R/FD_dendro.R

In ibartomeus/fundiv: tools to calculate several functional trait diversity indexes

#' 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
}