Title |
Survival of a recessive allele in a Mendelian diploid model
|
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Published in |
Journal of Mathematical Biology, November 2016
|
DOI | 10.1007/s00285-016-1081-6 |
Pubmed ID | |
Authors |
Rebecca Neukirch, Anton Bovier |
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. (J Math Biol 67(3):569-607, 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 [Formula: see text], where K is the size of the population and [Formula: see text]. |
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