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Pré-Publication, Document De Travail Année : 2022

Genetics of the biparental Moran model

Camille Coron
Yves Le Jan
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Résumé

Our goal is to study the genetic composition of a population in which each individual has 2 parents, who contribute equally to the genome of their ospring. We use a biparental Moran model, which is characterized by its xed number N of individuals. We x an individual and consider the proportions of the genomes of all individuals living n time steps later, that come from this individual. We rst prove that when n goes to innity, these proportions all converge almost surely towards the same random variable. We then rigorously prove that when N then goes to innity, this random variable multiplied by N (i.e. the stationary weight of any ancestor in the whole population) converges in law towards the mixture of a Dirac measure in 0 and an exponential law with parameter 1/2, and that the weights of several given ancestors are independent.
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Dates et versions

hal-02908431 , version 1 (29-07-2020)
hal-02908431 , version 2 (24-09-2021)
hal-02908431 , version 3 (30-03-2022)

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Camille Coron, Yves Le Jan. Genetics of the biparental Moran model. 2022. ⟨hal-02908431v3⟩
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