A reversibility problem for fleming-viot processes

Fleming-Viot processes incorporating mutation and selection are considered. It is well-known that if the mutation factor is of uniform type, the process has a reversible stationary distri- bution, and it has been an open problem to characterize the class of the processes that have reversible stationary distributions. This paper proves that if a Fleming-Viot process has a reversible stationary distribution, then the associated mutation operator is of uniform type.