A Fleming-Viot process with unbounded selection

Abstract

Tachida (1991) proposed a discrete-time model of nearly neutral mutation in which the selection coefficient of a new mutant has a fixed normal distribution with mean 0. The usual diffusion approximation leads to a probability-measure-valued diffusion process, known as a Fleming-Viot process, with the unusual feature of an unbounded selection intensity function. Although the existence of such a diffusion has been proved by Overbeck et al. (1995) using Dirichlet forms, we can now characterize the process via the martingale problem. This leads to a limit theorem justifying the diffusion approximation, using a stronger than usual topology on the state space. Also established are existence, uniqueness, and reversibility of the stationary distribution of the Fleming-Viot process.