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

Oksana Revutskaya (), Galina Neverova, Oksana Zhdanova and Efim Frisman
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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

Mathematics, 2023, vol. 11, issue 24, 1-23

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.

Keywords: population dynamics; sex structure; genetic structure; density-dependent regulation; dynamic modes; bistability; genetic variety; extinction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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