Calculating the variance of the finite rate of population change from a matrix model in 'Mathematica'

Skalski, John R; Millspaugh, Joshua J; Dillingham, Peter; Buchanan, Rebecca A

doi:10.1016/j.envsoft.2005.12.003

Author(s)

Skalski, John R

Millspaugh, Joshua J

Dillingham, Peter

Buchanan, Rebecca A

Publication Date

2007

Abstract

The finite annual rate of population increase (λ) is a fundamental demographic parameter that characterizes the relative annual change in animal numbers. Uncertainty in the estimation of λ from demographic population viability analyses (PVAs) has been largely limited to sensitivity analysis, calculating a pseudo-distribution 'λ' using Monte Carlo methods, or by use of bootstrap methods. The delta method has been used and suggested by several researchers, but no one has provided the computational means to implement it. In this paper, we present 'Mathematica' code to calculate λ and its variance based on eigenvalue calculations of a Leslie transition matrix. We demonstrate the procedure using data from a Hawaiian hawk ('Buteo solitarius') study.

Citation

Environmental Modelling & Software, 22(3), p. 359-364

ISSN

1873-6726

1364-8152

Link

https://hdl.handle.net/1959.11/15493

Language

en

Publisher

Elsevier Ltd

Title

Calculating the variance of the finite rate of population change from a matrix model in 'Mathematica'

Type of document

Journal Article

Entity Type

Publication

Author(s)	Skalski, John R Millspaugh, Joshua J Dillingham, Peter Buchanan, Rebecca A
Publication Date	2007
Abstract	The finite annual rate of population increase (λ) is a fundamental demographic parameter that characterizes the relative annual change in animal numbers. Uncertainty in the estimation of λ from demographic population viability analyses (PVAs) has been largely limited to sensitivity analysis, calculating a pseudo-distribution 'λ' using Monte Carlo methods, or by use of bootstrap methods. The delta method has been used and suggested by several researchers, but no one has provided the computational means to implement it. In this paper, we present 'Mathematica' code to calculate λ and its variance based on eigenvalue calculations of a Leslie transition matrix. We demonstrate the procedure using data from a Hawaiian hawk ('Buteo solitarius') study.
Citation	Environmental Modelling & Software, 22(3), p. 359-364
ISSN	1873-6726 1364-8152
Link	https://hdl.handle.net/1959.11/15493
Language	en
Publisher	Elsevier Ltd
Title	Calculating the variance of the finite rate of population change from a matrix model in 'Mathematica'
Type of document	Journal Article
Entity Type	Publication

Calculating the variance of the finite rate of population change from a matrix model in 'Mathematica'

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