This paper provides a countable representation for a class of infinite-dimensional diffusions which extends the infinitely-many-neutral-alleles model and is related to the two-parameter Poisson-Dirichlet process. By means of Gibbs sampling procedures, we define a reversible Moran-type population process. The associated process of ranked relative frequencies of types is shown to converge in distribution to the two-parameter family of diffusions, which is stationary and ergodic with respect to the two-parameter Poisson-Dirichlet distribution. The construction provides interpretation for the limiting process in terms of individual dynamics.
"Countable representation for infinite dimensional diffusions derived from the two-parameter Poisson-Dirichlet process." Electron. Commun. Probab. 14 501 - 517, 2009. https://doi.org/10.1214/ECP.v14-1508