Advances in Applied Probability

A convergence theorem for Markov chains arising in population genetics and the coalescent with selfing

M. Möhle

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Abstract

A simple convergence theorem for sequences of Markov chains is presented in order to derive new `convergence-to-the-coalescent' results for diploid neutral population models.

For the so-called diploid Wright-Fisher model with selfing probability s and mutation rate θ, it is shown that the ancestral structure of n sampled genes can be treated in the framework of an n-coalescent with mutation rate ̃θ := θ(1-s/2), if the population size N is large and if the time is measured in units of (2-s)N generations.

Article information

Source
Adv. in Appl. Probab. Volume 30, Number 2 (1998), 493-512.

Dates
First available in Project Euclid: 21 October 2002

Permanent link to this document
http://projecteuclid.org/euclid.aap/1035228080

Digital Object Identifier
doi:10.1239/aap/1035228080

Mathematical Reviews number (MathSciNet)
MR1642851

Zentralblatt MATH identifier
0910.60007

Subjects
Primary: 60F05: Central limit and other weak theorems 92D10: Genetics {For genetic algebras, see 17D92}
Secondary: 60237 92D25: Population dynamics (general)

Keywords
Coalescent diploid population models genealogical process population genetics robustness selfing

Citation

Möhle, M. A convergence theorem for Markov chains arising in population genetics and the coalescent with selfing. Adv. in Appl. Probab. 30 (1998), no. 2, 493--512. doi:10.1239/aap/1035228080. http://projecteuclid.org/euclid.aap/1035228080.


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