Volume 18 - Article 3 | Pages 59-116

Perturbation analysis of nonlinear matrix population models

By Hal Caswell

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Date received:04 Oct 2007
Date published:12 Mar 2008
Word count:11996
Keywords:age averages, barnacles, density-dependence, dependency ratios, elasticity, homeostasis, immigration, matrix calculus, matrix population models, population cycles, sensitivity, Tribolium, two-sex models


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.

Author's Affiliation

Hal Caswell - University of Amsterdam, Netherlands [Email]

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