Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T08:05:14.188Z Has data issue: false hasContentIssue false
  • English
  • Français

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) [email protected], (2) [email protected]
Get access Rights & Permissions [Opens in a new window]

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 theorems 92D10: Genetics
Secondary: 92D25: Population dynamics (general)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 2 , June 1998 , pp. 513 - 520
Copyright
Copyright © Applied Probability Trust 1998 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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