## Supplementary material to the paper: Sabatini F.M., Burrascano S., Tuomisto H. and Blasi C. 
## Ground layer plant species turnover and beta diversity in Southern-European old-growth forests. Plos One

## Appendix S1 – True diversity decomposition Script for R.

### Calculates alpha beta and gamma diversity according to Tuomisto 2010.
### Arguments:
### dataset: must be a sites x species tab (either p\a, absolute or relative freq).
### q: must be a vector of the exponents of Hill's weighted generalised mean ("Inf" not accepted).
### w: weights the plots in different ways, "even" =evenly weighted plots,
###           "bycover" = plots weighted according to the sum of their species' frequencies
###           or it can be a vector of weights of length==number of sites; whether the sum of weights for each
###           group of sites (factor, see below) is not ==1, then they will be automatically rescaled.
### factor: a factor vector of length ==number of sites that clusters sites into groups.
### div.dec returns a list of length=length(q), each element of the list is a dataframe 
###           reporting alpha beta and gamma levels for each group of sites.
### version 01/10/2013 by Francesco Sabatini, thanks to Hanna Tuomisto
### Please cite as: Sabatini F.M., Burrascano S., Tuomisto H. and Blasi C. 
### Ground layer plant species turnover and beta diversity in Southern-European old-growth forests. 
### Plos One.
 

div.dec <- function(dataset, q, w=c("even", "bycover",w), factor=NULL){
require(vegan)
     	if(min(q)<0)
      	stop("q must be greater than 0")
     ###implement when there is no factor!
     if(is.null(factor)){
      factor <- factor(rep("A",dim(dataset)[1]))}
     if(length(factor)!=dim(dataset)[1]){
        stop("factor length is not equal to the number of rows in the dataset")
        }
     res <- vector(0, mode="list" )
#     res <- list(NA, dim=c(length(levels(factor)),3, length(q)))
     for(qq in 1:length(q)){
      q1 <- q[qq]
      res[[qq]] <- as.data.frame(matrix(NA, nrow=length(levels(factor)), ncol=3))
      colnames(res[[qq]]) <- c("alpha", "beta", "gamma")
      rownames(res[[qq]]) <- levels(factor)
       for (k in 1:length(levels(factor)) ){
        x <- dataset[which(factor==levels(factor)[k]),]

        if(length(w)>1){
          if(length(w)==dim(dataset)[1]){
            w1 <- w[which(factor==levels(factor)[k])]
            if(sum(w1)!=1)
#             stop("sum(w) must be==1, for each factor")  
              w1 <- w1/sum(w1)
              x <- w1*(x/rowSums(x))
              }
         
          if(length(w)!=dim(dataset)[1])
            stop("w must have the same length as dim(dataset)[1]")
          }
      if(length(w)==1){
          if(!w %in% c("even", "bycover"))
           stop("w must be specified, either as 'even' or 'bycover' or a numeric vector")
          if(w=="bycover")
            w1 <- rowSums(x)/sum(x)
         
          if(w=="even"){
            w1 <- rep(1/dim(x)[1], dim(x)[1])
            x <- x/rowSums(x)
           }
          }
      
        ifelse(q1 != 1,
          res[[qq]]$alpha[k] <- (sum(w1*(renyi(x, scale=q1, hill=T)^(1-q1))))^(1/(1-q1)),
          res[[qq]]$alpha[k] <- exp(sum(w1*diversity(x))) )
          res[[qq]]$gamma[k] <- renyi(colSums(x), scale=q1, hill=T)
#          res[[qq]]$gamma[k] <- renyi(colSums( w1*(x/rowSums(x)) ), scale=q1, hill=T)
          res[[qq]]$beta[k] <- res[[qq]]$gamma[k]/res[[qq]]$alpha[k]
        }
      }
     names(res) <- paste("q=",q, sep="")
     if(length(levels(factor))==1){
       res <- t(matrix((unlist(res)), nrow=3, ncol=length(q)))    
       colnames(res) <- c("alpha", "beta", "gamma")
       rownames(res) <- paste(rep("q=", length(q)), q, sep="")
       }
     return(res)
     }