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Journal of Mathematical Biology

, Volume 76, Issue 6, pp 1421–1463 | Cite as

A stochastic model for speciation by mating preferences

  • Camille Coron
  • Manon Costa
  • Hélène Leman
  • Charline Smadi
Article

Abstract

Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial points of view, and differ only by their mating preference: two individuals with the same genotype have a higher probability to mate and produce a viable offspring. The population is subdivided in several patches and individuals may migrate between them. We show that mating preferences by themselves, even if they are very small, are enough to entail reproductive isolation between patches, and we provide the time needed for this isolation to occur as a function of the carrying capacity. Our results rely on a fine study of the stochastic process and of its deterministic limit in large population, which is given by a system of coupled nonlinear differential equations. Besides, we propose several generalisations of our model, and prove that our findings are robust for those generalisations.

Keywords

Birth and death process with competition Mating preference Reproductive isolation Dynamical systems 

Mathematics Subject Classification

60J27 37N25 92D40 

Notes

Acknowledgements

The authors would like to warmly thank Sylvie Méléard for her continual guidance during their respective thesis works. They would also like to thank Pierre Collet for his help on the theory of dynamical systems, Sylvain Billiard for many fruitful discussions on the biological relevance of their model, Violaine Llaurens for her help during the revision of the manuscript, and the anonymous reviewers for their constructive comments that greatly contributed to improve the final version of the paper. C. C. and C. S. are grateful to the organizers of “The Helsinki Summer School on Mathematical Ecology and Evolution 2012: theory of speciation” which motivated this work. This work was partially funded by the Chair “Modélisation Mathématique et Biodiversité” of VEOLIA-Ecole Polytechnique-MNHN-F.X, and was also supported by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques d’OrsayUniv. Paris-Sud, CNRS, Université Paris-SaclayOrsayFrance
  2. 2.Institut de Mathématiques de Toulouse. CNRS UMR 5219Université Paul SabatierToulouse Cedex 09France
  3. 3.CIMATGuanajuatoMexico
  4. 4.IRSTEA UR LISC, Laboratoire d’ingénierie des Systèmes ComplexesAubièreFrance
  5. 5.Complex Systems Institute of Paris le-de-France (ISC-PIF, UPS3611)ParisFrance

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