Bayesian Nonparametric Construction of the Fleming-Viot Process with Fertility Selection

Abstract

This paper provides the construction in a Bayesian setting of the Fleming-Viot measurevalued process with diploid fertility selection and highlights new connections between Bayesian nonparametrics and population genetics. Via a generalisation of the Blackwell-MacQueen Polya-urn scheme, a Markov particle process is defined such that the associated process of empirical measures converges to the Fleming-Viot diffusion. The stationary distribution, known from Ethier and Kurtz (1994), is then derived through an application of the Dirichlet process mixture model and shown to be the de Finetti measure of the particle process. The Fleming-Viot process with haploid selection is derived as a special case.Fleming-Viot process; Measure-valued process; Fertility selection; Gibbs sampler; Dirichlet process mixture model; Blackwell-MacQueen urn-scheme