Reversibility of Interacting Fleming-Viot Processes with Mutation, Selection, and Recombination

TL;DR

This paper investigates the reversibility of interacting Fleming-Viot processes across multiple colonies, revealing that reversibility generally fails when both migration and mutation are present.

Contribution

It extends the understanding of Fleming-Viot processes by analyzing the reversibility in a multi-colony setting with migration, mutation, and interaction.

Findings

Reversibility is well understood for single-colony processes.

Reversibility fails in multi-colony systems with both migration and mutation.

The study clarifies conditions under which reversibility does not hold.

Abstract

Reversibility of the Fleming-Viot process with mutation, selection, and recombination is well understood. In this paper, we study the reversibility of a system of Fleming-Viot processes that live on a countable number of colonies interacting with each other through migrations between the colonies. It is shown that reversibility fails when both migration and mutation are non-trivial.