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Journal of Mathematical Biology

, Volume 77, Issue 4, pp 971–1033 | Cite as

The recovery of a recessive allele in a Mendelian diploid model

  • Anton Bovier
  • Loren Coquille
  • Rebecca Neukirch
Article
  • 113 Downloads

Abstract

We study the large population limit of a stochastic individual-based model which describes the time evolution of a diploid hermaphroditic population reproducing according to Mendelian rules. Neukirch and Bovier (J Math Biol 75:145–198, 2017) proved that sexual reproduction allows unfit alleles to survive in individuals with mixed genotype much longer than they would in populations reproducing asexually. In the present paper we prove that this indeed opens the possibility that individuals with a pure genotype can reinvade in the population after the appearance of further mutations. We thus expose a rigorous description of a mechanism by which a recessive allele can re-emerge in a population. This can be seen as a statement of genetic robustness exhibited by diploid populations performing sexual reproduction.

Keywords

Adaptive dynamics Population dynamics Mendelian reproduction Diploid population Nonlinear birth-and-death process Genetic variability 

Mathematics Subject Classification

60K35 92D25 60J85 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für Angewandte MathematikRheinische Friedrich-Wilhelms-UniversitätBonnGermany
  2. 2.Univ. Grenoble Alpes, CNRS, Institut FourierGrenobleFrance

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