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The Evolutionary Dynamics of a Sex-Structured Population with Non-Overlapping Generations

Author

Listed:
  • Oksana Revutskaya

    (Institute for Complex Analysis of Regional Problems, Far East Branch, Russian Academy of Sciences, 679016 Birobidzhan, Russia)

  • Galina Neverova

    (Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences, 690041 Vladivostok, Russia)

  • Oksana Zhdanova

    (Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences, 690041 Vladivostok, Russia)

  • Efim Frisman

    (Institute for Complex Analysis of Regional Problems, Far East Branch, Russian Academy of Sciences, 679016 Birobidzhan, Russia)

Abstract

This paper proposes and studies a discrete-time model for a sex-structured population with non-overlapping generations under density-dependent regulation of survival. The population is assumed to have genetic variety among individuals in terms of reproductive potential, controlled by a single autosomal diallelic locus. We consider a panmictic population with Mendelian inheritance rules. We examine the stability model and show that increasing the average value of reproductive potential destabilizes the population dynamics. The scenario of stability loss in fixed points via period doubling or Neimark–Sacker bifurcations depends on the intensity of the self-regulation. The growth rate at which the population survives and develops is shown to depend on the fitness of the genotypes and the secondary sex ratio. As a result, the asymptotic genetic composition of the population is determined by the values of the reproductive potentials of the heterozygote and homozygotes, the initial conditions, and the parameter describing the ratio of newborn females to males. With disruptive selection, the influence of external factors changing the current genetic composition of a population can alter the direction of evolution and lead to the extinction of a successful developing population or a gradual population recovery due to evolutionary rescue after a noticeable decline in its abundance.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4971-:d:1301191
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    References listed on IDEAS

    as
    1. Yuri V. Tyutyunov, 2023. "Spatial Demo-Genetic Predator–Prey Model for Studying Natural Selection of Traits Enhancing Consumer Motility," Mathematics, MDPI, vol. 11(15), pages 1-18, August.
    2. Bertram, Jason & Masel, Joanna, 2019. "Density-dependent selection and the limits of relative fitness," Theoretical Population Biology, Elsevier, vol. 129(C), pages 81-92.
    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.
    4. Kyrre L. Kausrud & Atle Mysterud & Harald Steen & Jon Olav Vik & Eivind Østbye & Bernard Cazelles & Erik Framstad & Anne Maria Eikeset & Ivar Mysterud & Torstein Solhøy & Nils Chr. Stenseth, 2008. "Linking climate change to lemming cycles," Nature, Nature, vol. 456(7218), pages 93-97, November.
    5. Tyutyunov, Yuri & Zhadanovskaya, Ekaterina & Bourguet, Denis & Arditi, Roger, 2008. "Landscape refuges delay resistance of the European corn borer to Bt-maize: A demo-genetic dynamic model," Theoretical Population Biology, Elsevier, vol. 74(1), pages 138-146.
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