secder: Second derivatives of the dominant eigenvalue
In popbio: Construction and Analysis of Matrix Population Models

Description Usage Arguments Details Value Note Author(s) References See Also Examples

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

1	secder(A, k, l)

`A`	projection matrix
`k`	row index for the specified transition
`l`	column index for the specified transition

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

A square matrix of the same rank as A where each element s_ij is the second derivative of the dominant eigenvalue of A.

The eigenvalue second derivatives are essential for calculating both perturbation analyses of the eigenvalue elasticities and stochastic sensitivities.

James Holland Jones

Caswell, H. 2001. Matrix population models: construction, analysis, and interpretation, Second edition. Sinauer, Sunderland, Massachusetts, USA.

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

eigen.analysis

## 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