R help - Jan 2008 - stochastic growth rate (package biopop)

Dear all,

I am running matrix population models using package "popbio".

In a deterministic model {i.e., transition matrix is defined as A <-
matrix(c(0.70, 0.70,0.35,0.50), nrow=2,byrow=TRUE}, population growth rate
can be estimated from the dominant eigenvalue {command
"eigen.analysis"}.

However, I cannot figure out the way to compute the asymptotic stochastic
population growth rate using ?popbio?. I would like to perform a stochastic
model in which my demographic rates are sampled from beta distribution with
known mean and SD. For example, rather than 0.50 (4th term of my matrix), I
want to sample this parameter from a beta function at each time-step {e.g.,
betaval(0.5, 0.05)}. Then I want to run the model for 1000 time steps (or
more) and estimate the asymptotic stochastic growth rate. Is there a command
that enable this kind of modelling?

Thank you,

Best wishes,

Privalan

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privalan wrote:
> 
> However, I cannot figure out the way to compute the asymptotic stochastic
> population growth rate using ?popbio?. I would like to perform a
> stochastic model in which my demographic rates are sampled from beta
> distribution with known mean and SD. For example, rather than 0.50 (4th
> term of my matrix), I want to sample this parameter from a beta function
> at each time-step {e.g., betaval(0.5, 0.05)}. 
> 
I guess you can't do this right now, but it shouldn't be too difficult
to
add an option to accept an expression as input to stoch.growth.rate or
stoch.projection in the next version of popbio.

Maybe this will get you started.

A<-expression(c(0.70, 0.70,0.35, betaval(0.5, 0.05)))

## stoch.growth.rate(A)  ## this doesn't work yet, so try...

matrix(eval(A), nrow=2,byrow=TRUE)
 
## code from simulation section in stoch.growth.rate 
##  just replace A with matrix(eval(A), nrow=2,byrow=TRUE) 
maxt<-10000
r<-numeric(maxt)
n0<-c(1,1)

 for (t in 1:maxt)
   {
      n0<- matrix(eval(A), nrow=2,byrow=TRUE)  %*% n0
      N<-sum(n0)
      r[t]<-log(N)
      n0<-n0/N
   }
   loglsim<-mean(r)
   dse<-1.96*sqrt(var(r)/maxt)
   CI<-c(loglsim-dse, loglsim+dse)

 loglsim
#[1] 0.09982282
 CI
#[1] 0.0994700 0.1001757


# check
 eigen.analysis( matrix(c(0.70, 0.70,0.35,0.50), nrow=2,byrow=TRUE))$lambda1
 exp(loglsim)


Thanks,

Chris





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