## Varying r in Bedding host parasitoid model


##  preliminaries
Nt<- 1000
Pt<- 20
alpha<-0.002
r<-3
c<-1
K<-2000 
Beddington<-function(fNt,fPt,fr,falpha,fK,fc){
NtPlus1<-fNt*exp((fr*(1-(fNt/fK)))-(falpha*fPt))
PtPlus1<-fc*fNt*(1-(exp(-falpha*fPt)))
answer<-c(NtPlus1,PtPlus1)
answer
}

hosts<-Nt #starting these two vectors with the initial host and parasitoid populations
parasitoids<-Pt
number_of_generations<-1000
for(i in 1: number_of_generations){
answer<-Beddington(Nt,Pt,r,alpha,K,c)
hosts<-c(hosts,answer[1])
parasitoids<-c(parasitoids,answer[2])
Nt<-answer[1]
Pt<-answer[2]
} # end of i loop

plot(1:length(hosts), hosts, ylim=c(0,max(hosts)), col= "green", pch=20, xlab="Generations", ylab="Population size",main="Parasitoid-Host Population Dynamics")
points(1:length(hosts), parasitoids,col="red", pch=20)
points (number_of_generations/4.5, max(hosts)*1.07, col= "green", pch=20, xpd=NA)
text (number_of_generations/3.5, max(hosts)*1.07, "Hosts", xpd=NA)
points (number_of_generations/2, max(hosts)*1.07, col= "red", pch=20, xpd=NA)
text (number_of_generations/1.65, max(hosts)*1.07, "Parasitoids", xpd=NA)


Part 1
# in our current model increasing r to 3.472 is about the limit
# incresing alpha canlead to chaotic behaviur
Part 2


# here alpha is set to 0.003

alpha<-0.003

par(mfrow=c(2,2))

# top left
plot(1:length(hosts), hosts, ylim=c(0,max(hosts)), col= "green", pch=20, xlab="Generations", ylab="Population size",main="Parasitoid-Host Population Dynamics")
points(1:length(hosts), parasitoids,col="red", pch=20)
points (number_of_generations/4.5, max(hosts)*1.07, col= "green", pch=20, xpd=NA)
text (number_of_generations/3.5, max(hosts)*1.07, "Hosts", xpd=NA)
points (number_of_generations/2, max(hosts)*1.07, col= "red", pch=20, xpd=NA)
text (number_of_generations/1.65, max(hosts)*1.07, "Parasitoids", xpd=NA)

# top right
plot(hosts,parasitoids,pch=20,xlab="Host population size",ylab="Parasitoid population size",main="Parasitoid-Host Phase Plot", cex=0.5)

# bottom left
plot(hosts,parasitoids,pch=20,xlab="Host population size",ylab="Parasitoid population size", main="Parasitoid-Host Phase Plot", cex=0.5)
lines(hosts,parasitoids)

# bottom # bottom left
plot(hosts/parasitoids,log(hosts),pch=20,xlab="Host population size",ylab="Host:parasitoid ratio", main="Parasitoid-Host Ratio Plot", cex=0.5)