The Neutral Population Model and Bayesian Nonparametrics

In this paper a widely-studied model in Population Genetics, the so-called Infinitely- Many-Alleles model with neutral mutation, is reinterpreted in terms of a timedependent Bayesian nonparametric statistical model, where the prior of the model is described by the Neutral Fleming-Viot process. A natural likelihood process is introduced such that every collection of k observations, at each time point, is essentially a vector of i.i.d. samples from the state of the Fleming-Viot process at that time. The dynamic properties of the particle process induced by such a likelihood are studied. The Moran model is derived as the marginal distribution of a timedependent sample induced by such a choice of prior and likelihood. The derivation of all results relies on the transition density of the Neutral Fleming-Viot process and on a new representation for the Dirichlet process.