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

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

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

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 for over(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.

Original languageEnglish
Pages (from-to)359-364
Number of pages6
JournalEnvironmental Modelling and Software
Volume22
Issue number3
DOIs
StatePublished - Mar 2007

Keywords

  • Delta method
  • Eigenvalue
  • Lambda
  • Leslie matrix
  • Rate of increase
  • Wildlife

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