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The coalescent process in a population with stochastically varying size

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Ingemar Kaj  and
Stephen M. Krone
Ingemar Kaj*
Affiliation:
Uppsala University
Stephen M. Krone*
Affiliation:
University of Idaho
*
∗ Postal address: Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden.
∗∗ Postal address: Department of Mathematics, University of Idaho, Moscow, ID 83844-1103, USA. Email address: krone@uidaho.edu
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Abstract

We study the genealogical structure of a population with stochastically fluctuating size. If such fluctuations, after suitable rescaling, can be approximated by a nice continuous-time process, we prove weak convergence in the Skorokhod topology of the scaled ancestral process to a stochastic time change of Kingman's coalescent, the time change being given by an additive functional of the limiting backward size process.

Keywords

Coalescentstochastically fluctuating population sizeweak convergencestochastic time change

MSC classification

Primary: 92D10: Genetics 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 60F05: Central limit and other weak theorems
Secondary: 92D25: Population dynamics (general)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 1 , March 2003 , pp. 33 - 48
Copyright
Copyright © Applied Probability Trust 2003 

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