The Annals of Probability

A Classification of Coalescent Processes for Haploid Exchangeable Population Models

Martin Möhle and Serik Sagitov

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Abstract

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.

Article information

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

Dates
First available: 5 March 2002

Permanent link to this document
http://projecteuclid.org/euclid.aop/1015345761

Digital Object Identifier
doi:10.1214/aop/1015345761

Mathematical Reviews number (MathSciNet)
MR1880231

Zentralblatt MATH identifier
1013.92029

Subjects
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

Keywords
Ancestral processes coalescent exchangeability generator neutrality population genetics weak convergence

Citation

Möhle, Martin; Sagitov, Serik. A Classification of Coalescent Processes for Haploid Exchangeable Population Models. The Annals of Probability 29 (2001), no. 4, 1547--1562. doi:10.1214/aop/1015345761. http://projecteuclid.org/euclid.aop/1015345761.


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