Disturbance and the Lotka Volterra competition model

lotka-volterra.png

One of the works that provided constant inspiration both as an undergraduate and graduate student was Huston’s huge 1994 monograph. Despite some inevitable repetition in a book of this length I have continued to find new ideas in it over the years. The book contained a very simple demonstration of the intermediate disturbance hypothesis using the Lotka Volterra competition equations that I continue to use in classes. It can be implemented very concisely in R. The idea is simple. Reset the classic competition equations at periodic intervals and see how it affects the balance between species with r or K strategies. A very simple model with important implications.

R<-c(0.1,0.12,0.15,0.2,0.3)
K<-c(1000,800,600,200,100)

Run<-function(runtime=100,freq=101,intensity=0.1){
N<-numeric(runtime*5)
N<-matrix(N,nrow=runtime,ncol=5)
N[1,]<-10

for (i in 2:runtime){
 Totpop<-sum(N[i-1,])
  for (j in 1:5){
   N[i,j]<-N[i-1,j]+N[i-1,j]*R[j]*(1-Totpop/K[j])
    }
    
 if(!i%%freq){
  N[i,]<-N[i,]*intensity
 }
}
res<-data.frame(N)
res
}
#####################################
par(mfcol=c(2,2))
res<-Run()
matplot(1:100,res,type="l",xlab="Time",ylab="Populations",lwd=2)
title("No disturbance")
res<-Run(freq=60)
matplot(1:100,res,type="l",xlab="Time",ylab="Populations",lwd=2)
title("Infrequent disturbance")
res<-Run(freq=25)
matplot(1:100,res,type="l",xlab="Time",ylab="Populations",lwd=2)
title("Intermediate disturbance")
res<-Run(freq=12)
matplot(1:100,res,type="l",xlab="Time",ylab="Pobulations",lwd=2)
title("Frequent disturbance")

Reference
Huston, M.A. 1994. Biological Diversity: The Coexistence of Species on Changing Landscapes. Cambridge University Press, 708 pp.

Source In Spanish here …lotka-volterra.doc

2 thoughts on “Disturbance and the Lotka Volterra competition model

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