TY - JOUR

T1 - Pedigree in the biparental Moran model

AU - Coron, Camille

AU - Le Jan, Yves

N1 - Funding Information:
We are very thankful to the referees as well as the associate editor for their useful comments and criticisms which helped us considerably improve the manuscript.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022/5

Y1 - 2022/5

N2 - 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 offspring. We use a biparental Moran model, which is characterized by its fixed number N of individuals. We fix an individual and consider the proportions of the genomes of all individuals living n time steps later, that come from this individual. When n goes to infinity, these proportions all converge almost surely towards the same random variable. When N then goes to infinity, 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 the weights of several given ancestors are independent. This gives an explicit formula for the limiting (deterministic) distribution of all ancestors’ weights.

AB - 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 offspring. We use a biparental Moran model, which is characterized by its fixed number N of individuals. We fix an individual and consider the proportions of the genomes of all individuals living n time steps later, that come from this individual. When n goes to infinity, these proportions all converge almost surely towards the same random variable. When N then goes to infinity, 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 the weights of several given ancestors are independent. This gives an explicit formula for the limiting (deterministic) distribution of all ancestors’ weights.

KW - Ancestor’s genetic contribution

KW - Biparental Moran model

KW - Genealogy

KW - k-particle Markov chain

KW - Large population size limit

KW - Pedigree

KW - Stationary distribution

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U2 - 10.1007/s00285-022-01752-0

DO - 10.1007/s00285-022-01752-0

M3 - Article

C2 - 35532838

AN - SCOPUS:85129459316

VL - 84

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 6

M1 - 51

ER -