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Diffusion Approximation of a Multilocus Model with Assortative Mating

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1.	Title	Title of document	Diffusion Approximation of a Multilocus Model with Assortative Mating
2.	Creator	Author's name, affiliation, country	Alison M Etheridge; University of Oxford; United Kingdom
2.	Creator	Author's name, affiliation, country	Sophie Lemaire; Université Paris-Sud Orsay; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Moran model; population genetics; multilocus models; assortative mating; diploid selection; diffusion approximation
3.	Subject	Subject classification	60J20; 92D25; 60J70
4.	Description	Abstract	To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population evolves according to a Moran model with weak assortative mating, strong recombination and low mutation rates. With an appropriate rescaling of time, we obtain that the evolution of the genotypic frequencies in a large population can be approximated by the evolution of the product of the allelic frequencies at each locus, and the vector of the allelic frequencies is approximately governed by a diffusion. The same diffusion limit can be obtained for a multilocus model of a diploid population subject to selection. 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 diffusion is reversible and, under some assumptions, the critical points of the stationary density can be characterised.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	AME supported in part by EPSRC grant no. EP/G052026/1
7.	Date	(YYYY-MM-DD)	2011-11-07
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/932
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-932
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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