Interacting Fleming-Viot processes

AbstractWe construct a class of interacting Ohta-Kimura stepwise-mutation models and study their macroscopic behavior, i.e., we prove their weak convergence when the population size n increases to infinity, the evolution is speeded up by a factor n2, the increment effects of a change in each population's distribution of characteristics under study is scaled down by a factor n-12 and the level of interaction between populations is decreased by a factor n-1. The measure-valued limits—interacting Fleming-Viot processes—are characterized as unique solutions to certain martingale problems using the method of duality. Finally, we prove a scaling theorem for these processes