After a short exchange with the original questioner, I wrote the following function to calculate the elasticities of lower level variables in population transition matrices (Leslie matrices etc.) Perhaps it will be of use to others. There is no error-checking, so use with care. Users should consult Caswell (2001) for reference.

Cheers,

Simon.

# example values to construct leslie matrix

vl <- list(f1=1, f2=4, s0=.6, s=.4, v=.9, sigma=.5)

# Expressions for each matrix element
F1 <- expression(sigma*s0*f1)
F2 <- expression(sigma*s0*f2)
S <- expression(s)
V <- expression(v)
el <- c(F1, F2, S, V)

elas.var <- function (elements, varlist) {
  # elements should be a vector of expressions corresponding to the elements
  # of the leslie matrix, in terms of the variables in varlist

  require(demogR)
  res <- vector("list", length(varlist))
  deriv.funcs <- sapply(elements, deriv, namevec=names(varlist),
function.arg=TRUE)
  devs <- lapply(deriv.funcs, function (x) do.call(x, varlist))
  leslie.mat <-  matrix(as.numeric(devs), nrow=sqrt(length(elements)),
byrow=TRUE)
  eig <- eigen.analysis(leslie.mat)

  for (i in 1:length(varlist)) {
    derivs <- matrix( as.numeric(lapply(devs, function (x)
x@gradient[i])), nrow=sqrt(length(elements)), byrow=TRUE)
    res[[i]] <- varlist[[i]]/eig$lambda1*sum(derivs*eig$sensitivities)
    names(res)[i] <- names(varlist)[i]
  }
  res
}

# example output

> elas.var(el, vl)
$f1
[1] 0.06671376

$f2
[1] 0.2346064

$s0
[1] 0.3013201

$s
[1] 0.2346064

$v
[1] 0.4640735

$sigma
[1] 0.3013201


Simon Blomberg, BSc (Hons), PhD, MAppStat. 
Lecturer and Consultant Statistician 
Faculty of Biological and Chemical Sciences 
The University of Queensland 
St. Lucia Queensland 4072 
Australia 
T: +61 7 3365 2506 
email: S.Blomberg1_at_uq.edu.au

Policies:
1.  I will NOT analyse your data for you.
2.  Your deadline is your problem.

The combination of some data and an aching desire for 
an answer does not ensure that a reasonable answer can 
be extracted from a given body of data. - John Tukey.










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