#' Taxonimic betadiversity among several communities
#'
#' Calculate taxonomic trait beta diversity among all pairwise communities using Carvalho et al. 2012 decomposition
#' and creates a dist object.
#'
#' @param W matrix containing the abundances of the species per site (or presence-absence,
#' i.e. 0 or 1). Rows are sites and species are columns. NA not tolerated. \code{}
#'
#' @return Btot Total Beta diversity dist object
#' @return B_3 Beta diversity due to replacement dist object
#' @return Brich Beta diversity due to richness diferences dist object
#' @return quality the ouptput will print the quality of the dendogram representation.
#' clustering performance is assessed by the correlation with the cophenetic distance
#'
#'
#' @export
#'
#' @examples
#' ex1 <- beta_dist(W = dummy$abun)
#' ex1
#'
beta_dist = function(W){
dWN = matrix(NA, ncol = nrow(W), nrow= nrow(W))
colnames(dWN) = rownames(W)
rownames(dWN) = rownames(W)
dBtot = dWN
dB_3 = dWN
dBrich = dWN
for(i in 1:nrow(W)){
for(j in 1:nrow(W)){
partition = beta_part(names(which(W[i,] > 0)),names(which(W[j,] > 0)))
dBtot[i,j] = partition$Btot
dB_3[i,j] = partition$B_3
dBrich[i,j] = partition$Brich
}
}
distances = list(Btot = dBtot, B_3 = dB_3, Brich = dBrich)
distances = lapply(distances,as.dist)
return(distances)
}
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