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A matrix model for density-dependent selection in stage-classified populations, with application to pesticide resistance in Tribolium

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  • de Vries, Charlotte
  • Desharnais, Robert A.
  • Caswell, Hal

Abstract

The study of eco-evolutionary dynamics is based on the idea that ecological and evolutionary processes may operate on the same, or very similar, time scales, and that interactions of ecological and evolutionary processes may have important consequences. Here we develop a model that combines Mendelian population genetics with nonlinear demography to create a truly eco-evolutionary model. We use the vec-permutation matrix approach, classifying individuals by stage and genotype. The demographic component is female dominant and density-dependent. The genetic component includes random mating by stage and genotype, and arbitrary effects of genotype on the demographic phenotype. Mutation is neglected. The result is a nonlinear matrix population model that projects the stage × genotype distribution. We show that the results can include bifurcations of population dynamics driven by the response to selection. We present analytical criteria that determine whether one allele excludes the other or if they persist in a protected polymorphism. The results are based on local stability analysis of the homozygous boundary equilibria.

Suggested Citation

  • de Vries, Charlotte & Desharnais, Robert A. & Caswell, Hal, 2020. "A matrix model for density-dependent selection in stage-classified populations, with application to pesticide resistance in Tribolium," Ecological Modelling, Elsevier, vol. 416(C).
    • Handle: RePEc:eee:ecomod:v:416:y:2020:i:c:s0304380019303837
    DOI: 10.1016/j.ecolmodel.2019.108875
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    References listed on IDEAS

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    1. Magnus, J.R. & Neudecker, H., 1985. "Matrix differential calculus with applications to simple, Hadamard, and Kronecker products," Other publications TiSEM 1b2f1740-bfd1-4ea5-986c-9, Tilburg University, School of Economics and Management.
    2. Hal Caswell, 2008. "Perturbation analysis of nonlinear matrix population models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 18(3), pages 59-116.
    3. de Vries, Charlotte & Caswell, Hal, 2019. "Selection in two-sex stage-structured populations: Genetics, demography, and polymorphism," Theoretical Population Biology, Elsevier, vol. 130(C), pages 160-169.
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