Advances in Applied Probability

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

Robert C. Griffiths, Paul A. Jenkins, and Yun S. Song

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Adv. in Appl. Probab. Volume 40, Number 2 (2008), 473-500.

First available: 1 July 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 93E25: Other computational methods 92D15: Problems related to evolution

Coalescent process recombination diffusion process importance sampling migration subdivided population


Griffiths, Robert C.; Jenkins, Paul A.; Song, Yun S. Importance sampling and the two-locus model with subdivided population structure. Advances in Applied Probability 40 (2008), no. 2, 473--500. doi:10.1239/aap/1214950213.

Export citation


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