Abstract
Fleming and Viot [Indiana Univ. Math. J., 28 (1979), pp. 817–843] introduced a class of probability-measure-valued diffusion processes that has attracted the interest of both pure and applied probabilists. This paper surveys the subject of Fleming–Viot processes as it relates to population genetics. Topics include:1. Introduction.2. Some measure-valued Markov chains.2.1. A diploid model. 2.2. The Wright–Fisher model.2.3. A Moran model.3. The Fleming–Viot process: characterization.4. Convergence.5. Ergodicity.6. An infinite particle system.7. Bounded mutation operators.8. Reversibility.9. Examples.9.1. Continuous-state stepwise-mutation model.9.2. Infinitely-many-neutral-alleles model.9.3. Infinitely-many-neutral-alleles model with ages.9.4. Two-locus model with recombination.9.5. n-locus model with gene conversion.9.6. Infinitely-many-sites model without recombination.9.7. Infinitely-many-neutral-alleles model with allelic genealogies.
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