RESUMO
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.
Assuntos
Genes Recessivos , Modelos Genéticos , Alelos , Animais , Evolução Biológica , Simulação por Computador , Diploide , Transtornos do Desenvolvimento Sexual/genética , Feminino , Aptidão Genética , Genética Populacional/estatística & dados numéricos , Genótipo , Masculino , Conceitos Matemáticos , Mutação , Dinâmica não Linear , Dinâmica Populacional , Reprodução/genética , Processos EstocásticosRESUMO
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].