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Coalescent results for two-sex population models

Part of:Limit theorems

Published online by Cambridge University Press:  01 July 2016

M. Möhle
M. Möhle*
Affiliation:
University of Oxford and Johannes Gutenberg-Universität Mainz
*
∗ Postal address: (1) University of Oxford, Department of Statistics, 1 South Parks Road, Oxford OX1 3TG, UK, (2) Johannes Gutenberg-Universität Mainz, Fachbereich Mathematik, Saarstraße 21, 55099 Mainz, Germany. Email address: (1) moehle@stats.ox.ac.uk, (2) moehle@mathematik.uni-mainz.de
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Abstract

‘Convergence-to-the-coalescent’ theorems for two-sex neutral population models are presented. For the two-sex Wright-Fisher model the ancestry of n sampled genes behaves like the usual n-coalescent, if the population size N is large and if the time is measured in units of 4N generations. Generalisations to a larger class of two-sex models are discussed.

Keywords

Coalescenttwo-sex population modelsgenealogical processpopulation geneticsrobustnesstwo-sex Wright-Fisher model

MSC classification

Primary:60F05: Central limit and other weak theorems92D10: Genetics
Secondary:92D25: Population dynamics (general)

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 2 , June 1998, pp. 513 - 520
Copyright
Copyright © Applied Probability Trust 1998 

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References

[1] Donnelly, P. and Tavaré, S. (1995). Coalescents and genealogical structure under neutrality. Ann. Rev. Genet. 29, 401–421.Google Scholar
[2] Griffiths, R. C. and Majoram, P. (1997). An ancestral recombination graph. In Progress in Population Genetics and Human Evolution, ed. Donnelly, P.. Springer, pp. 257–270.CrossRefGoogle Scholar
[3] Hudson, R. R. and Kaplan, N. L. (1988). The coalescent process in models with selection and recombination. Genetics 120, 831–840.Google Scholar
[4] Kingman, J. F. C. (1982). On the genealogy of large populations. J. Appl. Prob. 19, 27–43.Google Scholar
[5] Kingman, J. F. C. (1982). Exchangeability and the evolution of large populations. In Exchangeability in Probability and Statistics, eds. Koch, G. and Spizzichino, F.. North-Holland Publishing Company, pp. 97–112.Google Scholar
[6] Kingman, J. F. C. (1982). The coalescent. Stoch. Process Appl. 13, 235–248.Google Scholar
[7] Möhle, M., (1994). Forward and backward processes in bisexual models with fixed population sizes. J. Appl. Prob. 31, 309–332.CrossRefGoogle Scholar
[8] Möhle, M., Fixation in bisexual models with variable population sizes. J. Appl. Prob. 34, 436–448.CrossRefGoogle Scholar
[9] Möhle, M., Robustness results for the coalescent. J. Appl. Prob. 35, 437–446.Google Scholar
[10] Möhle, M., A convergence theorem for Markov chains arising in population genetics and the coalescent with selfing. Adv. Appl. Prob. 30, 493–512.Google Scholar
[11] Tavaré, S., (1984). Line-of-descent and genealogical processes, and their applications in population genetics models. Theor. Pop. Biol. 26, 119–164.Google Scholar