Private alleles in a partially isolated population. II. Distribution of persistence time and probability of...

Two diffusion limits were derived from a discrete Wright-Fisher model of migration, mutation, and selection with an arbitrary degree of dominance. Instantaneous killing of the process due to emigration of a mutant leads to one of two diffusion processes with a killing term. One (weak gene flow) is the boundary case of the other (strong gene flow), which can cover a wide range of gene flow. The diffusion process subject to strong gene flow is similar to that studied by S. Karlin and S. Tavaré (1983, SIAM J. Appl. Math. 43, 31-41). The spectral decomposition of the transition probability density of "private" allele frequencies is presented in the case of strong gene flow. The fate of mutant in a deme is discussed in terms of the probabilities of survival and emigration.