607819660 0.040943928 -2.843305e-02 -0.0094659260 -4.601792e-02
## 33 0.0045373109 0.067389722 -2.319957e-02 -0.0034037391 2.076090e-02
## 34 0.0368734257 0.071470037 3.443703e-02 0.0824718564 3.117178e-02
## 35 0.0371702856 -0.098710408 7.431323e-02 -0.0376516222 6.491082e-02
## 36 0.0933149922 -0.040027136 -4.465444e-02 0.0241852246 4.020198e-02
## 37 -0.0279709564 -0.021500230 -2.957365e-02 -0.0346951700 -3.805964e-03
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## 39 0.0284423229 0.059594153 1.160889e-02 -0.0859147631 -4.960028e-02
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## 54 -0.0328707243 0.002347393 -8.012554e-02 0.0883252354 9.331706e-03
## 55 -0.0484887994 -0.005276396 9.941347e-02 0.0361611022 6.189897e-02
## 56 0.0517700741 0.010802576 -3.645885e-02 -0.0009123045 6.037057e-03
## 57 -0.0395791660 0.053748584 2.946709e-02 -0.0300215283 5.607730e-03
## 58 0.0001176404 0.082635361 7.826619e-02 0.0270434193 5.502414e-02
## 59 0.0038324723 -0.037320361 3.703481e-02 -0.0154898388 -3.500361e-03
## 60 0.1137277250 -0.014767457 1.561514e-02 -0.0265594630 3.291779e-02
## 61 -0.0951175525 0.042426940 6.911839e-02 0.0515500430 -3.085042e-02
## 62 0.0089725872 -0.070216513 1.281842e-02 -0.0094503827 3.716633e-02
## 63 0.0209640183 -0.019030209 9.329783e-02 -0.0476428722 5.604272e-02
## 64 0.0515301184 0.057439040 -7.125371e-02 0.0144992628 1.912438e-03
## 65 0.0175077373 0.052011376 -2.425524e-02 -0.0053238447 -8.402267e-05
## 66 0.0006241893 0.062492289 -6.235889e-02 -0.0400704707 -4.015490e-03
## 67 -0.0999975705 -0.136561831 4.218747e-03 0.0527335325 2.944207e-02
## 68 0.0217427651 -0.046231320 -4.242624e-02 -0.0204847899 2.724055e-02
## 69 -0.0087569996 0.010837335 -1.182085e-02 0.1362221611 1.375847e-02
## 70 0.0581093253 0.019087137 6.625245e-02 -0.0595246707 -1.097167e-02
## Axis.22 Axis.23 Axis.24 Axis.25 Axis.26
## 1 -0.040438790 0.125439145 -0.0158793790 0.0262169979 -0.032543847
## 2 0.024387648 0.052065779 0.0996724163 0.0778077538 -0.018061388
## 3 -0.086269637 -0.004168564 0.0059333937 0.0319543989 0.030626656
## 4 -0.034869674 -0.027382294 -0.0269101345 -0.0378773239 -0.016921288
## 5 0.030036779 0.017268441 -0.0570507358 -0.0483347534 0.036998227
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## 7 -0.026626594 0.023744458 0.0491038626 0.0080658526 -0.042326060
## 8 0.055670770 0.026121291 0.0795813958 -0.0688369706 0.037219596
## 9 0.028711855 0.101320249 0.0075709486 -0.0186710912 -0.036963304
## 10 -0.037428010 -0.071222853 -0.0106918310 0.0120690037 0.062894539
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## 12 0.015282092 -0.068984778 -0.0448919987 0.0111739053 -0.055270619
## 13 0.057862965 -0.041122358 -0.0157497206 0.0525205040 -0.023667241
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## 16 0.062953161 -0.025449487 0.0487586788 -0.0320571196 0.008712794
## 17 -0.065844169 -0.033248458 0.0032921762 0.0293899323 0.010017483
## 18 0.014359120 0.021467721 0.0572970856 0.0096608775 0.031206379
## 19 0.020732901 -0.039225060 -0.0062623818 0.0313303492 -0.003068978
## 20 -0.041895805 -0.002836519 -0.0543506259 0.0420522045 -0.005171203
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## 22 -0.075749328 0.075033764 0.0053072401 0.0131357455 0.066577826
## 23 0.054769278 0.072622241 -0.0522673146 -0.0225822069 0.072173421
## 24 -0.040920527 -0.020185112 -0.0582119418 -0.0335844503 -0.031989594
## 25 0.038694389 0.021979269 0.0043703205 0.0232399786 -0.014549540
## 26 -0.046802676 -0.076040334 0.0061659757 0.0366376061 0.031848755
## 27 -0.066950931 0.018125759 -0.0459701521 -0.0763413162 -0.006922873
## 28 -0.033027601 0.053894472 -0.0136118152 -0.0186692837 0.045289970
## 29 0.035596749 0.041101907 0.0369002804 0.0131349928 -0.018393462
## 30 0.000574700 -0.050649792 0.0448469749 0.0599955591 0.033001055
## 31 0.018808949 -0.029277182 -0.0060642064 -0.0492494512 -0.000744636
## 32 -0.082658736 -0.031005109 0.0192482593 -0.0031248121 -0.074999080
## 33 -0.012704324 0.014495574 -0.0184860075 -0.0228263670 -0.028498236
## 34 -0.052949707 -0.010914719 -0.0013438113 0.0349431552 0.027926227
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## 36 0.085110553 -0.064240287 0.0275202169 -0.0224393346 0.072291953
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## 38 -0.029285505 -0.003169859 -0.0100256145 -0.0330001883 0.002370786
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## 42 0.043757716 0.032100523 -0.0634511186 0.0569057716 0.055658047
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## 44 0.023088835 -0.030036862 -0.0040772600 0.0081787304 0.025915021
## 45 -0.024694763 0.006235557 -0.0726691809 -0.0007567561 -0.044539992
## 46 0.008429598 -0.030943379 0.0074557175 0.0006690425 -0.055852617
## 47 0.100211466 0.049625021 0.0003304394 0.0193240285 -0.019074317
## 48 0.006258276 0.018976399 0.0313634016 -0.0816237730 0.013241165
## 49 -0.019233910 -0.019050685 0.0239066695 0.0072822930 -0.006487026
## 50 -0.010233299 -0.010108650 0.0377406017 -0.0651116988 -0.003898574
## 51 -0.074751459 0.014285158 0.0156977988 -0.0307723783 0.024073411
## 52 -0.012044019 -0.019118957 -0.0002444917 0.0269709743 -0.013376911
## 53 -0.013271391 -0.028553139 0.0191524295 0.0473963414 0.008459835
## 54 0.022151144 -0.028516945 -0.0073250495 0.0149849351 -0.008001277
## 55 -0.092169655 -0.020978271 0.0142256494 -0.0537558984 -0.024583900
## 56 -0.003534186 -0.033763089 0.0275567374 -0.0077100766 -0.004994291
## 57 -0.001567351 0.041151180 -0.0049713337 0.0179639307 0.006567013
## 58 -0.009633274 0.046536452 -0.0275773624 0.0561740808 0.012139881
## 59 -0.004593441 -0.018482965 -0.0007014041 -0.0091956304 0.012275173
## 60 -0.003909064 -0.013973943 0.0578358560 -0.0310650176 -0.036089210
## 61 -0.030654312 0.003009323 0.0307571021 -0.0417347298 0.033439548
## 62 -0.039770554 0.041403620 -0.0038409700 0.0020715501 0.004420062
## 63 0.024598141 -0.027629067 -0.0415701289 -0.0052244439 0.019515687
## 64 -0.021989961 0.015417525 -0.0112320353 -0.0109183137 -0.024856001
## 65 0.017642506 0.005680885 0.0085821287 0.0145294451 -0.071757676
## 66 0.062371139 0.022188952 -0.0158903073 0.0332440661 -0.003534504
## 67 -0.020347562 0.010346666 -0.0153019275 0.0218580579 -0.012637531
## 68 0.008436941 0.014104598 -0.0236966750 0.0194280894 0.026667414
## 69 0.053653426 0.029991254 0.0006474882 -0.0149502523 -0.023683592
## 70 -0.021546320 -0.006824151 0.0228603599 0.0204461225 0.023800278
## Axis.27 Axis.28 Axis.29 Axis.30 Axis.31
## 1 -0.0214489348 -0.0062493017 0.0005904075 -0.0098185124 -0.0002576620
## 2 -0.0018257707 0.0007192033 -0.0060382759 0.0252139281 -0.0449648727
## 3 -0.0230905950 0.0459988987 -0.0145453326 -0.0069991267 -0.0133689950
## 4 0.0106510843 -0.0582517939 -0.0183645997 0.0121981876 0.0358175465
## 5 0.0310533762 -0.0017150785 0.0514465327 0.0714369118 0.0151264400
## 6 -0.0413952413 0.0277986881 -0.0127963105 -0.0132924710 -0.0249466938
## 7 -0.0434234759 0.0126047551 0.0038049668 -0.0052145017 0.0632259337
## 8 -0.0280980176 -0.0175207970 -0.0059972747 0.0092652975 0.0039279369
## 9 0.0150038615 0.0522817116 0.0082975396 -0.0177932521 0.0210459397
## 10 0.0550203506 -0.0064864577 -0.0035575446 -0.0108387469 -0.0185434607
## 11 -0.0042753709 -0.0150529779 0.0670866905 -0.0080975105 -0.0337201840
## 12 -0.0312721604 -0.0037783797 0.0222792189 -0.0351956927 -0.0423692092
## 13 0.0177882370 0.0133480681 -0.0052239919 -0.0208074324 0.0132163250
## 14 -0.0358830147 -0.0279213051 0.0014769046 0.0004334194 0.0043077515
## 15 -0.0248318804 -0.0092380051 -0.0177418509 0.0128708998 -0.0061136295
## 16 -0.0252088165 -0.0271021422 0.0467064640 0.0190021463 0.0224382992
## 17 -0.0377047263 -0.0591888106 0.0013912891 -0.0192558738 -0.0215036364
## 18 0.1110065546 0.0204471578 0.0266087892 -0.0486169465 -0.0003625703
## 19 -0.0117987667 -0.0257447959 -0.0667356492 0.0217256780 -0.0203420725
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## 25 0.0476790031 -0.0143709167 -0.0707650961 -0.0476826989 0.0238758739
## 26 -0.0134611769 0.0318026261 -0.0305535669 0.0055644150 0.0050692293
## 27 0.0369995086 0.0053703578 -0.0110926849 -0.0105625149 0.0592820566
## 28 -0.0038029798 0.0070580280 -0.0011800054 -0.0161664275 0.0166779299
## 29 -0.0100094651 0.0162433440 -0.0041247438 0.0218673099 0.0241213008
## 30 0.0327289508 -0.0516424466 -0.0059136579 0.0397235717 0.0147868792
## 31 0.0135065688 0.0376298489 0.0017446882 0.0222509850 -0.0088253457
## 32 -0.0033455770 -0.0008101316 -0.0488419005 0.0089879326 0.0373315002
## 33 -0.0255530572 0.0731260724 0.0324018886 -0.0052977609 -0.0332144234
## 34 -0.0530728067 -0.0042314954 0.0714480322 0.0134570285 0.0166931185
## 35 0.0109757721 -0.0284798781 -0.0017207441 0.0628434968 -0.0235285119
## 36 -0.0034083605 0.0628324835 -0.0282645754 0.0116761180 0.0211710294
## 37 0.0034393932 -0.0111674618 0.0305521344 -0.0364791504 0.0019428642
## 38 -0.0315624396 -0.0168141537 0.0129373373 -0.0240528204 0.0034672596
## 39 0.0097854651 0.0279607816 0.0089584803 -0.0100916690 -0.0061073178
## 40 -0.0352206447 0.0206039473 -0.0062121194 -0.0173187156 -0.0036841251
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## 46 0.0121643678 -0.0127435487 0.0193114085 0.0023655311 -0.0030121056
## 47 0.0026465175 0.0323911632 0.0150391106 0.0080151446 -0.0197120488
## 48 -0.0484105081 -0.0726902697 -0.0197390565 -0.0362241219 -0.0239513142
## 49 -0.0134510101 -0.0128910977 -0.0104135389 0.0097521029 -0.0045581559
## 50 0.0167054437 0.0199320911 -0.0193070994 0.0546327629 -0.0190375608
## 51 0.0252331870 -0.0009875097 0.0034476035 -0.0081223988 -0.0299794563
## 52 0.0294332679 0.0130384055 -0.0030962415 0.0223830028 0.0030494214
## 53 0.0042006345 -0.0007718911 0.0056639463 -0.0227457598 0.0132682296
## 54 0.0024225437 0.0258593133 -0.0228528265 0.0021265663 -0.0019810891
## 55 0.0254698968 0.0065970763 0.0113244053 0.0054839764 -0.0103950787
## 56 0.0174164770 0.0240398402 -0.0119526633 -0.0054691526 -0.0177730547
## 57 -0.0297689604 0.0238298835 -0.0151576827 -0.0136784538 0.0025749689
## 58 0.0289761364 -0.0400599929 -0.0009706409 0.0035309994 0.0094606071
## 59 0.0132983773 -0.0010944863 0.0030521686 0.0138627378 -0.0204883760
## 60 -0.0049639073 -0.0309751304 0.0028734066 -0.0557648928 -0.0056917335
## 61 -0.0160031598 0.0167434304 0.0053205537 0.0087701552 0.0197227818
## 62 0.0032113281 0.0030168213 -0.0162370868 0.0221897116 0.0092914700
## 63 -0.0437055098 0.0212661966 -0.0028278305 0.0199058418 0.0151101158
## 64 0.0171760139 0.0077014306 0.0016350446 0.0014059253 -0.0046139875
## 65 0.0232413040 -0.0133783814 0.0348026147 0.0096684387 -0.0058536784
## 66 0.0071036630 -0.0195644072 -0.0129221615 0.0263891796 0.0127991543
## 67 0.0167799078 -0.0236396424 0.0248162406 -0.0042188572 0.0440954317
## 68 -0.0193685409 0.0037146733 -0.0322523694 0.0004210092 -0.0242485474
## 69 -0.0053493050 0.0009760003 -0.0671527188 -0.0321081413 -0.0062049494
## 70 -0.0004065372 0.0056111297 0.0300030748 -0.0234506602 0.0121713013
## Axis.32 Axis.33 Axis.34 Axis.35
## 1 -3.510752e-02 0.0330537797 0.0064130595 -3.099937e-03
## 2 7.282958e-03 0.0084330757 0.0124690915 -6.786092e-03
## 3 -1.217735e-02 -0.0092968600 0.0134000578 2.125948e-02
## 4 5.574305e-02 0.0149621804 -0.0117199065 -4.489755e-03
## 5 1.324568e-02 -0.0075264555 -0.0034528252 -1.647750e-03
## 6 9.055993e-03 -0.0126035392 0.0155388726 -7.666602e-03
## 7 1.212234e-03 0.0127056432 -0.0056336788 -1.394855e-02
## 8 -4.594964e-02 0.0173325658 -0.0015677204 1.062034e-02
## 9 1.638890e-02 -0.0119287062 -0.0338301707 4.068784e-04
## 10 -1.801940e-02 -0.0020138441 -0.0314317463 -1.322075e-03
## 11 2.123204e-02 -0.0213312551 -0.0114671193 -9.854437e-03
## 12 1.249415e-02 0.0390694185 0.0071184506 2.401359e-02
## 13 -5.987312e-03 -0.0101920667 0.0049739037 1.566912e-03
## 14 2.980406e-03 0.0174372896 0.0066029480 -1.843012e-02
## 15 -7.454551e-03 0.0050672473 0.0238078426 1.283033e-03
## 16 -4.664383e-03 -0.0412186706 0.0415721350 3.950347e-05
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## 20 3.450014e-02 0.0144161544 -0.0025490666 8.333917e-03
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## 22 2.470002e-02 -0.0082942666 0.0067085986 5.809050e-03
## 23 -1.383753e-02 0.0324447828 -0.0032135908 -2.392182e-03
## 24 -3.801842e-02 -0.0131890589 -0.0017748227 -9.571190e-03
## 25 1.414439e-02 -0.0041638583 0.0147097953 9.891806e-03
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## 30 -8.585959e-05 0.0191575625 -0.0193990584 8.605473e-03
## 31 -5.624822e-03 -0.0002089641 -0.0075711978 5.410577e-04
## 32 -1.120639e-02 -0.0190568202 0.0057916623 9.588107e-03
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## 46 5.291376e-03 -0.0026911453 -0.0067170862 -4.111421e-03
## 47 2.065112e-02 0.0001675641 -0.0251276297 -1.554287e-02
## 48 -1.597797e-03 -0.0082973070 -0.0264576803 1.451270e-02
## 49 1.245360e-02 0.0065924763 0.0073839142 6.417907e-03
## 50 -3.272533e-03 0.0177346351 -0.0087642293 5.738138e-03
## 51 2.984018e-02 -0.0042623257 0.0285669454 -5.221643e-03
## 52 -1.579617e-02 0.0086392722 0.0179429757 -1.226834e-03
## 53 -1.499405e-02 0.0043424790 -0.0049312717 -1.843771e-04
## 54 -1.397514e-02 0.0082247936 0.0002817281 -1.785904e-03
## 55 2.566738e-02 0.0054366397 0.0057942811 -7.943804e-03
## 56 -1.199141e-02 0.0013465563 -0.0034659503 -1.493599e-03
## 57 -4.490482e-03 0.0043205427 -0.0093614018 8.452111e-04
## 58 -7.178215e-03 0.0027775535 0.0311719961 1.310182e-04
## 59 1.609972e-03 -0.0105622044 0.0085364730 2.390268e-03
## 60 -2.523931e-03 -0.0067345871 -0.0232747076 2.962267e-03
## 61 7.867086e-04 0.0127251920 0.0048373495 5.676931e-05
## 62 1.834353e-02 -0.0027708817 0.0063045039 5.620415e-03
## 63 -3.018902e-03 -0.0121693026 -0.0005458156 5.555145e-03
## 64 -1.863758e-02 -0.0067412687 -0.0086869155 -1.096419e-02
## 65 2.374383e-02 0.0394753730 0.0119960228 1.590973e-02
## 66 -4.393773e-03 -0.0058721577 -0.0106343099 2.647808e-03
## 67 1.203905e-02 -0.0288067193 -0.0066613416 6.225101e-03
## 68 -3.970740e-03 -0.0193941859 -0.0080688470 -7.618608e-03
## 69 1.967131e-03 -0.0121338719 0.0014419782 -4.158236e-03
## 70 -3.056504e-03 -0.0006255353 0.0128961404 -1.171213e-02
##
## $trace
## [1] 27.20504
##
## attr(,"class")
## [1] "pcoa"biplot.pcoa(mite.spe.h.pcoa, mite.spe.hel, dir.axis2 = -1)
Les espèces 16 et 31 sont plus éloignées des autres espèces en termes de distance, et donc leur distribution entre les sites est très différente de celle des autres espèces d’acariens. Les sites dont les étiquettes se chevauchent sont de bons exemples de sites à forte similarité en termes de communautés d’acariens.