secder: Second derivatives of the dominant eigenvalue

In popbio: Construction and Analysis of Matrix Population Models

Second derivatives of the dominant eigenvalue

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

Details

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

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.

Note

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

Author(s)

James Holland Jones

References

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.

See Also

eigen.analysis

Examples

## 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

popbio documentation built on May 29, 2024, 4:35 a.m.