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The Emergence of Complex Dynamics during the Evolution of a Structured Limited Population

  • MATHEMATICAL MODELS AND METHODS
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Abstract

The paper considers a microevolution model of two-stage population with limitation under the influence of natural selection that regulates juvenile survival rate. An analytical and numerical study of the model is performed; the parametric areas of various dynamic modes are determined. It is shown that an emergence of new alleles (for example, as a result of mutations) providing a greater reproductive potential of individuals leads to a natural selection of these alleles and evolutionary growth of the average value of the reproductive potential in the population. However, in the case of density dependent regulation of birth rate, the increase in the average value of reproductive potential leads to destabilization of the dynamics for the age group sizes. Scenarios of changes in the dynamics are various and depend on the parameter values of the model, but the main result is always the same: the dynamics become more and more complex and, as a rule, chaotic.

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Funding

This study was performed within the scope of the state tasks of the Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences (FEB RAS), and the Institute for Complex Analysis of Regional Problems, FEB RAS, as well as with the partial financial support of the Russian Foundation for Basic Research (project no. 18-04-00073 a).

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Authors and Affiliations

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

    G. P. Neverova & O. L. Zhdanova

  2. Institute for Complex Analysis of Regional Problems, Far Eastern Branch, Russian Academy of Sciences, 679016, Birobidzhan, Russia

    E. Ya. Frisman

Authors
  1. G. P. Neverova
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  2. O. L. Zhdanova
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  3. E. Ya. Frisman
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Correspondence to G. P. Neverova or E. Ya. Frisman.

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Neverova, G.P., Zhdanova, O.L. & Frisman, E.Y. The Emergence of Complex Dynamics during the Evolution of a Structured Limited Population. Russ J Genet 56, 747–757 (2020). https://doi.org/10.1134/S102279542006006X

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