The genealogical process of neutral genes with mutation in geographically structured populations

The genealogical process of neutral genes with mutation in geographically structured populations is investigated. Following Watterson 24], the sampled genes are partitioned into two types, old equivalence classes and new equivalence classes. The model is described by a bivariate continuous time Markov chain as an interactive particle system. Some results are obtained in the two-population model and the stepping stone model with symmetric nearest-neighbour migration.