# The recovery of a recessive allele in a Mendelian diploid model

## TL;DR

This paper demonstrates how a recessive allele can re-emerge in a diploid population through a formal model, highlighting the genetic robustness enabled by sexual reproduction and mutation dynamics.

## Contribution

It provides a formal description of the mechanism allowing recessive alleles to reappear in populations, extending previous work on allele survival in sexual diploid models.

## Key findings

- Recessive alleles can re-invade populations after mutations.
- Sexual reproduction enhances genetic robustness and allele persistence.
- The model formalizes the re-emergence process of recessive alleles.

## 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. In [Neukirch, Bovier, 2016] it is 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 formal 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.