The Annals of Applied Probability

Genealogical processes for Fleming-Viot models with selection and recombination

Peter Donnelly and Thomas G. Kurtz

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Abstract

Infinite population genetic models with general type space incorporating mutation, selection and recombination are considered. The Fleming-Viot measure-valued diffusion is represented in terms of a countably infinite-dimensional process. The complete genealogy of the population at each time can be recovered from the model. Results are given concerning the existence of stationary distributions and ergodicity and absolute continuity of the stationary distribution for a model with selection with respect to the stationary distribution for the corresponding neutral model.

Article information

Source
Ann. Appl. Probab., Volume 9, Number 4 (1999), 1091-1148.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1029962866

Digital Object Identifier
doi:10.1214/aoap/1029962866

Mathematical Reviews number (MathSciNet)
MR1728556

Zentralblatt MATH identifier
0964.60075

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces 92D10: Genetics {For genetic algebras, see 17D92}
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]

Keywords
Genetic models recombination selection Fleming-Viot process particle representation measure-valued diffusion exchangeability genealogical processes coalescent

Citation

Donnelly, Peter; Kurtz, Thomas G. Genealogical processes for Fleming-Viot models with selection and recombination. Ann. Appl. Probab. 9 (1999), no. 4, 1091--1148. doi:10.1214/aoap/1029962866. https://projecteuclid.org/euclid.aoap/1029962866


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References

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