Private alleles in a partially isolated population II. Distribution of persistence time and probability of emigration (Q1084039)

[For part I see ibid. 28, 314-331 (1985; Zbl 0573.92014).] 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 \textit{S. Karlin} and \textit{S. Tavaré}, SIAM J. Appl. Math. 43, 31-41 (1983; Zbl 0549.92013). 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.