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arXiv · 1505.02109

Survival of a recessive allele in a Mendelian diploid model

Anton Bovier·Rebecca Neukirch
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Abstract

In this paper we analyse the genetic evolution of a diploid hermaphroditic population, which is modelled by a three-type nonlinear birth-and-death process with competition and Mendelian reproduction. In a recent paper, Collet et al., 2013 have shown that, on the mutation time-scale, the process converges to the Trait-Substitution Sequence of adaptive dynamics, stepping from one homozygotic state to another with higher fitness. We prove that, under the assumption that a dominant allele is also the fittest one, the recessive allele survives for a time of order at least K^{1/4-a}, where K is the size of the population and a>0.

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Anton Bovier, Rebecca Neukirch. 2016-08-23. Survival of a recessive allele in a Mendelian diploid model. https://doi.org/10.1007/s00285-016-1081-6

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