School of Mathematical Sciences

A coalescent dual process for a Wright-Fisher diffusion with recombination and its application to haplotype partitioning menu

A coalescent dual process for a Wright-Fisher diffusion with recombination and its application to haplotype partitioning

Speaker: 
Robert Griffiths (Oxford)
Date/Time: 
Wed, 15/03/2017 - 13:00
Room: 
W316

The Wright-Fisher diffusion process with recombination models the haplotype frequencies in a population where a length of DNA contains $L$ loci, or in a continuous model where the length of DNA is regarded as an interval $[0,1]$. Recombination may occur at any point in the interval and split the length of DNA. A typed dual process to the diffusion, backwards in time, is related to the ancestral recombination graph, which is a random branching coalescing graph. Transition densities in the diffusion have a series expansion in terms of the transition functions in the dual process. The history of a single haplotype back in time describes the partitioning of the haplotype into fragments by recombination. The stationary distribution of the fragments is of particular interest and we show an efficient way of computing this distribution. This is joint research with
Paul A. Jenkins, University of Warwick, and
Sabin Lessard, Universit{\'e } de Montr{\'e}al.