IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i24p4971-d1301191.html
   My bibliography  Save this article

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 1-24, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4971-:d:1301191
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/24/4971/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/24/4971/
    Download Restriction: no
    ---><---

    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.
    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. Wang, Guiming & Getz, Lowell L. & Linzey, Alicia V. & Slade, Norman A. & Kesner, Michael H., 2012. "Fast and slow dynamics of northern small mammal populations," Ecological Modelling, Elsevier, vol. 225(C), pages 95-102.
    2. Bourhis, Yoann & Poggi, Sylvain & Mammeri, Youcef & Le Cointe, Ronan & Cortesero, Anne-Marie & Parisey, Nicolas, 2017. "Foraging as the landscape grip for population dynamics—A mechanistic model applied to crop protection," Ecological Modelling, Elsevier, vol. 354(C), pages 26-36.
    3. Michael Neuman & Lorenzo Chelleri & Thorsten Schuetze, 2021. "Post-Pandemic Urbanism: Criteria for a New Normal," Sustainability, MDPI, vol. 13(19), pages 1-6, September.
    4. Mendes, Pedro B. & Faria, Lucas D.B., 2020. "The eco-evolutionary dynamics of a predator-prey system across an r/K continuum," Ecological Modelling, Elsevier, vol. 436(C).
    5. Zhang, Zhibin & Yan, Chuan & Krebs, Charles J. & Stenseth, Nils Chr., 2015. "Ecological non-monotonicity and its effects on complexity and stability of populations, communities and ecosystems," Ecological Modelling, Elsevier, vol. 312(C), pages 374-384.
    6. Bani-Yaghoub, Majid & Reed, Aaron, 2018. "A methodology to quantify the long-term changes in social networks of competing species," Ecological Modelling, Elsevier, vol. 368(C), pages 147-157.
    7. Andreas Sundelöf & Valerio Bartolino & Mats Ulmestrand & Massimiliano Cardinale, 2013. "Multi-Annual Fluctuations in Reconstructed Historical Time-Series of a European Lobster (Homarus gammarus) Population Disappear at Increased Exploitation Levels," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-10, April.
    8. 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).
    9. Vuilleumier, S. & Goudet, J. & Perrin, N., 2010. "Evolution in heterogeneous populations: From migration models to fixation probabilities," Theoretical Population Biology, Elsevier, vol. 78(4), pages 250-258.
    10. Barraquand, Frédéric & New, Leslie F. & Redpath, Stephen & Matthiopoulos, Jason, 2015. "Indirect effects of primary prey population dynamics on alternative prey," Theoretical Population Biology, Elsevier, vol. 103(C), pages 44-59.
    11. Matvey Kulakov & Efim Frisman, 2023. "Clustering Synchronization in a Model of the 2D Spatio-Temporal Dynamics of an Age-Structured Population with Long-Range Interactions," Mathematics, MDPI, vol. 11(9), pages 1-21, April.

    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:gam:jmathe:v:11:y:2023:i:24:p:4971-:d:1301191. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.