Journal article
Dirichlet approximation of equilibrium distributions in Cannings models with mutation
HL Gan, A Röllin, N Ross
Advances in Applied Probability | CAMBRIDGE UNIV PRESS | Published : 2017
DOI: 10.1017/apr.2017.27
Abstract
Consider a haploid population of fixed finite size with a finite number of allele types and having Cannings exchangeable genealogy with neutral mutation. The stationary distribution of the Markov chain of allele counts in each generation is an important quantity in population genetics but has no tractable description in general. We provide upper bounds on the distributional distance between the Dirichlet distribution and this finite-population stationary distribution for the Wright-Fisher genealogy with general mutation structure and the Cannings exchangeable genealogy with parent independent mutation structure. In the first case, the bound is small if the population is large and the mutatio..
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Funding Acknowledgements
We thank the anonymous referee for helpful comments and for pointing out an omission in an earlier version of the manuscript (proof of existence of partial derivatives of the solution to the Stein equation). N.R. received support from ARC grant DP150101459; A.R. received support from NUS Research Grant R-155-000-124-112. This work was done partially while the authors were visiting the Institute for Mathematical Sciences, National University of Singapore in 2015. The visit was supported by the Institute. H.G. would also like to thank the School of Mathematics at the University of Melbourne for their hospitality while some of this work was done.