#### ExerciseBox 25.1

hypotenuse<-function(x1,y1,x2,y2) sqrt((x1-x2)^2+(y1-y2)^2)


### part 1 random Weiss

plot(NULL, axes=F, xlim=c(1,1000), ylim=c(1,1000))
n<-150
xdata<-sample(1:1000,n)
ydata<-sample(1:1000,n)
diameter<-rnorm(n,mean=2,sd=1)
diameter<-abs(diameter)
points(xdata,ydata,pch=19,col="darkred",cex=diameter*0.2)

distances<-matrix(nrow=n,ncol=n) 
for(i in 1:n){
	for(j in 1:n){
	distances[i,j]<-hypotenuse(xdata[i],ydata[i],xdata[j],ydata[j])
	}}
NNDs<-NULL
for(i in 1:n) NNDs<-c(NNDs,min(distances[i,which(distances[i,]>0)]))
# hist(NNDs, col="darkred")

plot(sort(NNDs)^2,-log(1-((1:n)/(n+1))),ylab="Weiss Index",xlab="NND^2",pch=18,main="Weiss plot of anemone spacing")
lines(sort(NNDs)^2,-log(1-((1:n)/(n+1))),col="red") 

## Part 2 repeating 100 times

plot(NULL,ylab="Weiss Index",xlim=c(1,15000),ylim=c(0,5),xlab="NND^2",pch=18,main="Weiss plot of random points")
for(k in 1:100){
xdata<-sample(1:1000,n)
ydata<-sample(1:1000,n)
distances<-matrix(nrow=n,ncol=n) 
for(i in 1:n){
	for(j in 1:n){
	distances[i,j]<-hypotenuse(xdata[i],ydata[i],xdata[j],ydata[j])
	}}
NNDs<-NULL
for(i in 1:n) NNDs<-c(NNDs,min(distances[i,which(distances[i,]>0)]))
xWeiss<-sort(NNDs)^2
yWeiss<--log(1-((1:n)/(n+1)))
lines(xWeiss,yWeiss,col="darkred")
} # k 100 replicates

## Part 3 all0wing for real anemone pedaldisc size

data<-read.csv("ActiniaXYdata.csv",header=TRUE)
data$X<-round(data$X,1); data$Y<-round(data$Y,1)
#  round(data,1)
pdd<-c(4.9,1.3,5.3,1.6,3.9,3.8,1.8,3.5,3,2.9,3,3.9,3,3.3,2.1,4.5,3.2,4.2,6.1,3.8,4,4,3.8,1.5,3.9,4.3,4.1,3.9,1.8,3.2,4.2,3.2,1.9,4,2,3.8,1.5,5.9,3.9,4.1,3,3.6,3.2,3.8,3.9,2.5,5.5,3,1.5,3.9,2.5,4,1.2,4,3.9,3.7,1.8,4.4,3.2,3.9,3.7,3.7,4.4,3.9,4.6,4.2,5,4,4.6,5,3.7,3,4.1,1.5,4,3.2,3,1.7,4,3,3.1,3.8,4.2,5,2,4,4.1,3.9,3.1,3,1.6,3.7,3.5,3,3.8,3.9,4,4.9)

data<-cbind(data,pdd)
(plot(data, pch=19, xlim=c(0,50),ylim=c(0,50),col="darkred", cex=pdd/1.6, xlab="X coordinate (cm)", ylab="Y coordinate (cm)") #cex is adjusted to scale diameter of anemones
rect(0,0,50,50,lty=4,lwd=0.6)
hypotenuse2<-function(x1,y1,x2,y2,d1,d2) sqrt((x1-x2)^2 +(y1-y2)^2)-(d1+d2)*0.5
N<-nrow(data)
distances<-matrix(nrow=N,ncol=N) #the cells of the matrix are automatically filled with NAs if nothing is specified
for (i in 1:N){
for(j in 1:N){
distances[i,j]<-hypotenuse2(data$X[i],data$Y[i],data$X[j],data$Y[j],data$pdd[i],data$pdd[j])
}}
NNDs<-NULL
for  (i in 1:N) NNDs<-c(NNDs, min(distances[i,which(distances[i,]>0)]))
RE<-1/(2*sqrt(0.0392)) 
R<-mean(NNDs)/RE
t.test(NNDs, mu=RE)
plot(sort(NNDs)^2,-log(1-((1:N)/(N+1))),ylab="Weiss Index",xlab="NND^2",pch=18,main="Weiss plot of anemone spacing")
lines(sort(NNDs)^2,-log(1-((1:N)/(N+1))),col="red")