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Perturbation analysis of nonlinear matrix population models

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  • Hal Caswell

    (Woods Hole Oceanographic Institute)

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    Abstract

    Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models), feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios), age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.

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    File URL: http://www.demographic-research.org/volumes/vol18/3/18-3.pdf
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    Bibliographic Info

    Article provided by Max Planck Institute for Demographic Research, Rostock, Germany in its journal Demographic Research.

    Volume (Year): 18 (2008)
    Issue (Month): 3 (March)
    Pages: 59-116

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    Handle: RePEc:dem:demres:v:18:y:2008:i:3

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    Web page: http://www.demogr.mpg.de/

    Related research

    Keywords: age averages; barnacles; density-dependence; dependency ratios; elasticity; homeostasis; immigration; matrix calculus; matrix population models; population cycles; sensitivity; Tribolium; two-sex models;

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    Cited by:
    1. Michal Engelman & Hal Caswell & Emily Agree, 2014. "Why do lifespan variability trends for the young and old diverge? A perturbation analysis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(48), pages 1367-1396, May.
    2. Alyson Raalte & Hal Caswell, 2013. "Perturbation Analysis of Indices of Lifespan Variability," Demography, Springer, vol. 50(5), pages 1615-1640, October.

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