The Annals of Probability

A Classification of Coalescent Processes for Haploid Exchangeable Population Models

Martin Möhle and Serik Sagitov

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We consider a class of haploid population models with nonoverlapping generations and fixed population size $N$ assuming that the family sizes within a generation are exchangeable random variables. A weak convergence criterion is established for a properly scaled ancestral process as $N \to \infty$. It results in a full classification of the coalescent generators in the case of exchangeable reproduction. In general the coalescent process allows for simultaneous multiple mergers of ancestral lines.

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Ann. Probab. Volume 29, Number 4 (2001), 1547-1562.

First available in Project Euclid: 5 March 2002

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Zentralblatt MATH identifier

Primary: 92D25: Population dynamics (general) 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
Secondary: 92D15: Problems related to evolution 60F17: Functional limit theorems; invariance principles

Ancestral processes coalescent exchangeability generator neutrality population genetics weak convergence


Möhle, Martin; Sagitov, Serik. A Classification of Coalescent Processes for Haploid Exchangeable Population Models. Ann. Probab. 29 (2001), no. 4, 1547--1562. doi:10.1214/aop/1015345761.

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