Diffusion approximation of a multilocus model with assortative mating

Alison Etheridge (1) , Sophie Lemaire (2)

1 Department of Statistics [Oxford]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

To understand the effect of non-random mating on the genetic evolution of a population, we consider a finite population in which each individual is defined by a sequence of n diallelic loci. We assume that the population evolves according to a Moran model with assortative mating, recombination and mutation. Under weak assortative mating, loose linkage and low mutation rates, we obtain a class of diffusion approximations for allelic frequencies. We present some features of the limiting diffusions (in particular their boundary behaviour and conditions under which the allelic frequencies at different loci evolve independently). If mutation rates are strictly positive then the limiting diffusions are reversible and, under some assumptions, the critical points of the stationary density can be characterised.

Mots clés: Markov chains; Population genetics; Multilocus models; Assortative mating; Diffusion approximations

Domaines: Probabilités [math.PR]; Génétique des populations [q-bio.PE]

Alison Etheridge, Sophie Lemaire. Diffusion approximation of a multilocus model with assortative mating. 2011. ⟨hal-00560285v1⟩