Measuring Functional Diversity from Multiple Traits, and Other Tools for Functional Ecology

Description

FD is a package to compute different multidimensional functional diversity (FD) indices. It implements a distance-based framework to measure FD that allows any number and type of functional traits, and can also consider species relative abundances. It also contains other tools for functional ecologists (e.g. maxent).

Details

FD computes different multidimensional FD indices. To compute FD indices, a species-by-trait(s) matrix is required (or at least a species-by-species distance matrix). gowdis computes the Gower dissimilarity from different trait types (continuous, ordinal, nominal, or binary), and tolerates NAs. It can treat ordinal variables as described by Podani (1999), and can handle asymetric binary variables and variable weights. gowdis is called by dbFD, the main function of FD.

dbFD uses principal coordinates analysis (PCoA) to return PCoA axes, which are then used as ‘traits’ to compute FD. dbFD computes several multidimensional FD indices, including the three indices of Villéger et al. (2008): functional richness (FRic), functional evenness (FEve), and functional divergence (FDiv). It also computes functional dispersion (FDis) (Laliberté and Legendre 2010), Rao's quadratic entropy (Q) (Botta-Dukát 2005), a posteriori functional group richness (FGR), and the community-level weighted means of trait values (CWM), an index of functional composition. Some of these indices can be weighted by species abundances. dbFD includes several options for flexibility.

Author(s)

Etienne Laliberté, Pierre Legendre and Bill Shipley

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

References

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 91:299-305.

Podani, J. (1999) Extending Gower's general coefficient of similarity to ordinal characters. Taxon 48:331-340.

Villéger, S., N. W. H. Mason and D. Mouillot (2008) New multidimensional functional diversity indices for a multifaceted framework in functional ecology. Ecology 89:2290-2301.

Examples

# examples with a dummy dataset

ex1 <- gowdis(dummy$trait)
ex1

ex2 <- functcomp(dummy$trait, dummy$abun)
ex2

ex3 <- dbFD(dummy$trait, dummy$abun)
ex3

# examples with real data from New Zealand short-tussock grasslands
# these examples may take a few seconds to a few minutes each to run

ex4 <- gowdis(tussock$trait)

ex5 <- functcomp(tussock$trait, tussock$abun)

# 'lingoes' correction used because 'sqrt' does not work in that case
ex6 <- dbFD(tussock$trait, tussock$abun, corr = "lingoes")

## Not run: 
# ward clustering to compute FGR, cailliez correction
ex7 <- dbFD(tussock$trait, tussock$abun, corr = "cailliez",
calc.FGR = TRUE, clust.type = "ward")
# choose 'g' for number of groups
# 6 groups seems to make good ecological sense
ex7

# however, calinksi criterion in 'kmeans' suggests
# that 6 groups may not be optimal
ex8 <- dbFD(tussock$trait, tussock$abun, corr = "cailliez",
calc.FGR = TRUE, clust.type = "kmeans", km.sup.gr = 10)

## End(Not run)

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/FD-package.Rd_%03d_medium.png", width=480, height=480)
> ### Name: FD-package
> ### Title: Measuring Functional Diversity from Multiple Traits, and Other
> ###   Tools for Functional Ecology
> ### Aliases: FD-package FD
> ### Keywords: package
> 
> ### ** Examples
> 
> # examples with a dummy dataset
> 
> ex1 <- gowdis(dummy$trait)
> ex1
          sp1       sp2       sp3       sp4       sp5       sp6       sp7
sp2 0.2181884                                                            
sp3 0.5240052 0.6678082                                                  
sp4 0.6737443 0.5610028 0.8225701                                        
sp5 0.5291113 0.8145699 0.4862253 0.4843264                              
sp6 0.6100161 0.5932587 0.2784736 0.7073925 0.6067323                    
sp7 0.4484235 0.6863374 0.4848663 0.5575126 0.3023416 0.6187844          
sp8 0.4072834 0.2039443 0.5958904 0.2390962 0.5585525 0.4470207 0.7030186
> 
> ex2 <- functcomp(dummy$trait, dummy$abun)
> ex2
          num1     num2 fac1 fac2 ord1 ord2 bin1 bin2
com1  5.887500 4.037500    C    X    2    6    0    0
com2  4.212500 5.562500    B    Z    1    3    0    1
com3  5.716667 6.166667    A    Z    1    3    0    1
com4  9.000000 2.575000    C    Y    5    3    1    1
com5  4.500000 3.050000    C    X    2    7    0    0
com6  5.095238 5.528571    C    Z    2    1    0    1
com7  7.009091 5.427273    A    Z    3    1    0    1
com8  5.245455 3.572727    C    X    2    6    1    0
com9  6.870000 4.245455    A    X    3    2    0    1
com10 7.427273 3.783333    B    X    3    2    1    0
> 
> ex3 <- dbFD(dummy$trait, dummy$abun)
Species x species distance matrix was not Euclidean. 'sqrt' correction was applied. 
FEVe: Could not be calculated for communities with <3 functionally singular species. 
FRic: To respect s > t, FRic could not be calculated for communities with <3 functionally singular species. 
FRic: Dimensionality reduction was required. The last 5 PCoA axes (out of 7 in total) were removed. 
FRic: Quality of the reduced-space representation (based on corrected distance matrix) = 0.6108352 
FDiv: Could not be calculated for communities with <3 functionally singular species. 
> ex3
$nbsp
 com1  com2  com3  com4  com5  com6  com7  com8  com9 com10 
    4     3     3     2     3     5     3     4     5     4 

$sing.sp
 com1  com2  com3  com4  com5  com6  com7  com8  com9 com10 
    4     3     3     2     3     5     3     4     5     4 

$FRic
       com1        com2        com3        com4        com5        com6 
0.174201349 0.102097174 0.002157642          NA 0.143151204 0.231083703 
       com7        com8        com9       com10 
0.073683375 0.174220613 0.337446205 0.228904118 

$qual.FRic
[1] 0.6108352

$FEve
     com1      com2      com3      com4      com5      com6      com7      com8 
0.8432334 0.4628635 0.8659657        NA 0.9081209 0.8651734 0.7681991 0.7606650 
     com9     com10 
0.7994638 0.4944601 

$FDiv
     com1      com2      com3      com4      com5      com6      com7      com8 
0.8429221 0.8593250 0.6303031        NA 0.7631346 0.8966687 0.8356095 0.8681163 
     com9     com10 
0.7015118 0.9712554 

$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 

$RaoQ
      com1       com2       com3       com4       com5       com6       com7 
0.12835440 0.04063622 0.06497224 0.03003235 0.11858388 0.11738479 0.07868047 
      com8       com9      com10 
0.09308505 0.12431265 0.12490783 

$CWM
          num1     num2 fac1 fac2 ord1 ord2 bin1 bin2
com1  5.887500 4.037500    C    X    2    6    1    0
com2  4.212500 5.562500    B    Z    1    3    0    1
com3  5.716667 6.166667    A    Z    1    3    0    1
com4  9.000000 2.575000    C    Y    5    3    1    1
com5  4.500000 3.050000    C    X    2    6    0    0
com6  5.095238 5.528571    C    Z    2    1    0    1
com7  7.009091 5.427273    A    Z    3    1    0    1
com8  5.245455 3.572727    C    X    2    6    1    0
com9  6.870000 4.245455    A    X    3    2    0    1
com10 7.427273 3.783333    B    X    3    2    1    1

> 
> # examples with real data from New Zealand short-tussock grasslands
> # these examples may take a few seconds to a few minutes each to run
> 
> ex4 <- gowdis(tussock$trait)
> 
> ex5 <- functcomp(tussock$trait, tussock$abun)
> 
> # 'lingoes' correction used because 'sqrt' does not work in that case
> ex6 <- dbFD(tussock$trait, tussock$abun, corr = "lingoes")
Species x species distance matrix was not Euclidean. Lingoes correction was applied. 
FRic: Dimensionality reduction was required. The last 40 PCoA axes (out of 51 in total) were removed. 
FRic: Quality of the reduced-space representation (based on corrected distance matrix) = 0.5624752 
> 
> ## Not run: 
> ##D # ward clustering to compute FGR, cailliez correction
> ##D ex7 <- dbFD(tussock$trait, tussock$abun, corr = "cailliez",
> ##D calc.FGR = TRUE, clust.type = "ward")
> ##D # choose 'g' for number of groups
> ##D # 6 groups seems to make good ecological sense
> ##D ex7
> ##D 
> ##D # however, calinksi criterion in 'kmeans' suggests
> ##D # that 6 groups may not be optimal
> ##D ex8 <- dbFD(tussock$trait, tussock$abun, corr = "cailliez",
> ##D calc.FGR = TRUE, clust.type = "kmeans", km.sup.gr = 10)
> ## End(Not run)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>