popbio (version 2.8)

secder: 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)

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.

Arguments

A

projection matrix

k

row index for the specified transition

l

column index for the specified transition

Author

James Holland Jones

Details

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

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