#' Dendrogram-Based Functional Diversity Indices
#'
#' Calculate functional trait diversity for a set of communities using Ptchey and Gaston 2002 index and
#' its weighted version used in Gagig et al. In prep.
#'
#' @param S matrix or data frame of functional traits. Traits can be numeric, ordered,
#' or factor. NAs are tolerated.\code{}
#' @param A matrix containing the abundances of the species in S (or presence-absence,
#' i.e. 0 or 1). Rows are sites and species are columns. NA not tolerated. The number of
#' species (columns) in A must match the number of species (rows) in S. In addition,
#' the species labels in A and S must be identical and in the same order.\code{}
#' @param w vector listing the weights for the traits in x. Can be missing,
#' in which case all traits have equal weights.\code{}
#' @param Distance.method metric to calculate the species distance matrix. Only Gower is
#' implemented. \code{}
#' @param ord character string specifying the method to be used for ordinal traits
#' (i.e. ordered). "podani" refers to Eqs. 2a-b of Podani (1999), while "metric"
#' refers to his Eq. 3. See gowdis for more details.\code{}
#' @param Cluster.method Distance method used to produce the tree. UPGMA="average" is
#' usually giving th ebest results (Podani et al. 2011)\code{}
#' @param stand.x ogical; if all traits are numeric, should they be standardized
#' to mean 0 and unit variance? If not all traits are numeric, Gower's (1971)
#' standardization by the range is automatically used; see gowdis for more details.\code{}
#' @param stand.FD logical; should FD be standardized by the max FD, so that FD
#' is constrained between 0 and 1?\code{}
#' @param Weigthedby character string indicating if should be weighted by `abundance`
#' or `biomassValue`. If biomassValue is in length units for Carabids or bees,
#' use options `biomasCarabids` or `biomasBees` to autmatically convert to mass.\code{}
#' @param biomassValue numerical vector with body weigh (or length) values for each species
#' in the same order as species are provided. It can also be a matrix or data
#' frame with one mass value for each community and species (both communities and species
#' arranged like in A). \code{}
#'
#' @return comm vector with the name of the community
#' @return n_sp vector listing the number of species for each community
#' @return n_tr vector listing the number of traits used
#' @return FDpg vector listing FDpg (petchey and gaston) for each community
#' @return FDw vector listing FD weighthed by species relative abundances/biomass
#' in each community
#' @return FDwcomm vector listing FD weighthed by species abundances/biomass
#' across all communities
#' @return qual.FD vector repeating the quality of the dendogram representation.
#' clustering performance is assessed by the correlation with the cophenetic distance
#'
#'
#' @export
#'
#' @examples
#' ex1 <- FD_dendro(S = dummy$trait, A = dummy$abun, Cluster.method = "average", ord = "podani",
#' Weigthedby = "abundance")
#' ex1
FD_dendro <- function(S, A, w = NA, Distance.method = "gower", ord= c("podani", "metric"),
Cluster.method = c(ward="ward",single="single",complete="complete",
UPGMA="average",UPGMC="centroid",WPGMC="median",
WPGMA="mcquitty"), stand.x = TRUE, stand.FD = FALSE,
Weigthedby = c("abundance", "biomasCarabids", "biomasBees", "biomassValue"),
biomassValue = NA){
require(FD)
require(cluster)
require(vegan)
Out <- data.frame(comm = rep(NA,nrow(A)),
n_sp = rep(NA,nrow(A)),
n_tr = rep(NA,nrow(A)),
FDpg = rep(NA,nrow(A)),
FDw = rep(NA,nrow(A)),
FDwcomm = rep(NA,nrow(A)),
qual.FD = rep(NA,nrow(A))
)
Out$comm <- rownames(A)
Out$n_tr <- ncol(S)
#richness
Arich <- as.matrix(A)
Arich[which(Arich > 0)] <- 1
Out$n_sp <- rowSums(Arich, na.rm = TRUE)
if(is.na(w)[1]){w <- rep(1,ncol(S))}
#Obtain the distance matrix
if(Distance.method == "gower"){
D <- gowdis(S, w = w, ord= ord)
}else{
if (stand.x == TRUE){
S2 <- scale(S, center = TRUE, scale = TRUE)
D <- dist(S2, method = Distance.method)
}else{
D <- dist(S, method = Distance.method)
}
}
#Obtain the general dendrogram
tree <- hclust(D, method = Cluster.method)
plot(tree)
#Get the total branch length
xtree <- Xtree(tree)
#calculate clustering performance by using correlation between the cophenetic distance
c_distance <- cor(D,cophenetic(tree))
Out[, 7] <- rep(c_distance, nrow(Out))
#if Weigthedby is not abundance, transform weight to biomass
AA <- A
if(Weigthedby != "abundance"){
if(Weigthedby == "biomasCarabids"){
biomassValue2 <- Jelaska(biomassValue)
}
if(Weigthedby == "biomasBees"){
biomassValue2 <- Cane(biomassValue)
}else{
biomassValue2 <- biomassValue
}
#if biomassValue2 is a marix (with a different value for each community /species)
if(is.vector(biomassValue2)){
for(j in 1:ncol(A)) AA[,j] <- A[,j]*biomassValue2[j]
}else{
AA <- AA * biomassValue2
}
}
#create an AFw matrix of relative abundances (/by max)
AFw <- AA
for(k in 1:nrow(AA)){
AFw[k,] <- AA[k,]/max(AA[k,])
}
#and also weigthed by total
AFcomm <- AA
for(k in 1:nrow(AA)){
AFcomm[k,] <- AA[k,]/max(AA)
}
#Calculate FD for each community
for(i in 1:nrow(A)){
species_in_C <- ifelse(A[i,]>0, 1, 0)
select_xtree <- xtree$H1[which(species_in_C > 0),]
if(is.array(select_xtree) == TRUE){
i.primeC <- ifelse(colSums(select_xtree)>0, 1, 0)
} else{
i.primeC <- select_xtree
}
Out[i,4] <- sum(i.primeC*xtree$h2.prime)
##calculate Fw
#Substitute all branches where a given species is present (=1) by its weigth
xtree.weigths <- xtree$H1
for(k in 1:nrow(S)){
xtree.weigths[k,] <- ifelse(xtree$H1[k,] > 0, AFw[i,k], 0)
}
#Get the total weigthing for each branch in a vector (i.primeW)
i.primeW <- c(1:ncol(xtree.weigths))
for(k in 1:ncol(xtree.weigths)){
#For each branch chunk, take the mean weight,
#This is equivalent to a weighted mean of the branch lenght contribution
if(sum(xtree.weigths[which(xtree.weigths[,k] > 0),k]) != 0){
i.primeW[k] <- mean(xtree.weigths[which(xtree.weigths[,k] > 0),k], na.rm = TRUE)
}else{
i.primeW[k] <- 0
}
}
#FDw is the sum of the product of i.primeW (weigth) and h2.prime (branch length)
Out[i,5] <- sum(i.primeW*xtree$h2.prime)
##Calculate FDwcom
#Substitute all branches where a given species is present (=1) by its weigth
#now is raw species numbers... here we divide by the max across comunities
#that takes into account the abundance.
xtree.weigths <- xtree$H1
for(k in 1:nrow(S)){
xtree.weigths[k,] <- ifelse(xtree$H1[k,] > 0, AFcomm[i,k], 0)
}
#Get the total weigthing for each branch in a vector (i.primeW)
i.primeW <- c(1:ncol(xtree.weigths))
for(k in 1:ncol(xtree.weigths)){
if(sum(xtree.weigths[which(xtree.weigths[,k] > 0),k]) != 0){
i.primeW[k] <-mean(xtree.weigths[which(xtree.weigths[,k] > 0),k], na.rm = TRUE)
}else{
i.primeW[k] <- 0
}
}
#FD is the sum of the product of i.primeW and h2.prime
Out[i,6] <- sum(i.primeW*xtree$h2.prime)
}
#standardize FD if needed
if(stand.FD == TRUE){
Out[,4] <- Out[,4]/max(Out[,4])
}
Out
}
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.