Pedigree in the biparental Moran model

Camille Coron, Yves Le Jan

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number51
JournalJournal Of Mathematical Biology
Issue number6
StatePublished - May 2022


  • Ancestor’s genetic contribution
  • Biparental Moran model
  • Genealogy
  • k-particle Markov chain
  • Large population size limit
  • Pedigree
  • Stationary distribution

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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