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A Mathematical Model for Alternation of Polygamy and Parthenogenesis: Stability Versus Efficiency and Analogy with Parasitism

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Abstract

The present work is a contribution to the understanding of the sempiternal problem of the “burden of factor two” implied by sexual reproduction versus asexual one, as males are energy consumers not contributing to the production of offspring. We construct a deterministic mathematical model in population dynamics where a species enjoys both sexual and parthenogenetic capabilities of reproduction and lives on a limited resource. We then show how polygamy implies instability of a parthenogenetic population with a small number of sexually born males. This instability implies evolution of the system towards an attractor involving both (sexual and asexual) populations (which does not imply optimality of the population). We also exhibit the analogy with a parasite/host system.

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Notes

  1. It is obviously possible to carry out all the ulterior developments in terms of the populations of males and females instead of sexually-born and asexually-born. According to (4) there is an equivalence between both descriptions. Biologists prefer the x and y description as it emphasizes the reproduction way instead of the sex of individuals.

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Authors and Affiliations

  1. Institut Jean Le Rond d’Alembert, UPMC Univ Paris 06 and CNRS, UMR 7190, Sorbonne Universités, 75005, Paris, France

    Evariste Sanchez-Palencia

  2. Château du Fontenil, 61300, Saint Sulpice, France

    Philippe Lherminier

  3. Laboratoire Jacques-louis Lions, UPMC Univ Paris 06 and CNRS, UMR 7598, Sorbonne Universités, 75005, Paris, France

    Jean-Pierre Françoise

Authors
  1. Evariste Sanchez-Palencia
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  2. Philippe Lherminier
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  3. Jean-Pierre Françoise
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Correspondence to Jean-Pierre Françoise.

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Sanchez-Palencia, E., Lherminier, P. & Françoise, JP. A Mathematical Model for Alternation of Polygamy and Parthenogenesis: Stability Versus Efficiency and Analogy with Parasitism. Acta Biotheor 64, 537–552 (2016). https://doi.org/10.1007/s10441-016-9293-0

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  • DOI: https://doi.org/10.1007/s10441-016-9293-0

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