demogR (version 0.6.0)

secder: secder

Description

Calculates the second derivatives of the dominant eigenvalue of the demographic projection matrix for all non-zero transitions with respect to one specified transition.

Usage

secder(A, k, l)

Arguments

A

demographic projection matrix

k

row index for the specified transition

l

column index for the specified transition

Value

A square matrix of the same rank as A where each element \(s_{ij}\) is the second derivative of the dominant eigenvalue of A, \(\partial^2 \lambda/\partial a_{ij} \partial a_{kl}\).

Details

See Caswell (1996, 2001) for details on second derivatives of the dominant eigenvalue.

References

Caswell, H. 1996. Second derivatives of population growth rate: Calculation and applications. Ecology 77 (3):870-879.

Caswell, H. 2001. Matrix population models: Construction, analysis, and interpretation. 2nd ed. Sunderland, MA: Sinauer.

See Also

fullsecder, elassens, eigen.analysis, stoch.sens

Examples

# NOT RUN {
## eigenvalue second derivatives of the US projection matrix from 1967
## with respect to infant survival
data(goodman)
ult <- with(goodman, life.table(x=age, nKx=usa.nKx, nDx=usa.nDx))
mx <- goodman$usa.bx/goodman$usa.nKx
usa <- leslie.matrix(lx=ult$nLx,mx=mx)

sd21 <- secder(usa,2,1)
# }