Seminar on Probability and Statistics

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Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike


14:30-16:00   Room # (Graduate School of Math. Sci. Bldg.)
Han Liang Gan (University of Waikato)
Stationary distribution approximations for two-island and seed bank models
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)

Two-island Wright-Fisher models are used to model genetic frequencies and variability for subdivided populations. One of the key components of the model is the level of migration between the two islands. We show that as the population size increases, the appropriate approximation and limit for the stationary distribution of a two-island Wright-Fisher Markov chain depends on the level of migration. In a seed bank model, individuals in one of the islands stay dormant rather than reproduce. We give analogous results for the seed bank model, compare and contrast the differences and examine the effect the seed bank has on genetic variability. Our results are derived from a new development of Stein's method for the two-island diffusion model and existing results for
Stein's method for the Dirichlet distribution.

This talk is based on joint work with Adrian Röllin, Nathan Ross and Maite Wilke Berenguer.
[ Reference URL ]