Dual processes and an invariance result for exchangeable models in population genetics.

By means of a representation as interactive particle systems, dual processes are constructed for a large class of exchangeable models in population genetics. It is shown that as the population size becomes large these dual processes tend in distribution to a particularly tractable limiting dual process. Properties of the models are analyzed using the duality relationship and approximate expressions are obtained for various quantities. Diffusion approximations follow easily from the invariance result.