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Robustness results for the coalescent

Part of: Limit theorems

Published online by Cambridge University Press:  14 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. E-mail address: (1) moehle@galton.uchicago.edu, (2) moehle@mathematik.uni-mainz.de
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Abstract

A variety of convergence results for genealogical and line-of-descendent processes are known for exchangeable neutral population genetics models. A general convergence-to-the-coalescent theorem is presented, which works not only for a larger class of exchangeable models but also for a large class of non-exchangeable population models. The coalescence probability, i.e. the probability that two genes, chosen randomly without replacement, have a common ancestor one generation backwards in time, is the central quantity to analyse the ancestral structure.

Keywords

Coalescence probabilitygenealogical processmean crowdingMoran modelpopulation geneticsrobustnessWright-Fisher model

MSC classification

Primary: 60F05: Central limit and other weak theorems 92D10: Genetics
Secondary: 92D25: Population dynamics (general)
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 438 - 447
Copyright
Copyright © Applied Probability Trust 1998 

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