secder {popbio} | R Documentation |
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
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