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

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.

James Holland Jones

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.

1 2 3 4 5 6 7 8 9 10 11 | ```
## 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.

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