Genealogical processes for Fleming-Viot models with selection and recombination

Abstract

Infinite population genetic models with general type space incorporating mutation, selection and recombination are considered. The Fleming-Viot measure-valued diffusion is represented in terms of a countably infinite-dimensional process. The complete genealogy of the population at each time can be recovered from the model. Results are given concerning the existence of stationary distributions and ergodicity and absolute continuity of the stationary distribution for a model with selection with respect to the stationary distribution for the corresponding neutral model.