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A convergence theorem for markov chains arising in population genetics and the coalescent with selfing

Part of: Limit theorems

Published online by Cambridge University Press:  01 July 2016

M. Möhle
M. Möhle*
Affiliation:
University of Chicago and Johannes Gutenberg-Universität Mainz
*
∗ Postal address: (1) The University of Chicago, Department of Statistics, 5734 University Avenue, Chicago, IL 60637, USA, (2) Johannes Gutenberg-Universität Mainz, Fachbereich Mathematik, Saarstraße 21, 55099 Mainz, Germany. Email address: (1)moehle@galton.uchicago.edu, (2) moehle@mathematik.uni-mainz.de
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Abstract

A simple convergence theorem for sequences of Markov chains is presented in order to derive new ‘convergence-to-the-coalescent’ results for diploid neutral population models.

For the so-called diploid Wright-Fisher model with selfing probability s and mutation rate θ, it is shown that the ancestral structure of n sampled genes can be treated in the framework of an n-coalescent with mutation rate ̃θ := θ(1-s/2), if the population size N is large and if the time is measured in units of (2-s)N generations.

Keywords

Coalescentdiploid population modelsgenealogical processpopulation geneticsrobustnessselfing

MSC classification

Primary: 60F05: Central limit and other weak theorems 92D10: Genetics
Secondary: 92D25: Population dynamics (general)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 2 , June 1998 , pp. 493 - 512
Copyright
Copyright © Applied Probability Trust 1998 

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