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The time back to the most recent common ancestor in exchangeable population models

Part of:Markov processes

Published online by Cambridge University Press:  01 July 2016

M. Möhle
M. Möhle*
Affiliation:
Eberhard Karls Universität Tübingen
*
∗ Postal address: Mathematisches Institut, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany. Email address: martin.moehle@uni-tuebingen.de
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Abstract

A class of haploid population models with population size N, nonoverlapping generations and exchangeable offspring distribution is considered. Based on an analysis of the discrete ancestral process, we present solutions, algorithms and strong upper bounds for the expected time back to the most recent common ancestor which hold for arbitrary sample size n ∈ {1,…,N}. New insights into the asymptotic behaviour of the expected time back to the most recent common ancestor for large population size are presented relating the results to coalescent theory.

Keywords

Absorption timeancestral processcoalescentexchangeabilityMoran modelmost recent common ancestorWright-Fisher model

MSC classification

Primary:60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Secondary:92D25: Population dynamics (general)

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 1 , March 2004, pp. 78 - 97
Copyright
Copyright © Applied Probability Trust 2004 

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