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Acta Applicandae Mathematicae

, Volume 149, Issue 1, pp 11–51 | Cite as

The Effect of Recurrent Mutations on Genetic Diversity in a Large Population of Varying Size

Article
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Abstract

Recurrent mutations are a common phenomenon in population genetics. They may be at the origin of the fixation of a new genotype, if they give a phenotypic advantage to the carriers of the new mutation. In this paper, we are interested in the genetic signature left by a selective sweep induced by recurrent mutations at a given locus from an allele \(A\) to an allele \(a\), depending on the mutation frequency. We distinguish three possible scales for the mutation probability per reproductive event, which entail distinct genetic signatures. Besides, we study the hydrodynamic limit of the \(A\)- and \(a\)-population size dynamics when mutations are frequent, and find non trivial equilibria leading to several possible patterns of polymorphism.

Keywords

Eco-evolution Birth and death process with immigration Selective sweep Coupling Competitive Lotka-Volterra system with mutations 

Mathematics Subject Classification

92D25 60J80 60J27 92D15 60F15 37N25 

Notes

Acknowledgements

The author would like to thank Helmut Pitters for fruitful discussions at the beginning of this work. She also wants to thank Jean-René Chazottes and Pierre Collet for advice and references on planar dynamical systems, as well as Pierre Recho for his help with the use of Mathematica, and two anonymous reviewers for their careful reading of the paper, and several suggestions and improvements. This work was partially funded by the Chair “Modélisation Mathémathique et Biodiversité” of Veolia Environnement—Ecole Polytechnique—Museum National d’Histoire Naturelle—Fondation X and the French national research agency ANR-11-BSV7-013-03.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Laboratoire d’Ingénierie des Systèmes Complexes, IrsteaUR LISCAubièreFrance
  2. 2.Department of StatisticsUniversity of OxfordOxfordUK

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