```
#' Heuristic algorithm optimising the accumulation of Phylogenetic Diversity
#' from aggregating sites
#'
#' A heuristic algorithm that seeks to prioritise sites for conservation by
#' optimising the accumulation of Phylogenetic Diversity (PD). PD will acumulate
#' most rapidly when the samples are pooled in a particular sequence such that
#' the gain in PD of each additional sample is maximised.
#' @param x is the community data given as a \code{data.frame} or \code{matrix}
#' with species/OTUs as columns and samples/sites as rows (like in the
#' \code{vegan} package). Columns are labelled with the names of the
#' species/OTUs. Rows are labelled with the names of the samples/sites. Data
#' can be either abundance or incidence (0/1). Column labels must match tip
#' labels in the phylogenetic tree exactly!
#' @param phy is a rooted phylogenetic tree with branch lengths stored as a
#' phylo object (as in the \code{ape} package) with terminal nodes labelled
#' with names matching those of the community data table. Note that the
#' function trims away any terminal taxa not present in the community data
#' table, so it is not necessary to do this beforehand.
#' @param iterations is the number of iterations of the algorithm (to resolve
#' ties). Default is 1.
#' @details \code{phylorebelo} takes community data and a phylogenetic tree
#' (rooted and with branch lengths) and calculates the optimal sequence of
#' samples for accumulating Phylogenetic Diversity (PD). The algorithm starts
#' by first selecting the sample with the highest PD. It will then choose the
#' sample most complementary to the first (giving the largest gain in PD).
#' Additional samples are chosen based on their complementarity to the set
#' already chosen until all sites have been selected. At each step, ties are
#' resolved by choosing at random from the available equally complementary
#' options. The algorithm is an adaptation of that described by Rebelo &
#' Siegfried (1992). The phylogenetic version implemented here is that used by
#' Asmyhr et al. (2014).
#' @return A list of two numeric matrices. The first matrix gives the optimised
#' sequence (rank) of the samples as rows, with a column for each iteration of
#' the algorithm. The second matrix is gives the corresponding gains in PD for
#' each sample (row) and iteration.
#' @importFrom ape drop.tip
#' @references \itemize{ \item{Asmyhr MG, Linke S, Hose G, & Nipperess DA. 2014.
#' Systematic Conservation Planning for Groundwater Ecosystems Using
#' Phylogenetic Diversity. \emph{PLoS One} 9: e115132} \item{Rebelo AG &
#' Siegfried WR. 1992. Where should nature reserves be located in the Cape
#' Floristic Region, South Africa? Models for the spatial configuration of a
#' reserve network aimed at maximizing the protection of floral diversity.
#' \emph{Conservation Biology} 6: 243–252.}}
#' @export
#'
#' @examples
phylorebelo <- function (x, phy, iterations=1) {
### step 1: matching taxa and trimming the tree to match the community data
### table thus creating a "community tree" (sensu Cam Webb).
taxon_check <- phylomatchr(x,phy)
if(length(taxon_check[[2]])>0) {
stop('The following taxa in the community data table were not found on the',
' tips of the tree: ', paste(taxon_check[[2]], collapse=', '),
'.\nPlease fix your taxonomy!',
call.=FALSE)
}
if(length(taxon_check[[1]])>0) {
warning(length(taxon_check[[1]]), " taxa were not in x, and were trimmed",
" from the tree prior to calculation of PD.")
phy <- drop.tip (phy, taxon_check[[1]])
}
### step 2: converting a community tree into a MRP matrix
# A MRP matrix, used in supertree methods, is where the membership of an OTU
# in a clade spanned by a branch is indicated by a 0 (no) or 1 (yes). Unlike
# supertree MRP matrices, our matrix includes terminal branches. using Peter
# Wilson's function
phylomatrix <- FastXtreePhylo(phy)$H1
# this script fills a matrix of 0's with 1's corresponding to the incidence of
# an OTU on a particular branch.
### step 3: re-ordering the OTUs of the occurrence table and MRP matrix to
### match.
phylomatrix <- phylomatrix[order(phy$tip.label), ]
x <- x[ ,order(colnames(x))]
# data are sorted to a common ordering standard, that is alphabetic order, so
# that OTUs match up.
### step 4: creating a community phylogeny matrix from a MRP matrix and an
### occurrence matrix
x <- as.matrix(x)
phylomatrix <- x %*% phylomatrix
# the above code performs simple matrix multiplication to produce a composite
# branch by sample matrix (the community phylogeny matrix) where each cell now
# contains either OTU richness or total abundance for each branch in each
# sample.
### step 5: converting a community phylogeny matrix into an incidence (0/1)
### form
phylomatrix[phylomatrix>1] <- 1
### step 6: run the heuristic
sequence_matrix <- matrix(nrow=nrow(x),ncol=iterations)
rownames(sequence_matrix) <- rownames(x)
gains_matrix <- matrix(nrow=nrow(x),ncol=iterations)
rownames(gains_matrix) <- rownames(x)
for(i in 1:iterations) {
PD <- phylomatrix %*% phy$edge.length
rank_PD <- rank(PD,ties.method="random") # because of this randomness, need to repeat a large no. of times
winner <- which(rank_PD==max(rank_PD))
gains <- PD[winner]
sequence <- winner
for(j in 1:(nrow(x)-1)) {
reserved <- phylomatrix[sequence,]
if(length(sequence)>1) {
reserved <-colSums(reserved)
}
complement <- phylomatrix
complement[,which(reserved>0)] <- 0
PD <- complement %*% phy$edge.length
PD[sequence] <- -1
rank_PD <- rank(PD,ties.method="random")
winner <- which(rank_PD==max(rank_PD))
sequence <- c(sequence,winner)
gains <- c(gains,PD[winner])
}
sequence_matrix[sequence,i] <- 1:nrow(x)
gains_matrix[sequence,i] <- gains
}
### step 7: output the matrices
return(list(sequence_matrix,gains_matrix))
}
```

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