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Importance sampling and the two-locus model with subdivided population structure

Part of: Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Robert C. Griffiths ,
Paul A. Jenkins  and
Yun S. Song
Robert C. Griffiths*
Affiliation:
University of Oxford
Paul A. Jenkins*
Affiliation:
University of Oxford
Yun S. Song*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK.
∗ Postal address: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK.
∗∗ Postal address: Departments of EECS and Statistics, University of California, Berkeley, CA 94720, USA. Email address: yss@stat.berkeley.edu
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Abstract

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The diffusion-generator approximation technique developed by De Iorio and Griffiths (2004a) is a very useful method of constructing importance-sampling proposal distributions. Being based on general mathematical principles, the method can be applied to various models in population genetics. In this paper we extend the technique to the neutral coalescent model with recombination, thus obtaining novel sampling distributions for the two-locus model. We consider the case with subdivided population structure, as well as the classic case with only a single population. In the latter case we also consider the importance-sampling proposal distributions suggested by Fearnhead and Donnelly (2001), and show that their two-locus distributions generally differ from ours. In the case of the infinitely-many-alleles model, our approximate sampling distributions are shown to be generally closer to the true distributions than are Fearnhead and Donnelly's.

Keywords

Coalescent processrecombinationdiffusion processimportance samplingmigrationsubdivided population

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 93E25: Other computational methods 92D15: Problems related to evolution
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 2 , June 2008 , pp. 473 - 500
Copyright
Copyright © Applied Probability Trust 2008 

References

Bahlo, M. and Griffiths, R. C. (2000). Inference from gene trees in a subdivided population. Theoret. Pop. Biol. 57, 79–95.CrossRefGoogle Scholar
Beaumont, M. (1999). Detecting population expansion and decline using microsatellites. Genetics 153, 2013–2029.CrossRefGoogle ScholarPubMed
Cornuet, J. M. and Beaumont, M. A. (2007). A note on the accuracy of PAC-likelihood inference with microsatellite data. Theoret. Pop. Biol. 71, 12–19.CrossRefGoogle ScholarPubMed
De Iorio, M. and Griffiths, R. C. (2004a). Importance sampling on coalescent histories. I. Adv. Appl. Prob. 36, 417–433.CrossRefGoogle Scholar
De Iorio, M. and Griffiths, R. C. (2004b). Importance sampling on coalescent histories. II: subdivided population models. Adv. Appl. Prob. 36, 434–454.CrossRefGoogle Scholar
Ethier, S. N. and Griffiths, R. C. (1990). On the two-locus sampling distribution. J. Math. Biol. 29, 131–159.CrossRefGoogle Scholar
Fearnhead, P. and Donnelly, P. (2001). Estimating recombination rates from population genetic data. Genetics 159, 1299–1318.CrossRefGoogle ScholarPubMed
Fearnhead, P. and Smith, N. G. C. (2005) A novel method with improved power to detect recombination hotspots from polymorphism data reveals multiple hotspots in human genes. Amer. J. Human Genetics 77, 781–794.CrossRefGoogle ScholarPubMed
Golding, G. B. (1984). The sampling distribution of linkage disequilibrium. Genetics 108, 257–274.CrossRefGoogle ScholarPubMed
Griffiths, R. C. and Marjoram, P. (1996). Ancestral inference from samples of DNA sequences with recombination. J. Comput. Biol. 3, 479–502.CrossRefGoogle ScholarPubMed
Griffiths, R. C. and Tavaré, S. (1994a). Ancestral inference in population genetics. Statist. Sci. 9, 307–319.CrossRefGoogle Scholar
Griffiths, R. C. and Tavaré, S. (1994b). Sampling theory for neutral alleles in a varying environment. Proc. R. Soc. London B 344, 403–410.Google Scholar
Griffiths, R. C. and Tavaré, S. (1994c). Simulating probability distributions in the coalescent. Theoret. Pop. Biol. 46, 131–159.CrossRefGoogle Scholar
Hudson, R. R. (2001). Two-locus sampling distributions and their application. Genetics 159, 1805–1817.CrossRefGoogle ScholarPubMed
Kuhner, M. K., Yamato, J. and Felsenstein, J. (1995). Estimating effective population size and mutation rate from sequence data using Metropolis–Hastings sampling. Genetics 140, 1421–1430.CrossRefGoogle ScholarPubMed
Kuhner, M. K., Yamato, J. and Felsenstein, J. (2000). Maximum likelihood estimation of recombination rates from population data. Genetics 156, 1393–1401.CrossRefGoogle ScholarPubMed
Li, N. and Stephens, M. (2003). Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data. Genetics 165, 2213–2233.CrossRefGoogle ScholarPubMed
McVean, G., Awadalla, P. and Fearnhead, P. (2002). A coalescent-based method for detecting and estimating recombination from gene sequences. Genetics 160, 1231–1241.CrossRefGoogle ScholarPubMed
McVean, G. et al. (2004). The fine-scale structure of recombination rate variation in the human genome. Science 304, 581–584.CrossRefGoogle ScholarPubMed
Myers, S. et al. (2005). A fine-scale map of recombination rates and hotspots across the human genome. Science 310, 321–324.CrossRefGoogle ScholarPubMed
Stephens, M. and Donnelly, P. (2000). Inference in molecular population genetics. J. R. Statist. Soc. Ser. B 62, 605–655.CrossRefGoogle Scholar
Wilson, I. J. and Balding, D. J. (1998). Genealogical inference from microsatellite data. Genetics 150, 499–510.CrossRefGoogle ScholarPubMed