Hello Jeffrey.
I have done something similar for a course on "Modelling in Conservation
Biology". Here is a simple example of an age-based Leslie model with three
classes:
L=matrix(c(0.5, 0.6666, 0, 1.0, 0, 0.3333, 0.75, 0, 0), nrow=3, ncol=3)
time=10
No=c(2,0,0)
POP=c(No)
Nt=No
for (i in 1:time){
Nt = drop(L %*% Nt)
POP=rbind(POP,Nt)
}
plot(0:time,POP[,1], type="l", ylim=range(POP), ylab="numbers", xlab="time")
for (i in 2:length(POP[1,])){
lines(0:time,POP[,i],col=i)
}
legend(0.5*time,max(POP),
c(paste("class",(1:length(No)))),
lwd=1,
col=c(1:length(No)))
###Eigenvalues (info on pop trajectory and distribution)
sum(POP[(time),])/sum(POP[(time-1),]) # the rate of population change
between the last two iterations
x=eigen(L)
x
#dominant eigen value
abs(x$values)
#The stable population distribution is specified by the 1st vector. The
proportion of each element of the vector sum equals the corresponding class
proportions.
abs(x$vectors[,1]/sum(x$vectors[,1]))
Another nice example from a real study is that of Crouse et al. (1987). the
paper comes with all the information needed to reproduce a 7 stage Usher
matrix model (i.e. individuals have the possibility to stay in the same
class and not advance).
Crouse, Deborah T., Larry B. Crowder, and Hal Caswell. "A stage-based
population model for loggerhead sea turtles and implications for
conservation." *Ecology* 68.5 (1987): 1412-1423.
Cheers,
Marc
On Thu, Nov 29, 2012 at 5:36 PM, Alan Haynes <[email protected]> wrote:
> Is this what you want?
>
> Your code
> #the data
> A <- c(0,0,100, 0.4,0,0, 0,0.7,0)
> #create a matrix from the data
> L <- matrix(A, nrow=3, byrow=T)
> #check out the matrix
> L
> #the starting population
> n_0 <- c(1000, 400, 100)
> #the next generation
> #n_1 <- L %*% n_0
> #check it out
> #n_1
> #run another generation
> #n_2 <- L %*% n_1
> #check it out
> #n_2
>
> my code:
>
> pops <- list()
> pops[[1]] <- n_0
>
> for(i in 2: 20){ # gives 19 generations
> pops[[i]] <- L %*% pops[[i-1]] # assign your matrix mult to a list slot
> }
> pops[[20]] # the 19th generation (because the first slot is the 0
> generation)
>
> HTH
>
> Alan
>
> --------------------------------------------------
> Email: [email protected]
> Mobile: +41794385586
> Skype: aghaynes
>
>
> On 29 November 2012 17:07, Jeffrey Stratford
> <[email protected]>wrote:
>
> > Hi everyone,
> >
> > I have a two part population lab in my Ecology course. The first part was
> > showing exponential and logistic growth. For the second section, I would
> > like to introduce them to Leslie/Lefkovitch models. I'm able to multiply
> > the matrix and the age classes step by step but I would like to have them
> > run projections for as many generations as they choose and show the
> > population structure by plotting the number in each age class over time.
> >
> > I know software programs like Populus do this but I would like to have
> them
> > (and myself) learn the programming.
> >
> > Here's what I have so far:
> >
> > #the data
> > A <- c(0,0,100, 0.4,0,0, 0,0.7,0)
> > #create a matrix from the data
> > L <- matrix(A, nrow=3, byrow=T)
> > #check out the matrix
> > L
> > #the starting population
> > n_0 <- c(1000, 400, 100)
> > #the next generation
> > n_1 <- L %*% n_0
> > #check it out
> > n_1
> > #run another generation
> > n_2 <- L %*% n_1
> > #check it out
> > n_2
> >
> >
> > Many thanks,
> >
> > Jeff
> > --
> > ********************************************************
> > Jeffrey A. Stratford, PhD
> > Department of Biology and Health Sciences
> > Wilkes University, PA 18766 USA
> > 570-332-2942
> > http://web.wilkes.edu/jeffrey.stratford/
> > ********************************************************
> >
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