Fleming-Viot processes are probability-measure-valued diffusion processes that can be used as stochastic models in population genetics. Here we use duality methods to prove ergodic theorems for Fleming-Viot processes, including those with recombination. Coupling methods are also used to establish ergodicity of Fleming-Viot processes, first without and then with selection. A special type of selection known as symmetric overdominance is treated by other methods.
"Coupling and ergodic theorems for Fleming-Viot processes." Ann. Probab. 26 (2) 533 - 561, April 1998. https://doi.org/10.1214/aop/1022855643