Approximate Ewens formulae for symmetric overdominance selection

We derive a family of approximate sampling distributions for the symmetric overdominance model of population genetics. The distributions are selective versions of the Ewens Sampling Formula, which gives sample likelihoods under a model of neutral evolution. We draw on basic results for the general selection model of Ethier and Kurtz, and use mathematical tools well-suited for calculating expectations of symmetric functions of Poisson--Dirichlet atoms. We conclude by briefly examining a Human Leukocyte Antigen data set, in light of a distribution conditional on the number of sample atoms.