Quasi-invariance and reversibility in the Fleming–Viot process

Abstract

Fleming–Viot processes with mutation, selection and recombination are studied. Their reversible distributions are shown to be characterized as quasi-invariant measures with a cocycle given in terms of the mutation operator, the selection intensity, and the recombination kernel. By using this, we derive not only a necessary and sufficient condition for the Fleming–Viot process to be reversible, but also identify the reversible distributions in the reversible case.