looping and plotting a Lefkovitch/Leslie projection

These are great examples.  Thanks so much guys!


On Thu, Nov 29, 2012 at 1:41 PM, Marc Taylor <marchtaylor at gmail.com> wrote:

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 <aghaynes at gmail.com> 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: aghaynes at gmail.com
Mobile: +41794385586
Skype: aghaynes


On 29 November 2012 17:07, Jeffrey Stratford
<jeffrey.stratford at wilkes.edu>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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--
********************************************************
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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