Notohara, M. The coalescent and genealogical process in geographically structured population. (English) Zbl 0726.92014 J. Math. Biol. 29, No. 1, 59-75 (1990). Summary: We shall extend Kingman’s coalescent [J. F. C. Kingman, Stochastic Processes Appl. 13, 235-248 (1982; Zbl 0491.60076)] to the geographically structured population model with migration among colonies. It is described by a continuous-time Markov chain, which is proved to be a dual process of the diffusion process of stepping-stone model. We shall derive a system of equations for the spatial distribution of a common ancestor of sampled genes from colonies and the mean time to getting to one common ancestor. These equations are solved in three particular models; a two- population model, the island model and the one-dimensional stepping-stone model with symmetric nearest-neighbour migration. Cited in 1 ReviewCited in 60 Documents MSC: 92D10 Genetics and epigenetics 60J27 Continuous-time Markov processes on discrete state spaces 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 92D15 Problems related to evolution Keywords:genealogical process; Kingman’s coalescent; geographically structured population model; migration among colonies; dual process of the diffusion process of stepping-stone model; spatial distribution of a common ancestor of sampled genes; two-population model; island model; symmetric nearest-neighbour migration Citations:Zbl 0491.60076 PDFBibTeX XMLCite \textit{M. Notohara}, J. Math. Biol. 29, No. 1, 59--75 (1990; Zbl 0726.92014) Full Text: DOI