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

    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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