Last data update: 2014.03.03

 R: Functional Dispersion
fdispR Documentation

Functional Dispersion

Description

fdisp measures the functional dispersion (FDis) of a set of communities, as described by Laliberté and Legendre (2010).

Usage

fdisp(d, a, tol = 1e-07)

Arguments

d

a species-by- species distance matrix computed from functional traits, such as that returned by dist or gowdis. NAs are not allowed.

a

matrix containing the abundances of the species in d (or presence-absence, i.e. 0 or 1). Rows are sites and species are columns. Can be missing, in which case fdisp assumes that there is only one community with equal abundances of all species. NAs will be replaced by 0. The number of species (columns) in a must match the number of species in d. In addition, the species labels in a and d must be identical and in the same order.

tol

tolerance threshold to test whether the distance matrix is Euclidean : an eigenvalue is considered positive if it is larger than -tol*lambda1, where lambda1 is the largest eigenvalue.

Details

fdisp computes, for a set of communities, the average distance of individual objects (species) in PCoA space from any distance or dissimilarity measure, as described by Anderson (2006). The average distance to the centroid is a measure of multivariate dispersion and as been suggested as an index of beta diversity (Anderson et al. 2006). However, in fdisp both the centroid and the average distance to this centroid can be weighted by individual objects. In other words, fdisp returns the weighted average distance to the weighted centroid. This was suggested so that multivariate dispersion could be used as a multidimensional functional diversity (FD) index that can be weighted by species abundances. This FD index has been called functional dispersion (FDis) and is described by Laliberté and Legendre (2010).

In sum, FDis can account for relative abundances by shifting the position of the centroid towards the most abundant species, and then computing a weighted average distance to this new centroid, using again the relative abundances as weights (Laliberté and Legendre 2010). FDis has no upper limit and requires at least two species to be computed. For communities composed of only one species, dbFD returns a FDis value of 0. FDis is by construction unaffected by species richness, it can be computed from any distance or dissimilarity measure (Anderson et al. 2006), it can handle any number and type of traits (including more traits than species), and it is not strongly influenced by outliers.

FDis is conceptually similar to Rao's quadratic entropy Q (Botta-Dukát 2005), and simulations (via simul.dbFD) have shown high positive correlations between the two indices (Laliberté and Legendre 2010). Still, one potential advantage of FDis over Rao's Q is that in the unweighted case (i.e. with presence-absence data), it opens possibilities for formal statistical tests for differences in FD between two or more communities through a distance-based test for homogeneity of multivariate dispersions (Anderson 2006); see betadisper for more details.

Corrections for PCoA axes corresponding to negative eigenvalues are applied following Anderson (2006); see also betadisper for more details on these corrections.

Value

FDis

vector listing the FDis of each community

eig

vector listing the eigenvalues of the PCoA

vectors

matrix containing the PCoA axes

Note

fdisp is implemented in dbFD and is used to compute the functional dispersion (FDis) index.

Author(s)

Etienne Laliberté etiennelaliberte@gmail.com http://www.elaliberte.info

References

Anderson, M. J. (2006) Distance-based tests for homogeneity of multivariate dispersions. Biometrics 62:245-253.

Anderson, M. J., K. E. Ellingsen and B. H. McArdle (2006) Multivariate dispersion as a measure of beta diversity. Ecology Letters 9:683-693.

Botta-Dukát, Z. (2005) Rao's quadratic entropy as a measure of functional diversity based on multiple traits. Journal of Vegetation Science 16:533-540.

Laliberté, E. and P. Legendre (2010) A distance-based framework for measuring functional diversity from multiple traits. Ecology 91299:305.

See Also

dbFD for computing multidimensional FD indices and betadisper from which fdisp borrows some code.

Examples

# dummy dataset
dummy.dist <- gowdis(dummy$trait)
ex1 <- fdisp(dummy.dist, dummy$abun)
ex1

# example with real data from New Zealand short-tussock grasslands
ex2 <- fdisp(gowdis(tussock$trait), tussock$abun)
ex2

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(FD)
Loading required package: ade4
Loading required package: ape
Loading required package: geometry
Loading required package: magic
Loading required package: abind
Loading required package: vegan
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-0

Attaching package: 'vegan'

The following object is masked from 'package:ade4':

    cca

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FD/fdisp.Rd_%03d_medium.png", width=480, height=480)
> ### Name: fdisp
> ### Title: Functional Dispersion
> ### Aliases: fdisp
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> # dummy dataset
> dummy.dist <- gowdis(dummy$trait)
> ex1 <- fdisp(dummy.dist, dummy$abun)
> ex1
$FDis
     com1      com2      com3      com4      com5      com6      com7      com8 
0.3481687 0.1670560 0.2375808 0.1146261 0.3211366 0.3302330 0.2532751 0.2877931 
     com9     com10 
0.3421687 0.3503927 

$eig
[1]  5.160145e-01  4.110861e-01  2.502112e-01  7.199211e-02  9.714451e-17
[6] -6.720081e-03 -7.421501e-02 -9.134555e-02

$vectors
          [,1]         [,2]        [,3]        [,4]        [,5]         [,6]
sp1 -0.0744394  0.105294908 -0.29549376  0.09279042 3.48469e-09 -0.028350201
sp2 -0.3701972  0.173019024 -0.13171354 -0.05961498 3.48469e-09  0.013636749
sp3  0.3001189  0.260331770  0.05048802  0.02657278 3.48469e-09  0.055659664
sp4 -0.2173810 -0.375764768  0.13496986 -0.06100319 3.48469e-09  0.013532869
sp5  0.2744944 -0.257528013  0.02819302  0.13606714 3.48469e-09 -0.012390501
sp6  0.1064444  0.258704692  0.25726275 -0.07593752 3.48469e-09 -0.047385029
sp7  0.2636490 -0.166838689 -0.19044468 -0.15065348 3.48469e-09 -0.001615436
sp8 -0.2826890  0.002781076  0.14673835  0.09177882 3.48469e-09  0.006911885
            [,7]        [,8]
sp1  0.057837857  0.13652367
sp2 -0.152567184 -0.08363815
sp3  0.009587281  0.06980583
sp4 -0.009023747  0.16194188
sp5 -0.127984688 -0.07630909
sp6 -0.017130634  0.02625090
sp7  0.087094877 -0.10013298
sp8  0.152186238 -0.13444206

> 
> # example with real data from New Zealand short-tussock grasslands
> ex2 <- fdisp(gowdis(tussock$trait), tussock$abun)
> ex2
$FDis
      Pen1       Pen2       Pen5       Pen9      Pen10      Pen11      Pen14 
0.15230272 0.14452911 0.15014406 0.18779761 0.20806569 0.17268836 0.14688418 
     Pen17      Pen18      Pen21      Pen22      Pen23      Pen27      Pen28 
0.14048193 0.18741467 0.15390892 0.17210804 0.16873227 0.18329050 0.16166099 
     Pen29      Pen32      Pen33      Pen34      Pen37      Pen40      Pen41 
0.03791758 0.12631495 0.13726383 0.14876799 0.25311748 0.26100304 0.27021023 
     Pen44      Pen45      Pen46      Pen49      Pen52      Pen53      Pen56 
0.14751071 0.16808696 0.20678939 0.19257061 0.17226341 0.20722643 0.16611873 
     Pen57      Pen58 
0.13875782 0.18075597 

$eig
 [1]  1.316856e+00  7.818934e-01  7.572785e-01  4.899976e-01  3.391411e-01
 [6]  3.080247e-01  1.692675e-01  1.346903e-01  1.159174e-01  7.539501e-02
[11]  7.182296e-02  4.952831e-02  4.725919e-02  3.150436e-02  2.571116e-02
[16]  2.095034e-02  1.689031e-02  9.500970e-03  8.429619e-03  4.599555e-03
[21]  3.984182e-03  1.966762e-03  1.110223e-16 -2.929365e-04 -1.476765e-03
[26] -3.051306e-03 -3.630578e-03 -4.499212e-03 -6.630583e-03 -7.262381e-03
[31] -9.407533e-03 -9.962955e-03 -1.134912e-02 -1.329596e-02 -1.598755e-02
[36] -1.623354e-02 -1.913274e-02 -2.171150e-02 -2.251124e-02 -2.539164e-02
[41] -2.976497e-02 -3.179103e-02 -3.767330e-02 -3.973460e-02 -4.450478e-02
[46] -4.756703e-02 -5.216460e-02 -6.365631e-02 -8.368565e-02 -9.048525e-02
[51] -1.052184e-01 -1.070898e-01 -1.352290e-01

$vectors
                  [,1]         [,2]          [,3]         [,4]         [,5]
Achi_mill -0.071208084 -0.105555753  0.0872884104 -0.114520805  0.091633156
Agro_capi  0.035906386  0.095649586 -0.0566558032 -0.173542222  0.070826210
Anth_odor  0.021145998  0.109862430 -0.0534881534  0.016116218 -0.014277349
Apha_arve -0.300202419  0.122911003  0.0043715454  0.066920135  0.091572660
Arre_elat  0.104457319  0.112165139 -0.1405833455 -0.034435566  0.049843989
Brac_bell -0.006001525 -0.057199694  0.0569576739 -0.066705794 -0.063603438
Brom_tect -0.305969937  0.311128972 -0.0303737598 -0.049955135 -0.001655767
Caps_burs -0.531288390 -0.045402984  0.0584892359 -0.094907316  0.038346180
Care_brev  0.232364904  0.026435534 -0.0940462717  0.042247068  0.028129555
Care_muel  0.243870061  0.125298265 -0.1084607147  0.080449505 -0.017686883
Carm_vexi  0.042906543 -0.068085127  0.1015404112  0.246813258 -0.155292209
Celm_grac  0.030907370 -0.018821959  0.0698965824 -0.041821485 -0.077781180
Cera_font -0.002036784 -0.149679918  0.2137561895  0.014890656  0.010867613
Colo_brev -0.032020143  0.130687682  0.2129956216  0.239759670  0.083693184
Copr_petr  0.108794460  0.141109395  0.2355934855 -0.036143971 -0.006296627
Dact_glom  0.004565688  0.133602463 -0.1246888164 -0.012945080 -0.059011376
Elym_falc  0.140147462  0.179275548  0.0230535807 -0.144874526 -0.094286257
Erod_cicu -0.387712334 -0.009438268 -0.0468865429  0.039329581  0.026427068
Fest_nova  0.070476535  0.180651488 -0.0485558988  0.055905860 -0.077173521
Fest_rubr  0.112635420  0.104871434 -0.0846565759 -0.012896980  0.061947204
Gera_sess -0.007289534 -0.062216895  0.0978225167  0.109002133 -0.001460834
Hier_caes  0.015864885 -0.105331546  0.0588614247 -0.178671458 -0.034053943
Hier_pilo  0.022330619 -0.110650623  0.0700564145 -0.176024572 -0.026138583
Hier_prae  0.071325363 -0.093962002  0.0935052122 -0.135157204 -0.066203874
Holc_lana -0.005580889  0.082771084  0.0062886798 -0.233171790 -0.022100371
Leuc_fras  0.095787936 -0.020890666  0.3112419993  0.040070252 -0.093637922
Lotu_corn  0.049082953 -0.146043228 -0.0910501766  0.023976328 -0.023453315
Lupi_poly -0.104354385 -0.123765289 -0.2269860323  0.072383289 -0.181616046
Luzu_rufa  0.104663657  0.061460265 -0.0717088569  0.058856972 -0.059106782
Malv_parv -0.408883686 -0.051684023 -0.0128905132  0.061874042  0.076802440
Medi_sati  0.001517437 -0.178286103 -0.0198532976  0.075890356  0.016265680
Myos_stri -0.338589921  0.027380985  0.0416249784  0.109403711  0.028125733
Oreo_cole  0.041204108 -0.119431552  0.0742538743  0.051084168  0.119191548
Phle_prat -0.047854534  0.119804743 -0.0974094071 -0.009663911 -0.006536951
Pime_oreo -0.010625789  0.006723434  0.1430813195  0.133775583 -0.023718500
Poa_cole   0.089936516  0.179953878 -0.0446780313  0.076346332 -0.074439632
Poa_mani   0.110297455  0.168566232  0.0008756056  0.093644241 -0.058901030
Poa_prat   0.034339236  0.083518812 -0.0951120116 -0.031609168  0.098793232
Pter_veno  0.237293407 -0.178938244 -0.0163352571  0.080246770  0.287367021
Pyrr_exig  0.175242743  0.044879861 -0.0490214783  0.007047887  0.072304119
Raou_hook  0.119936464  0.057550770  0.2918869705 -0.063516819  0.048320174
Raou_subs  0.047807076 -0.015204492  0.2670732582 -0.069219502 -0.050996874
Rume_acet  0.048592960  0.028083379 -0.1435980487 -0.019447111  0.081331236
Sche_phoe  0.029683903  0.086837838 -0.1085573884 -0.028109038  0.097276071
Stac_mini  0.116744086 -0.028012661 -0.0252470514  0.010449011  0.129679829
Tara_offi -0.046133096 -0.040357962 -0.0406658990 -0.164333018 -0.016832253
Trif_ambi  0.031364156 -0.205425553 -0.1546849243 -0.016961785  0.019499568
Trif_hybr -0.037002624 -0.146855672 -0.1122827453  0.034061831 -0.092528662
Trif_medi  0.093476932 -0.144730243 -0.0878576847  0.027798853 -0.003026954
Trif_prat -0.052930615 -0.164044809 -0.1255269743  0.031366256 -0.089651963
Trif_repe  0.004406665 -0.226754666 -0.0591705599 -0.059065573 -0.076187210
Verb_thap -0.125133943  0.028453973 -0.0821640699  0.021882923 -0.076344765
Wahl_albo  0.131741931 -0.132864262 -0.0673187000  0.046106939  0.015757597
                  [,6]         [,7]          [,8]          [,9]         [,10]
Achi_mill -0.105941304  0.061719217  0.1037486038 -8.025553e-02 -0.0216703076
Agro_capi -0.046666673  0.051157992  0.0399338439 -6.038583e-02  0.0090922853
Anth_odor  0.032532762 -0.075538540 -0.0596584611  2.763835e-02 -0.0126066897
Apha_arve  0.068432556  0.066862115 -0.0629896101 -8.182110e-03 -0.0557511537
Arre_elat -0.084819828 -0.076083586  0.0240242854 -1.398011e-02  0.0549554666
Brac_bell  0.150914047  0.030907352  0.0397770651 -2.781383e-02  0.0212159224
Brom_tect -0.042136221  0.072552431 -0.0449951263 -4.151182e-02  0.0776630636
Caps_burs -0.014181715 -0.051959318 -0.0022083217  3.771223e-02  0.0375436921
Care_brev  0.028966683  0.095760184 -0.0671309485  6.858997e-03  0.0041769637
Care_muel -0.076139242  0.050999816 -0.0154488042  1.480564e-02 -0.0080451914
Carm_vexi -0.054439188  0.031417280 -0.0303065509 -8.156966e-02 -0.0074851950
Celm_grac  0.140546979  0.040496266  0.0248831368 -3.733477e-02  0.0566530271
Cera_font -0.125049106 -0.150747164 -0.0498370227  7.634873e-02 -0.0289274638
Colo_brev  0.073378359 -0.024857757  0.0193451947 -3.979534e-02 -0.0511064655
Copr_petr -0.082053839  0.005086805 -0.0643844234  1.016449e-03  0.0146070978
Dact_glom -0.002962439 -0.129188804 -0.0005911521 -3.254507e-02  0.0130831921
Elym_falc -0.042304491 -0.039968885 -0.0103202656  6.846043e-02  0.0325617235
Erod_cicu -0.030560604 -0.029567077 -0.0079742556 -2.045110e-02  0.0054466239
Fest_nova  0.021561465 -0.058780163  0.0269061588 -1.364763e-02  0.0118233691
Fest_rubr -0.058127383 -0.038233966  0.0054366638 -2.748795e-04  0.0342993908
Gera_sess  0.069711778 -0.014991913  0.0155668871  1.494247e-03  0.0448360149
Hier_caes  0.050483614 -0.001256299 -0.0125900639  2.280223e-02  0.0144153556
Hier_pilo  0.056203833  0.008979092 -0.0105913204  2.426300e-02  0.0225194567
Hier_prae  0.082490657  0.059262394  0.0291926804  5.805582e-02 -0.0231593435
Holc_lana -0.041739662 -0.006941719 -0.0225505036  1.946949e-02 -0.0808358440
Leuc_fras -0.105913672  0.028983102  0.0663349771  1.143744e-01  0.0410239614
Lotu_corn -0.122706870  0.023799059 -0.0321489804  1.253297e-02 -0.0033525799
Lupi_poly -0.043706318  0.016635663  0.1628561377  1.102662e-02 -0.0789518277
Luzu_rufa  0.106386288  0.037785056 -0.1171672209 -1.733405e-02 -0.0070331809
Malv_parv  0.007615657 -0.022099548 -0.0263209143  4.254371e-02  0.0009911592
Medi_sati -0.228669404 -0.022347436 -0.0230229346 -8.824387e-02  0.0176535563
Myos_stri  0.052737146  0.103115891  0.0010618562  1.023245e-01 -0.0044792256
Oreo_cole -0.007744361  0.021467774  0.0053763431  6.343379e-05  0.0717789818
Phle_prat -0.006035581 -0.040028711  0.0202272066 -1.281638e-02 -0.0426376910
Pime_oreo -0.002599651 -0.018262741  0.0177107577 -4.363105e-02  0.0062841618
Poa_cole   0.032277836 -0.050743080  0.0502104025  2.344195e-02  0.0024510223
Poa_mani   0.065765528 -0.031867125  0.0202127883  6.492204e-02 -0.0295374533
Poa_prat  -0.068983247  0.001831072  0.0195832702  1.397490e-02 -0.0153483150
Pter_veno  0.124704310 -0.104962437  0.0687178789  3.358868e-02 -0.0080080188
Pyrr_exig  0.045269332  0.022571915 -0.0008203678  3.711153e-02  0.0455381310
Raou_hook  0.017694522 -0.010506854  0.0021994550 -8.904637e-02 -0.0833199000
Raou_subs -0.037953527  0.045537782 -0.0009644155 -6.092942e-02 -0.0109225921
Rume_acet -0.070572139  0.102656651 -0.0460460071  2.953731e-02 -0.0945870513
Sche_phoe -0.068043230  0.016841421  0.0456998201  2.132210e-02 -0.0058250558
Stac_mini  0.077573851  0.001363126 -0.0055277980 -7.634145e-03 -0.0037506445
Tara_offi  0.164525524 -0.068914984  0.0010554454 -9.146843e-02 -0.0250010081
Trif_ambi -0.025291049  0.003556877 -0.0126356413 -2.646028e-02  0.0354147412
Trif_hybr  0.049790398 -0.035089140 -0.0516086824 -3.778327e-02  0.0108114823
Trif_medi -0.011781015  0.060156721 -0.0280245673 -2.156458e-02  0.0422630241
Trif_prat  0.050387045 -0.044080272 -0.0465852003 -2.823084e-02  0.0072509253
Trif_repe -0.011248656 -0.043914634 -0.1030413896  5.890330e-02 -0.0515994606
Verb_thap  0.016103995  0.014074776  0.1344369616  1.000362e-02  0.0079015420
Wahl_albo  0.032316247  0.115354325  0.0109931291  4.829379e-02  0.0096863251
                 [,11]        [,12]         [,13]         [,14]         [,15]
Achi_mill  0.016278451  0.012631975 -0.0233119794 -0.0102271378  0.0297221248
Agro_capi  0.017944447  0.049981733 -0.0221725230 -0.0048220516  0.0036670545
Anth_odor -0.024351578  0.040207095 -0.0055194750 -0.0336743086  0.0160329739
Apha_arve -0.022124154  0.030724996  0.0148763831 -0.0052428906 -0.0243137632
Arre_elat -0.039249992 -0.017941729  0.0243342152 -0.0130004030  0.0089678901
Brac_bell -0.004364155  0.033275066 -0.0259128796 -0.0149983885  0.0489338499
Brom_tect  0.041585161 -0.026153143  0.0355197018  0.0273090923  0.0068410445
Caps_burs  0.077432627  0.025876415 -0.0519574582 -0.0105579770 -0.0199726025
Care_brev  0.037627412 -0.023732469  0.0016005939  0.0021981619 -0.0197534859
Care_muel  0.018136353  0.065149585  0.0018195239 -0.0162875831  0.0035560026
Carm_vexi  0.018428882  0.026229764 -0.0435940769  0.0268385436  0.0058607348
Celm_grac -0.005039595  0.041198493 -0.0342021823  0.0252665330 -0.0101450611
Cera_font -0.056238468  0.019669177 -0.0316007276  0.0030228200 -0.0051810094
Colo_brev  0.036719177 -0.012087648  0.0610333184 -0.0002686379  0.0157338672
Copr_petr  0.042399086 -0.070478223 -0.0618079063 -0.0236448330 -0.0142549189
Dact_glom -0.029809476 -0.016523949  0.0087541285 -0.0274699939  0.0158414832
Elym_falc  0.029488062 -0.016091016  0.0601830255  0.0236153541  0.0322361447
Erod_cicu -0.023811798  0.006746023  0.0600727100 -0.0220719296 -0.0153691569
Fest_nova -0.040091938  0.003725802 -0.0190791664  0.0142211378 -0.0290285639
Fest_rubr -0.038644441  0.020966613  0.0184452891 -0.0037669174  0.0018939800
Gera_sess  0.012432067 -0.065881110  0.0046146069 -0.0397349829 -0.0001058485
Hier_caes -0.029826889 -0.003887918  0.0097224328 -0.0151125913 -0.0361080886
Hier_pilo -0.023940178 -0.023310357  0.0073233179  0.0235824290  0.0385548529
Hier_prae -0.009765850 -0.006199271  0.0359028594  0.0022713888 -0.0252636617
Holc_lana  0.004158213 -0.003051328 -0.0144443681 -0.0013903694 -0.0020662046
Leuc_fras  0.074665203  0.036286572  0.0141556575 -0.0053270695 -0.0232088740
Lotu_corn -0.025959836  0.084196321  0.0156395747  0.0386040780 -0.0069264955
Lupi_poly  0.069380226 -0.052081459  0.0206804144  0.0080653899  0.0115651662
Luzu_rufa  0.013792313 -0.029661475 -0.0441370988  0.0101487914 -0.0226286229
Malv_parv -0.021599082 -0.017548734 -0.0168319948  0.0631053770  0.0630325783
Medi_sati  0.017715047 -0.004567302  0.0376187300 -0.0350727539 -0.0173556797
Myos_stri -0.018025691  0.022378049  0.0189960064 -0.0317798501 -0.0123376651
Oreo_cole -0.028979267 -0.021350393 -0.0253399049 -0.0173450018  0.0059285777
Phle_prat  0.016937699 -0.035485171 -0.0494413798  0.0052740365 -0.0037677961
Pime_oreo -0.046967434 -0.025337157 -0.0203810432 -0.0002901880  0.0060670477
Poa_cole   0.025335274  0.030825873  0.0058160966 -0.0164669571 -0.0030732908
Poa_mani  -0.007159186  0.034325779 -0.0165565915  0.0062731336  0.0363062658
Poa_prat   0.011721350  0.003757502 -0.0154016101  0.0309428664 -0.0136781895
Pter_veno  0.051219951  0.007552499 -0.0195445488  0.0120644757 -0.0073414144
Pyrr_exig  0.025610060 -0.015436143 -0.0037465445  0.0117706707  0.0142640787
Raou_hook -0.003987517 -0.001193498  0.0318681658  0.0374928327 -0.0132601533
Raou_subs -0.067391933 -0.012901357  0.0192495077 -0.0104062912  0.0279249714
Rume_acet -0.025208463 -0.011832459 -0.0421125702 -0.0306257786  0.0242594720
Sche_phoe  0.004906074 -0.033254424 -0.0209331808  0.0028562050 -0.0212147525
Stac_mini -0.015264186 -0.005875080  0.0636587653  0.0353831490 -0.0205582560
Tara_offi  0.043510760  0.029716835  0.0138296901 -0.0406646422 -0.0188589341
Trif_ambi  0.028613079  0.002447645 -0.0003675399  0.0083397678  0.0151674387
Trif_hybr  0.006034819  0.012175993  0.0063908106 -0.0030002029 -0.0058389923
Trif_medi -0.006569771 -0.005553192  0.0046856966  0.0480141923 -0.0154112191
Trif_prat  0.021739876  0.001671801 -0.0070678723 -0.0115177063  0.0091465597
Trif_repe  0.018438552 -0.040382845  0.0296418627  0.0156843090 -0.0053775658
Verb_thap -0.118203266 -0.029691307 -0.0303076530  0.0245485190 -0.0525973188
Wahl_albo -0.049676080 -0.014227448  0.0193391903 -0.0621258174  0.0234934258
                  [,16]         [,17]         [,18]         [,19]         [,20]
Achi_mill -0.0046643423 -3.015552e-03 -0.0191554219  0.0107520495  0.0044730007
Agro_capi -0.0153175803  2.526244e-03  0.0206973288 -0.0057687042  0.0062799932
Anth_odor -0.0174200019  1.070709e-02 -0.0023876307  0.0187865683  0.0126425737
Apha_arve  0.0521257596 -3.141971e-02 -0.0216371264  0.0061817010  0.0010880774
Arre_elat  0.0079445902 -1.041160e-02  0.0108446614  0.0258872154  0.0038590083
Brac_bell  0.0169918763  5.614161e-03  0.0111445574 -0.0077962028 -0.0260836404
Brom_tect -0.0108910325 -9.409170e-03  0.0038004878  0.0042612047 -0.0010217244
Caps_burs  0.0286805200  3.794263e-02  0.0110819042 -0.0008198617  0.0048978160
Care_brev -0.0277936942 -1.560072e-02  0.0080709374  0.0055921899  0.0089013472
Care_muel -0.0028723205  4.396408e-02  0.0004002342  0.0065624629 -0.0085529283
Carm_vexi -0.0021550823 -6.502020e-03 -0.0237523442  0.0108677279 -0.0143758485
Celm_grac -0.0234254928  6.951419e-03 -0.0002862224 -0.0084322280  0.0111265699
Cera_font -0.0147354481 -1.695588e-02 -0.0025716360 -0.0043343998 -0.0030459227
Colo_brev -0.0002376204  2.352855e-02  0.0164231071 -0.0049986126  0.0002197864
Copr_petr  0.0334138317  1.208806e-02  0.0015964227  0.0039225394  0.0083609732
Dact_glom  0.0074803210 -1.419191e-03  0.0155186768  0.0050566633  0.0005113676
Elym_falc  0.0191973012  1.979664e-02 -0.0194610913 -0.0023486650  0.0029062243
Erod_cicu -0.0245593841  2.932137e-03 -0.0187512859 -0.0234888804 -0.0129691763
Fest_nova  0.0157763247  1.750408e-02 -0.0082531775  0.0055877061 -0.0122630517
Fest_rubr -0.0001000719  1.850222e-02 -0.0258744212 -0.0085880100  0.0077097688
Gera_sess -0.0067847323 -3.716469e-02 -0.0104524948  0.0089290074 -0.0001965295
Hier_caes -0.0265039366  1.063994e-02  0.0092553992  0.0111264721 -0.0074106130
Hier_pilo  0.0223588682 -1.709744e-02  0.0171653342 -0.0159536510 -0.0025243801
Hier_prae -0.0120918704 -9.848974e-05 -0.0182007002  0.0169838388  0.0128123417
Holc_lana -0.0317376887 -1.522985e-02  0.0040940695 -0.0026499035 -0.0147877752
Leuc_fras  0.0220291345 -1.810196e-02  0.0103139673 -0.0021624977 -0.0030994463
Lotu_corn  0.0273303913 -3.504918e-02  0.0183785937  0.0006889185  0.0104345632
Lupi_poly  0.0055502978  5.803138e-03  0.0029875629  0.0044870812  0.0087392374
Luzu_rufa  0.0050477203  1.080395e-02  0.0091745046 -0.0149626394 -0.0018122822
Malv_parv -0.0060220387 -7.009379e-03  0.0033187090  0.0096773733  0.0033527024
Medi_sati -0.0011488492 -1.424299e-02  0.0174536010 -0.0056322240 -0.0019981976
Myos_stri -0.0455271292  7.483532e-03  0.0078743253  0.0096381622  0.0005257553
Oreo_cole  0.0045091229  5.091888e-03 -0.0092537316  0.0047614874 -0.0098322526
Phle_prat -0.0275972203 -1.783076e-02  0.0142940137 -0.0151358072  0.0006686787
Pime_oreo  0.0010909656  1.455214e-02  0.0009259975 -0.0098708856  0.0258306512
Poa_cole  -0.0110314002 -1.887406e-02 -0.0106060929 -0.0279142017 -0.0082972296
Poa_mani  -0.0026126550 -1.309844e-02  0.0057500979  0.0201848473  0.0064886047
Poa_prat  -0.0101716518  4.232406e-03 -0.0158462837 -0.0363292558  0.0110958542
Pter_veno -0.0117930668  1.022057e-02 -0.0018650019 -0.0003493879  0.0029379738
Pyrr_exig -0.0029660944 -4.705862e-02 -0.0180870806 -0.0127913873 -0.0062911592
Raou_hook -0.0035767979  3.249620e-03  0.0088647406  0.0044346600 -0.0086161378
Raou_subs -0.0240162735  1.369604e-02 -0.0063791302 -0.0053368164  0.0063903970
Rume_acet  0.0304022716  3.300956e-03 -0.0039028988  0.0004072953 -0.0002423888
Sche_phoe -0.0169601715 -5.315624e-03  0.0053901759  0.0201442861 -0.0175845840
Stac_mini  0.0367569453  1.111307e-02  0.0245671450  0.0019558949 -0.0086419432
Tara_offi  0.0273940247 -2.432659e-02 -0.0199596469  0.0113592640  0.0110754254
Trif_ambi  0.0062771502  2.371719e-02 -0.0232546805  0.0016042548 -0.0098337058
Trif_hybr -0.0092002951 -7.626520e-03  0.0159411781 -0.0175050598  0.0123292410
Trif_medi -0.0166918965  1.008027e-02 -0.0042790079  0.0185368442  0.0061203532
Trif_prat -0.0087821085 -1.013585e-04  0.0109550387  0.0135690726 -0.0080507772
Trif_repe  0.0031300019  2.395599e-02 -0.0152430322 -0.0052505071 -0.0038583769
Verb_thap  0.0265730824  3.900426e-03  0.0017379782 -0.0027922907 -0.0031867918
Wahl_albo  0.0193274463  9.061378e-03  0.0114393895 -0.0207347088  0.0027985771
                  [,21]         [,22]         [,23]         [,24]         [,25]
Achi_mill -0.0040003795  1.969956e-03 -1.447329e-09  4.836645e-04  1.839667e-03
Agro_capi -0.0008252815  6.867442e-04 -1.447329e-09  2.166664e-05 -4.394055e-05
Anth_odor -0.0150686509  4.177807e-03 -1.447329e-09  1.433106e-03 -1.126182e-02
Apha_arve  0.0055586674 -2.406891e-03 -1.447329e-09 -1.237339e-04  1.105699e-03
Arre_elat  0.0090435835  8.008980e-03 -1.447329e-09 -6.154450e-03 -4.833803e-03
Brac_bell  0.0040553684  8.726268e-04 -1.447329e-09  1.210074e-03 -9.164433e-03
Brom_tect -0.0056108199  1.500349e-03 -1.447329e-09  5.048550e-04  5.685666e-04
Caps_burs -0.0011047267  1.759111e-03 -1.447329e-09  5.965614e-04 -3.843875e-04
Care_brev  0.0141300613 -6.966237e-03 -1.447329e-09  8.267819e-04  5.754585e-03
Care_muel  0.0109448322 -5.022537e-04 -1.447329e-09  2.455273e-04  3.410490e-04
Carm_vexi -0.0084003494  7.582652e-03 -1.447329e-09  9.333135e-04  6.053542e-04
Celm_grac -0.0095524155  1.199449e-04 -1.447329e-09 -2.208937e-03  5.659971e-03
Cera_font  0.0001440245 -2.718440e-03 -1.447329e-09  5.190778e-04  2.225960e-03
Colo_brev  0.0048911006  1.035628e-03 -1.447329e-09 -1.330816e-03  1.162248e-03
Copr_petr -0.0015208668  5.446283e-04 -1.447329e-09 -2.099568e-04 -7.520289e-03
Dact_glom  0.0141292776  8.218125e-05 -1.447329e-09  3.403602e-03  1.847473e-03
Elym_falc -0.0119339650  5.989349e-04 -1.447329e-09 -1.325476e-04  4.242354e-03
Erod_cicu  0.0007774498  8.128327e-04 -1.447329e-09 -1.799854e-03  7.228796e-04
Fest_nova  0.0079164328  2.485923e-03 -1.447329e-09 -3.195352e-03  6.302141e-03
Fest_rubr -0.0117412810 -1.005237e-02 -1.447329e-09  6.532562e-03  1.066100e-02
Gera_sess -0.0088381320  4.073948e-03 -1.447329e-09  3.479518e-03  7.063160e-03
Hier_caes -0.0156854602  7.691302e-03 -1.447329e-09 -3.484171e-03  8.998437e-03
Hier_pilo  0.0083676461 -4.630671e-03 -1.447329e-09  2.898389e-03  2.017681e-03
Hier_prae  0.0089491503 -6.919928e-03 -1.447329e-09  1.409545e-03 -7.427290e-03
Holc_lana  0.0087897374  6.762665e-04 -1.447329e-09  7.203791e-04 -4.321627e-03
Leuc_fras  0.0024183330  2.643189e-04 -1.447329e-09 -3.488986e-04  3.915540e-03
Lotu_corn -0.0008958930 -7.337863e-03 -1.447329e-09 -1.527184e-03  3.398612e-04
Lupi_poly  0.0023653019 -4.946463e-04 -1.447329e-09 -9.603295e-05 -9.444398e-05
Luzu_rufa  0.0062054745 -7.922122e-03 -1.447329e-09  9.606419e-04  2.389211e-03
Malv_parv -0.0012545688 -4.448594e-03 -1.447329e-09 -8.418981e-05  9.580763e-04
Medi_sati -0.0003130717 -4.030962e-04 -1.447329e-09  1.175010e-03 -1.104013e-03
Myos_stri  0.0060528785  1.564921e-03 -1.447329e-09  3.202482e-04 -1.845957e-03
Oreo_cole  0.0193846790  1.522162e-03 -1.447329e-09 -2.521998e-04  1.375882e-03
Phle_prat -0.0089368357  2.323703e-04 -1.447329e-09 -2.171089e-03  1.006477e-02
Pime_oreo -0.0024220004 -1.208726e-02 -1.447329e-09 -3.026486e-03 -8.411988e-03
Poa_cole  -0.0119796924 -8.650089e-03 -1.447329e-09  6.215686e-04 -1.332352e-02
Poa_mani   0.0099822969  6.782717e-03 -1.447329e-09  7.539396e-04  9.169764e-03
Poa_prat   0.0143741076  7.336100e-03 -1.447329e-09 -2.416796e-03 -8.963956e-04
Pter_veno -0.0025990966  1.166254e-03 -1.447329e-09  4.779340e-04 -4.715509e-04
Pyrr_exig -0.0021349793  7.270779e-03 -1.447329e-09 -4.046681e-03 -7.893218e-03
Raou_hook -0.0054513853  2.231191e-03 -1.447329e-09  8.016898e-04  2.429214e-03
Raou_subs  0.0094132247 -2.582016e-03 -1.447329e-09 -1.046504e-03 -1.249412e-03
Rume_acet -0.0156573407  7.786230e-03 -1.447329e-09 -5.348107e-04  1.787298e-03
Sche_phoe -0.0050705601 -1.406407e-02 -1.447329e-09  3.839060e-03 -5.161459e-03
Stac_mini -0.0129601152  1.521960e-03 -1.447329e-09  7.556218e-04 -3.377170e-03
Tara_offi  0.0058381531 -2.492420e-03 -1.447329e-09 -1.021229e-03  2.106512e-03
Trif_ambi  0.0102212136 -5.127984e-03 -1.447329e-09 -5.299816e-05  3.997313e-03
Trif_hybr  0.0040742823  1.774048e-02 -1.447329e-09  6.037092e-03 -3.121334e-03
Trif_medi -0.0061037379  7.741171e-03 -1.447329e-09  1.586548e-03 -8.942776e-03
Trif_prat -0.0093900747 -1.637832e-02 -1.447329e-09 -5.603385e-03  1.381096e-03
Trif_repe  0.0025573311  5.061973e-03 -1.447329e-09 -1.558858e-03 -2.959013e-03
Verb_thap -0.0001589469  3.157232e-03 -1.447329e-09  1.647206e-03 -2.216015e-03
Wahl_albo -0.0109739808  1.255975e-04 -1.447329e-09 -1.768024e-03  4.993096e-03
                  [,26]         [,27]         [,28]         [,29]         [,30]
Achi_mill  0.0034047618  0.0080272480 -1.915966e-04  3.206529e-03 -8.227702e-03
Agro_capi -0.0020236141 -0.0058069723  4.387017e-03 -1.047331e-02  3.221847e-03
Anth_odor  0.0053329988  0.0123953428  1.440629e-02 -7.088209e-03 -1.671202e-02
Apha_arve -0.0006984423  0.0020490519 -4.035365e-03  1.416301e-03  5.550080e-03
Arre_elat -0.0006375517  0.0079289353  1.257767e-02 -4.002560e-03  3.029933e-02
Brac_bell  0.0061470220 -0.0086845633 -9.596192e-03 -3.491900e-02 -6.612145e-03
Brom_tect  0.0030221614  0.0013423082 -2.644319e-03 -2.462474e-03 -4.978370e-03
Caps_burs -0.0040744157 -0.0015509386  1.997648e-03 -9.086544e-04  1.387839e-03
Care_brev  0.0057631247  0.0037772838  8.984706e-03 -2.156689e-02 -1.159959e-03
Care_muel  0.0012635474  0.0095858581 -3.268975e-03  1.449615e-02 -1.184008e-05
Carm_vexi -0.0021043626  0.0052620690  2.241241e-03  3.200843e-03  9.732528e-03
Celm_grac -0.0064275550  0.0042891418  1.416355e-02  3.572460e-02  5.986542e-03
Cera_font  0.0030658668  0.0033503691  1.767439e-03 -2.527949e-03 -1.904351e-03
Colo_brev -0.0004274634 -0.0049991314  3.539111e-03  3.786782e-03  1.812197e-03
Copr_petr -0.0033060796 -0.0055238691  2.102107e-04  1.041299e-03  1.207393e-02
Dact_glom -0.0041321013  0.0022613306 -2.382127e-02  2.111123e-02 -1.052434e-02
Elym_falc  0.0080440948  0.0039488402 -3.342556e-03 -3.146083e-03 -1.110437e-02
Erod_cicu -0.0054108519 -0.0080934672  3.448417e-03  3.037024e-03  3.596339e-03
Fest_nova  0.0034396204 -0.0109406871  2.957438e-02 -1.035328e-02 -3.765121e-02
Fest_rubr -0.0104890840 -0.0179481973 -1.334513e-03 -1.490396e-02  9.330699e-03
Gera_sess -0.0008791652  0.0177019909  1.603596e-03 -8.580795e-03 -8.526342e-03
Hier_caes  0.0149791391 -0.0000608198 -2.620459e-02 -3.009539e-03  3.948430e-03
Hier_pilo -0.0153700112  0.0068538757  1.806373e-02  1.164978e-02 -5.279337e-03
Hier_prae  0.0021305795 -0.0012378379  7.996433e-03 -1.431792e-02  6.470998e-03
Holc_lana -0.0060272405  0.0026665378  3.352391e-03  1.063811e-02  1.994517e-03
Leuc_fras -0.0005587517 -0.0001064463 -1.459129e-03  1.509227e-04 -4.663923e-04
Lotu_corn  0.0088636166 -0.0065635194 -3.000058e-03 -1.321847e-03 -3.624056e-03
Lupi_poly  0.0006573145 -0.0034419223  3.652799e-04  8.013498e-05 -3.254346e-03
Luzu_rufa  0.0056000221  0.0074999350 -9.689074e-03  3.225311e-04  5.557697e-04
Malv_parv  0.0091199462  0.0067468899  1.483807e-03 -1.356898e-03  1.941396e-03
Medi_sati -0.0037664203 -0.0006057767  5.779899e-04 -5.299562e-03 -9.385143e-03
Myos_stri -0.0021189403 -0.0019890760  8.929144e-05  1.995688e-03 -3.642366e-03
Oreo_cole -0.0026944580 -0.0047716384  1.371801e-03 -1.937148e-03  4.561846e-03
Phle_prat  0.0010584425 -0.0110193919  7.424006e-03 -1.484884e-02  2.294037e-02
Pime_oreo  0.0107627972 -0.0098556856 -1.091837e-02  4.398805e-03 -8.891887e-03
Poa_cole  -0.0022383901  0.0106863589  9.357278e-04 -2.413116e-03  2.665175e-02
Poa_mani  -0.0099035601 -0.0093724140 -1.488850e-02  1.502585e-03  1.337735e-02
Poa_prat  -0.0056695365  0.0234463212 -1.526749e-02 -1.238560e-02 -1.973604e-02
Pter_veno -0.0010442109 -0.0005528739 -4.977500e-04 -8.194704e-04 -2.835929e-03
Pyrr_exig  0.0041098425 -0.0204324413 -7.020503e-03  1.659466e-02 -1.530614e-02
Raou_hook  0.0016515520  0.0050242068 -6.894159e-04 -5.709867e-05 -8.407396e-03
Raou_subs -0.0008276344 -0.0040805787 -1.846607e-03  3.508573e-04  1.028595e-02
Rume_acet -0.0032277115 -0.0036805217  2.872572e-03 -1.527575e-04 -1.161198e-03
Sche_phoe  0.0099738857 -0.0079065680  1.181408e-03  2.810763e-02 -1.099525e-02
Stac_mini -0.0010800080  0.0055803907  1.885463e-03 -2.184817e-04  1.491570e-02
Tara_offi -0.0000988655 -0.0028197435 -2.397258e-03  6.998295e-03 -2.084818e-03
Trif_ambi  0.0183896698  0.0063716180  1.605599e-03  5.749776e-03  2.387234e-02
Trif_hybr  0.0157769077 -0.0074842131  9.036552e-03  5.233671e-03  1.450566e-03
Trif_medi -0.0237735752 -0.0079173412 -1.182619e-02 -5.187492e-03 -5.575715e-03
Trif_prat -0.0180469630  0.0068145988 -5.633008e-03 -9.488612e-03 -1.313782e-02
Trif_repe -0.0048912366 -0.0093766615  3.025543e-03  5.116740e-03  5.858036e-03
Verb_thap -0.0004127988  0.0083622420 -5.164680e-03 -3.545827e-03  5.817565e-03
Wahl_albo -0.0001959144  0.0048505523  4.568539e-03  1.138244e-02 -6.437434e-03
                  [,31]         [,32]         [,33]         [,34]         [,35]
Achi_mill -0.0111167449  9.914218e-03 -6.330413e-04 -0.0238933295  0.0037552042
Agro_capi -0.0099959905 -1.985475e-02  1.709398e-02  0.0494669383 -0.0207099959
Anth


Created & Maintained by Osamu Ogasawara (osamu.ogasawara@gmail.com) and IMSBIO