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A Pólya urn model and the coalescent

Part of: Markov processes Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Gudrun Trieb
Gudrun Trieb*
Affiliation:
Johannes-Gutenberg-Universität, Mainz
*
∗ Postal address: Fachbereich Mathematik, Johannes-Gutenberg-Universität, DW-6500 Mainz, Germany.
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Abstract

In recent papers by Hoppe and Donnelly it has been shown that a Pólya urn model generating the Ewens sampling formula (population genetics) parallels a construction of Kingman using a Poisson–Dirichlet ‘paintbox'. Even the jump chain of Kingman's n-coalescent can be constructed using the urn. The properties of a certain process based on the coalescent also are derived. This process was introduced by Hoppe.

Keywords

EWENS SAMPLING FORMULAGENEALOGYMUTATIONPOPULATION GENETICS

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60C05: Combinatorial probability 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 92D10: Genetics
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 1 - 10
Copyright
Copyright © Applied Probability Trust 1992 

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References

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