functional.beta.multi {betapart}

Multiple-site functional dissimilarities

Description

Computes 3 multiple-site functional dissimilarities accounting for the spatial turnover and the nestedness components of functional beta diversity, and the sum of both values. Functional dissimilarities are based on volume of convex hulls intersections in a multidimensional functional space.

Usage

functional.beta.multi(x, traits, index.family="sorensen", warning.time=TRUE)

Arguments

x

data frame, where rows are sites and columns are species. Alternatively x can be a functional.betapart object derived from the functional.betapart.core function

traits

if x is not a functional.betapart object, a data frame, where rows are species and columns are functional space dimensions (i.e. quantitative traits or synthetic axes after PCoA). Number of species in each site must be strictly higher than number of dimensions. Number of dimensions should not exceed 4 and number of sites should not exceed 10. See Details.

index.family

family of dissimilarity indices, partial match of "sorensen" or "jaccard".

warning.time

a logical value indicating whether computation of multiple-site dissimilarities would stop if number of dimensions exceeds 4 or if number of sites exceeds 10. If turn to FALSE, computation process can be tracked in the step.fbc.txt file, see Details.

Details

For multiple-site dissimilarities metrics (N>2 sites), the volume of the union of the N convex hulls is computed using the inclusion-exclusion principle (Villéger et al., 2011). It requires to compute the volume of all the intersections between 2 to N convex hulls. Intersection between k>2 convex hulls is computed as the intersection between the two convex hulls shaping intersections between the corresponding k-1 convex hulls, e.g. V(AnBnC)=V( (AnB)n(BnC) ). For N sites, computing multiple-site dissimilarity metrics thus requires computing 2^N-(N+1) pair-wise intersections between convex hulls in a multidimensional functional space. Computation time of the intersection between two convex hulls increases with the number of dimensions (D) of the functional space. Therefore, to prevent from running very long computation process warning.time is set by default to stop the function if D>4 or N>10. Computation progress can be tracked in the "step.fbc.txt" file written in the working directory. This table shows proportion of steps completed for computing convex hull volume shaping each site ("FRi") and intersections between them ("intersection_k"). Note that the the betapart package now supports external parallel computing for null models. However, this functionality is only availabe in functional.betapart.core. In this case, use the functional.betapart object as x in this function. See functional.betapart.core for more details.

Value

The function returns a list with the three multiple site functional dissimilarity values.

For index.family="sorensen" the three indices are:

beta.SIM

value of the functional turnover component, measured as Simpson derived functional dissimilarity

beta.SNE

value of the functional nestedness component, measured as nestedness-resultant fraction of Sorensen derived functional dissimilarity

beta.SOR

value of the overall functional beta diversity, measured as Sorensen derived functional dissimilarity

For index.family="jaccard" the three indices are:

beta.JTU

value of the functional turnover component, measured as turnover fraction of Jaccard derived functional dissimilarity

beta.JNE

value of the functional nestedness component, measured as nestedness-resultant fraction of Jaccard derived functional dissimilarity

beta.JAC

value of the overall functional beta diversity, measured as Jaccard derived functional dissimilarity

Author(s)

Sébastien Villéger, Andrés Baselga and David Orme

References

Villéger S., Novack-Gottshal P. & Mouillot D. 2011. The multidimensionality of the niche reveals functional diversity changes in benthic marine biotas across geological time. Ecology Letters 14: 561-568

Baselga, A. 2012. The relationship between species replacement, dissimilarity derived from nestedness, and nestedness. Global Ecology and Biogeography 21: 1223-1232

Villéger, S. Grenouillet, G., Brosse, S. 2013. Decomposing functional beta-diversity reveals that low functional beta-diversity is driven by low functional turnover in European fish assemblages. Global Ecology and Biogeography 22: 671–681

See Also

functional.beta.pair, functional.betapart.core, beta.multi

Examples

##### 4 communities in a 2D functional space (convex hulls are rectangles)
traits.test<-cbind( c(1,1,1,2,2,3,3,4,4,5,5) , c(1,2,4,1,2,3,5,1,4,3,5) )
	dimnames(traits.test)<-list(paste("sp",1:11,sep="") , c("Trait 1","Trait 2") ) 

comm.test<-matrix(0,4,11,dimnames=list( c("A","B","C","D") , paste("sp",1:11,sep="") ) )
comm.test["A",c(1,2,4,5)]<-1
comm.test["B",c(1,3,8,9)]<-1
comm.test["C",c(6,7,10,11)]<-1
comm.test["D",c(2,4,7,9)]<-1

plot(5,5,xlim=c(0,6), ylim=c(0,6), type="n", xlab="Trait 1",ylab="Trait 2")
points(traits.test[,1],traits.test[,2], pch=21,cex=1.5,bg="black")
rect(1,1,4,4, col="#458B0050", border="#458B00") ; text(2.5,2.5,"B",col="#458B00",cex=1.5)	
polygon(c(2,1,3,4), c(1,2,5,4), col="#DA70D650", border="#DA70D6") ; 
text(2.5,3,"D",col="#DA70D6",cex=1.5)	
rect(1,1,2,2, col="#FF000050" , border="#FF0000") ; text(1.5,1.5,"A",col="#FF0000",cex=1.5)	
rect(3,3,5,5, col="#1E90FF50", border="#1E90FF") ; text(4,4.2,"C",col="#1E90FF",cex=1.5)	

test.multi<-functional.beta.multi(x=comm.test, traits=traits.test, index.family = "jaccard" )
test.multi

test.multi.ABC<-functional.beta.multi(x=comm.test[c("A","B","C"),], traits=traits.test, 
index.family = "jaccard" )
test.multi.ABC

test.multi.ABD<-functional.beta.multi(x=comm.test[c("A","B","D"),], traits=traits.test, 
index.family = "jaccard" )
test.multi.ABD