###Lande's (1996) scheme for additive partitioning of diversity for a site by species matrix with zeros requires vegan.

#by Marc Cadotte
#Oct 2008

addPart<-function (data,index="simpson") {
	
	INDICES <- c("shannon", "simpson", "richness")
    index <- match.arg(index, INDICES)

	no.spp<-apply(data[,2:ncol(data)],MARGIN=2,sum)
		
	q<-no.spp/sum(no.spp)
	
	p.bar<-apply(data[,2:ncol(data)],
		MARGIN=1,sum)/sum(
		apply(data[,2:ncol(data)],
		MARGIN=1,sum))
			
	
	if (index == "simpson") {
		
		alph<-diversity(data[,2:ncol(data)],
			index="simpson",MARGIN=2)
		
		lmbd<-1-alph
		
		d.sqr<-sum(q*lmbd)-sum(p.bar^2)

		D.bar<-sum(alph*q)

		Dt<-d.sqr+D.bar
		
		return(rbind(D.bar,d.sqr,Dt))
		}
	
	if (index == "shannon") {
		
		alph<-diversity(data[,2:ncol(data)],
			index="shannon",MARGIN=2)
			
		H.bar<-sum(alph*q)
		
		H.among<--sum(p.bar*log(p.bar))-sum(q*alph)
		
		Ht<-H.bar+H.among
		
		return(rbind(H.bar,H.among,Ht))
		}
		
	if (index == "richness") {
		
		for (i in 2:ncol(data[,2:ncol(data)])) {
			for (j in 1:nrow(data)) {
				if (data[j,i] > 1) data[j,i]=1
				}
			}
		
		alph<-apply(data[,2:ncol(data)],
		MARGIN=2,sum)
		
		S.bar<-sum(alph*q)
		
		St<-nrow(data)
		
		S.among<-St-S.bar
		
		return(rbind(S.bar,S.among,St))
		}	
		
		
	}