The asymptotic behavior of an urn model arising in population genetics

A Polya-like urn arises in studying stationary distributions and stationary sampling distributions in neutral (Fleming-Viot) genetics models with bounded mutation rates. This paper gives a detailed analysis of asymptotic properties of the urn. In particular, it is shown that in a sample of size n, the maximum number of mutations along any lineage from the common ancestor grows extremely slowly with n. Kestenʹs result on the growth rate of the number of types when the mutation process is simple symmetric random walk (the Ohta-Kimura model) follows similarly.