Approximating genealogies for partially linked neutral loci under a selective sweep

Speaker: Angelika Studeny (University of Munich)

Abstract

This talk is rooted in the field of mathematical population genetics and considers effects arising in the context of a selectice sweep: A genetic locus carries a strongly beneficial allele which has recently become fixed in a large population. With the quick fixation of the strongly beneficial allele, sequence diversity at partially linked neutral loci is reduced (Maynard-Smith & Haigh, 1974). As it seems not only sequence diversity at single neutral loci is affected but also the joint allelic distribution of several partially linked neutral loci. We studied the latter by means of a genealogical approach: Joint genealogies of selected and neutral loci can be described by the structured ancestral recombination graph, a certain continuous time stochastic process. In the regime of large selection coefficients , recent work by Durrett and Schweinsberg (2005) and Etheridge, Pfaffelhuber, Wakolbinger (2006) introduced a marked Yule tree as an approximation to the exact genealogy of a single neutral locus. We extended the Yule approximation to the case of two neutral loci. This led to the full description of the genealogy with accuracy of O ((log alpha^-2 ) in probability. As an application the expectation of Lewontin’s D as a measure for non-random association of alleles was calculated.