R/pairwise_betadiv_Baselga2009.R

In CeresBarros/ToolsCB: Ceres's Useful R Functions

##  Copyright (C) 2009 Andrés Baselga   <andres.baselga@usc.es>
##
##
##  This program is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  This program is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with this program; if not, write to the Free Software
##  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

# Three functions are included:

# beta.sor computes a distance matrix using Sorensen pair-wise dissimilarity
# beta.sim computes a distance matrix using Simpson pair-wise dissimilarity
# beta.nes computes a distance matrix using Nestedness-resultant pair-wise
# dissimilarity

#' Sorensen's beta-diversity
#' @param x a `data.frame`
#' @export
#' @importFrom stats as.dist
beta.sor <- function(x){
  ## x must be a data frame
  matr<-as.matrix(x);
  nr<-dim(matr)[1];
  result<-matrix(nrow=nr,ncol=nr);
  rownames(result)<-rownames(matr);
  colnames(result)<-rownames(matr);
  for(i in 1:nr) {
    for(j in i:nr) {
      bij<-sum(matr[i,]&(!matr[j,]));
      cij<-sum(matr[j,]&(!matr[i,]));
      aij<-sum(matr[i,]&(matr[j,]));
      Sorensen.ij<-(bij+cij)/((2*aij)+bij+cij);
      result[i,j]<-Sorensen.ij;
      result[j,i]<-Sorensen.ij;
    }
  }
  d <- as.dist(result);
  d
}

#' Simpsons's beta-diversity
#' @param x a `data.frame`
#' @export
#' @importFrom stats as.dist
beta.sim <- function(x){
  ## x must be a data frame
  matr<-as.matrix(x);
  nr<-dim(matr)[1];
  result<-matrix(nrow=nr,ncol=nr);
  rownames(result)<-rownames(matr);
  colnames(result)<-rownames(matr);
  for(i in 1:nr) {
    for(j in i:nr) {
      bij<-sum(matr[i,]&(!matr[j,]));
      cij<-sum(matr[j,]&(!matr[i,]));
      aij<-sum(matr[i,]&(matr[j,]));
      Simpson.ij<-min(bij,cij)/(min(bij,cij)+aij);
      result[i,j]<-Simpson.ij;
      result[j,i]<-Simpson.ij;
    }
  }
  d<-as.dist(result);
  d
}

#' Nested beta-diversity
#' @param x a `data.frame`
#' @export
#' @importFrom stats as.dist
beta.nes <- function(x){
  ## x must be a data frame
  matr<-as.matrix(x);
  nr<-dim(matr)[1];
  result<-matrix(nrow=nr,ncol=nr);
  rownames(result)<-rownames(matr);
  colnames(result)<-rownames(matr);
  for(i in 1:nr) {
    for(j in i:nr) {
      bij<-sum(matr[i,]&(!matr[j,]));
      cij<-sum(matr[j,]&(!matr[i,]));
      aij<-sum(matr[i,]&(matr[j,]));
      nestedness.ij<-((max(bij,cij)-min(bij,cij))/((2*aij)+bij+cij))*(aij/(min(bij,cij)+aij));
      result[i,j]<-nestedness.ij;
      result[j,i]<-nestedness.ij;
    }
  }
  d<-as.dist(result);
  d
}