This program is free software

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## 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 the Sorensen-based multiple-site dissimilarity

# beta.SIM computes the Simpson-based multiple-site dissimilarity

# beta.NES computes the Nestedness-based multiple-site dissimilarity

# Some previous functions are needed maxbibj<-function(matrix) {

## nr is the number of rows

nr<-dim(matrix)[1];

## This variable contains the sum of 'max(bi,bj)' on row pairs.

sum.maxbibj<-0.;

## We 'loop' on every different row pairs.

for(i in 1:nr-1) { for(j in (i+1):nr) {

## 'bi' and 'bj' are respectively the number of species appearing

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## only in the ith and the jth site (row).

bi<-sum(matrix[i,]&(!matrix[j,]));

bj<-sum(matrix[j,]&(!matrix[i,]));

## We sum up 'max(bi,bj)' on every different pair of rows.

sum.maxbibj<-sum.maxbibj+max(bi,bj);

} }

## We return the sum sum.maxbibj;

}

minbibj<-function(matrix) { ## nr is the number of rows nr<-dim(matrix)[1];

## This variable contains the sum of 'min(bi,bj)' on row pairs.

sum.minbibj<-0.;

## We 'loop' on every different row pairs.

for(i in 1:nr-1) { for(j in (i+1):nr) {

## 'bi' and 'bj' are respectively the number of species appearing ## only in the ith and the jth site (row).

bi<-sum(matrix[i,]&(!matrix[j,]));

bj<-sum(matrix[j,]&(!matrix[i,]));

## We sum up 'min(bi,bj)' on every different pair of rows.

sum.minbibj<-sum.minbibj+min(bi,bj);

} }

## We return the sum sum.minbibj;

}

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zeroColumn<-function(matrix) { sum<-0;

nc<-dim(matrix)[2];

for(i in 1:nc) if(!sum(matrix[,i])) sum<-sum+1;

if(sum!=0)

warning(sum," missing species. This fact does not affect the result since total number of species is calculated excluding these

columns.",call.=FALSE,immediate.=TRUE);

sum }

beta.SOR<-function(x) { ## x must be a data frame matrix<-as.matrix(x);

## Si is the number of species present in the ith site. We sum all ## these values.

sumSi<-sum(matrix);

## St is the total number of species in all sites, thus the number of columns, excepting if a given

## species is not present at all (in any site), so we must not count this column ## out.

St<-ncol(matrix)-zeroColumn(matrix);

## 'a' is the number of species shared for at least two sites a<-sumSi-St;

index<-(minbibj(matrix)+maxbibj(matrix))/(minbibj(matrix)+maxbibj(matrix)+(2*a));

if(any(matrix>1))

warning("The table contains values >1: the result may be meaningless.",call.=FALSE,immediate. = TRUE);

if(any(matrix<0))

warning("The table contains values <0: the result may be meaningless.",call.=FALSE,immediate. = TRUE);

index;

}

beta.SIM<-function(x) {

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## x must be a data frame matrix<-as.matrix(x);

sumSi<-sum(matrix);

## 'a' is the number of species shared for at least two sites a<-sumSi-St;

index<-minbibj(matrix)/(minbibj(matrix)+a);

if(any(matrix>1))

if(any(matrix<0))

index;

}

beta.NES<-function(x) { ## x must be a data frame matrix<-as.matrix(x);

sumSi<-sum(matrix);

## 'a' is the number of species shared for at least two sites

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a<-sumSi-St;

index<-(a/(minbibj(matrix)+a))*((maxbibj(matrix)-minbibj(matrix))/((2*a) +maxbibj(matrix)+minbibj(matrix)));

if(any(matrix>1))

if(any(matrix<0))

index;

}

setwd("C:/Users/francoro/Ibantxo/Finland/Eddy Co-Denmark/Spatial

study_seagrass_summer2017/Diversity paper/Beta diversity") # set working directory getwd()

dir() # folder in which data-files are stored diversity <- read.csv("diversity2.csv", header=T) data

dir()

##diversity<-read.table(file="diversity.txt", header=T) names (diversity)

str(diversity) #informs us of the status of each variable in a data frame:

attach(diversity) summary(diversity) library(betapart)

### From Baselga and Orme 2012 citation("betapart")

# Compute the three indices for the dataset

# get betapart objects

diversity.core <- betapart.core(diversity[2:31])

# multiple site measures

diversity.multi <- beta.multi(diversity.core)

# sampling across equal sites

diversity.samp <- beta.sample(diversity.core,

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sites=11, samples=31)

# plotting the distributions of components dist.diversity <- diversity.samp$sampled.values

windowsFonts(A=windowsFont("Times New Roman")) par(mar=c(5,5,2,2)) ##margins plot

plot(density(dist.diversity$beta.SOR),

xlim=c(0,1.1), ylim=c(0, 8.2), xlab='ß-diversity', main='', lty = 1, lwd=3, col="black", las=1, cex.lab=2, cex.axis=2, family="A")

lines(density(dist.diversity$beta.SNE), lty=2, lwd=2, col="red") lines(density(dist.diversity$beta.SIM), lty=3, lwd=2, col="blue") savePlot (type="tiff")

# pairwise for diversity across sites pair.diversity <- beta.pair(diversity[2:31])

# plotting clusters

dist.diversity <- diversity.samp$sampled.values

windowsFonts(A=windowsFont("Times New Roman")) par(mar=c(6,7,2,2))

plot(hclust(pair.diversity$beta.sim, method="average"),

hang=-1, main='', sub='', xlab='', ylab='',las=1,cex.lab=2, cex.axis=2,family="A") title(ylab=expression(Height), line=5, cex.lab=2,cex.axis=2, family="A")

title(xlab=expression(beta[sim]), line=2.3,cex.lab=2, cex.axis=2, family="A") savePlot (type="tiff")

par(mar=c(6,7,2,2))

plot(hclust(pair.diversity$beta.sne, method="average"),

hang=-1, main='', sub='',xlab='', ylab='',las=1,cex.lab=2, cex.axis=2,family="A" ) title(ylab=expression(Height), line=5, cex.lab=2,cex.axis=2, family="A")

title(xlab=expression(beta[nes]), line=2.3, cex.lab=2,cex.axis=2, family="A") savePlot (type="tiff")