secder: secder

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

View source: R/secder.R

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

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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 since 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, \partial^2 λ/\partial a_{ij} \partial a_{kl}.

Note

The eigenvalue second derivatives are essential for calculating both perturbation analyses of the eigenvalue elasticities and stochastic sensitivities. secder is used in functions to calculate both these quantities.

Author(s)

James Holland Jones

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

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## 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 4, 2018, 1:04 a.m.