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Robustness results for the coalescent

Part of: Limit theorems

Published online by Cambridge University Press:  14 July 2016

M. Möhle
M. Möhle*
Affiliation:
University of Chicago and Johannes Gutenberg-Universität Mainz
*
∗Postal address: (1) The University of Chicago, Department of Statistics, 5734 University Avenue, Chicago, IL 60637, USA. (2) Johannes Gutenberg-Universität Mainz, Fachbereich Mathematik, Saarstraße 21, 55099 Mainz, Germany. E-mail address: (1) moehle@galton.uchicago.edu, (2) moehle@mathematik.uni-mainz.de
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Abstract

A variety of convergence results for genealogical and line-of-descendent processes are known for exchangeable neutral population genetics models. A general convergence-to-the-coalescent theorem is presented, which works not only for a larger class of exchangeable models but also for a large class of non-exchangeable population models. The coalescence probability, i.e. the probability that two genes, chosen randomly without replacement, have a common ancestor one generation backwards in time, is the central quantity to analyse the ancestral structure.

Keywords

Coalescence probabilitygenealogical processmean crowdingMoran modelpopulation geneticsrobustnessWright-Fisher model

MSC classification

Primary: 60F05: Central limit and other weak theorems 92D10: Genetics
Secondary: 92D25: Population dynamics (general)
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 438 - 447
Copyright
Copyright © Applied Probability Trust 1998 

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References

Cannings, C. (1974). The latent roots of certain Markov chains arising in genetics: A new approach. [4] I. Haploid models. Adv. Appl. Prob. 6, 260–290.Google Scholar
Donnelly, P. and Tavaré, S. (1995). Coalescents and genealogical structure under neutrality. Ann. Rev. Genet. 29, 401–421.CrossRefGoogle ScholarPubMed
Gladstien, K. (1976). Loss of alleles in a haploid population with varying environment. Theor. Pop. Biol. 10, 383–394.CrossRefGoogle Scholar
Gladstien, K. (1977). Haploid populations subject to varying environment: the characteristic values and the rate of loss of alleles. SIAM J. Appl. Math. 32, 778–783.Google Scholar
Gladstien, K. (1978). The characteristic values and vectors for a class of stochastic matrices arising in genetics. SIAM J. Appl. Math. 34, 630–642.Google Scholar
Griffiths, R.C. and Tavaré, S. (1994). Sampling theory for neutral alleles in a varying environment. Phil. Trans. R. Soc. Lond. B 344, 403–410.Google Scholar
Kingman, J.F. C. (1982). On the genealogy of large populations. In Essays in Statistical Science, Papers in honour of P. A. P. Moran, ed. Gani, J. and Hannan, E.J. (J. Appl. Prob. Special Volume 19A.) Sheffield, UK, pp. 27–43.Google Scholar
Kingman, J.F. C. (1982). Exchangeability and the evolution of large populations. In Exchangeability in Probability and Statistics, ed. Koch, G. and Spizzichino, F. North-Holland Publishing Company, pp. 97–112.Google Scholar
Kingman, J.F. C. (1982). The coalescent. Stoch. Proc. Appl. 13, 235–248.Google Scholar
Lloyd, M. (1967). Mean crowding. J. Animal Ecology 36, 1–30.Google Scholar
Marjoram, P. (1992). Correlation structures in applied probability. , University College London.Google Scholar