The asymptotic behavior of an urn model arising (Q1374616)

A detailed analysis of asymptotic properties of a Polya-like urn arising in studying stationary distributions and stationary sampling distributions in neutral (Fleming-Viot) genetics models with bounded mutation rates is given. In particular, it is shown that the maximum number of mutations along any lineage from the common ancestor grows extremely slowly with the size of the sample. A similar analysis is applicable to the rate of growth of the number of types in the Ohta-Kimura model (the case in which the mutation process is a simple random walk).