popbio (version 2.4.4)

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

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

Function copied from demogR package since it was removed from CRAN. See section 9.7 in Caswell 2001.

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

eigen.analysis

Examples

# NOT RUN {
## eigenvalue second derivatives of the US projection matrix from 1967
## with respect to infant survival

x1 <- c(0, 0.0010478, 0.0820086, 0.2884376, 0.3777064, 
  0.2647110, 0.1405144, 0.0585568, 0.0134388, 0.0003327)
x2 <- diag(c(0.9972036, 0.9983625, 0.9978063, 0.9967535, 
  0.9961039, 0.9948677, 0.9923658, 0.9885968, 0.9828676))

usa <- rbind(x1, cbind(x2,0))
sd21 <- secder(usa,2,1)
sd21

# }