The recovery of a recessive allele in a Mendelian diploid model

Authored by Anton Bovier, Loren Coquille, Rebecca Neukirch

Date Published: 2018

DOI: 10.1007/s00285-018-1240-z

Sponsors: Swiss National Science Foundation (SNSF)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

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.

Tags

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