IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v416y2020ics0304380019303837.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380019303837
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecolmodel.2019.108875?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alyson Raalte & Hal Caswell, 2013. "Perturbation Analysis of Indices of Lifespan Variability," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1615-1640, October.
    2. Hal Caswell & Nora Sánchez Gassen, 2015. "The sensitivity analysis of population projections," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 33(28), pages 801-840.
    3. Caswell, Hal & Shyu, Esther, 2012. "Sensitivity analysis of periodic matrix population models," Theoretical Population Biology, Elsevier, vol. 82(4), pages 329-339.
    4. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    5. Kano, Yutaka, 1998. "More Higher-Order Efficiency: Concentration Probability," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 349-366, November.
    6. Anat Bracha & Donald Brown, 2013. "(Ir)rational Exuberance: Optimism, Ambiguity, and Risk," Levine's Working Paper Archive 786969000000000782, David K. Levine.
    7. Boyce, Mark S. & Baxter, Peter W.J. & Possingham, Hugh P., 2012. "Managing moose harvests by the seat of your pants," Theoretical Population Biology, Elsevier, vol. 82(4), pages 340-347.
    8. Caro-Lopera, Francisco J. & Leiva, Víctor & Balakrishnan, N., 2012. "Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 126-139, February.
    9. Jan R. Magnus & Karim M. Abadir, 2007. "On some definitions in matrix algebra," CIRJE F-Series CIRJE-F-476, CIRJE, Faculty of Economics, University of Tokyo.
    10. Hal Caswell, 2019. "The formal demography of kinship: A matrix formulation," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(24), pages 679-712.
    11. Mardi Dungey & John Harvey & Pierre Siklos & Vladimir Volkov, 2017. "Signed spillover effects building on historical decompositions," CAMA Working Papers 2017-52, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    12. Braga, Maria Debora & Nava, Consuelo Rubina & Zoia, Maria Grazia, 2023. "Kurtosis-based vs volatility-based asset allocation strategies: Do they share the same properties? A first empirical investigation," Finance Research Letters, Elsevier, vol. 54(C).
    13. M. D. Braga & C. R. Nava & M. G. Zoia, 2023. "Kurtosis-based risk parity: methodology and portfolio effects," Quantitative Finance, Taylor & Francis Journals, vol. 23(3), pages 453-469, March.
    14. Oksana Revutskaya & Galina Neverova & Oksana Zhdanova & Efim Frisman, 2023. "The Evolutionary Dynamics of a Sex-Structured Population with Non-Overlapping Generations," Mathematics, MDPI, vol. 11(24), pages 1-23, December.
    15. Hal Caswell & Xi Song, 2021. "The formal demography of kinship III: Kinship dynamics with time-varying demographic rates," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 45(16), pages 517-546.
    16. Haridas, C.V. & Eager, Eric Alan & Rebarber, Richard & Tenhumberg, Brigitte, 2014. "Frequency-dependent population dynamics: Effect of sex ratio and mating system on the elasticity of population growth rate," Theoretical Population Biology, Elsevier, vol. 97(C), pages 49-56.
    17. Chun Pong Lau, 2024. "Sensitivity Analysis for Dynamic Discrete Choice Models," Papers 2408.16330, arXiv.org.
    18. Oli, Madan K. & Loughry, W.J. & Caswell, Hal & Perez-Heydrich, Carolina & McDonough, Colleen M. & Truman, Richard W., 2017. "Dynamics of leprosy in nine-banded armadillos: Net reproductive number and effects on host population dynamics," Ecological Modelling, Elsevier, vol. 350(C), pages 100-108.
    19. Bruno Scalzo Dees, 2019. "Analysing Global Fixed Income Markets with Tensors," Papers 1908.02101, arXiv.org, revised Dec 2019.
    20. Tomasz Wrycza & Annette Baudisch, 2012. "How life expectancy varies with perturbations in age-specific mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 27(13), pages 365-376.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecomod:v:416:y:2020:i:c:s0304380019303837. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/ecological-modelling .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.