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January, 1992 Weak Convergence of Population Genealogical Processes to the Coalescent with Ages
Peter Donnelly, Paul Joyce
Ann. Probab. 20(1): 322-341 (January, 1992). DOI: 10.1214/aop/1176989929

Abstract

The population genealogical processes associated with a wide range of exchangeable reproductive models (including the Wright-Fisher model) are shown to converge weakly, as the population size becomes large, to a particularly tractable limiting process, the age-ordered analog of Kingman's coalescent. This result extends the known convergence results for sample processes and effectively completes the robustness theory for neutral genealogies. Its consequences, which include a unification of the results for neutral models, have already been exploited elsewhere. The techniques used rely heavily on knowledge of sample behavior, together with consistency arguments. They may be of more general interest.

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Peter Donnelly. Paul Joyce. "Weak Convergence of Population Genealogical Processes to the Coalescent with Ages." Ann. Probab. 20 (1) 322 - 341, January, 1992. https://doi.org/10.1214/aop/1176989929

Information

Published: January, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0747.60034
MathSciNet: MR1143423
Digital Object Identifier: 10.1214/aop/1176989929

Subjects:
Primary: 60F99
Secondary: 60J75 , 92A10

Keywords: coupling , exchangeability , genealogy , neutral models , sampling functions

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 1 • January, 1992
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