zbMATH — the first resource for mathematics

Closed-form asymptotic sampling distributions under the coalescent with recombination for an arbitrary number of loci. (English) Zbl 1241.92054
Summary: Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci a new framework based on an asymptotic series has recently been developed to derive closed-form results when the recombination rate is moderate to large. In this paper, an arbitrary number of loci is considered and combinatorial approaches are employed to find closed-form expressions for the first couple of terms in an asymptotic expansion of the multi-locus sampling distribution. These expressions are universal in the sense that their functional form in terms of the marginal one-locus distributions applies to all finite- and infinite-alleles models of mutation.

92D15 Problems related to evolution
65C50 Other computational problems in probability (MSC2010)
62E20 Asymptotic distribution theory in statistics
92D10 Genetics and epigenetics
Full Text: DOI Euclid arXiv
[1] Ethier, S. N. (1979). A limit theorem for two-locus diffusion models in population genetics. J. Appl. Prob. 16 , 402-408. · Zbl 0468.92011
[2] Ethier, S. N. and Griffiths, R. C. (1990). On the two-locus sampling distribution. J. Math. Biol. 29 , 131-159. · Zbl 0729.92012
[3] Ewens, W. J. (1972). The sampling theory of selectively neutral alleles. Theoret. Pop. Biol. 3 , 87-112. · Zbl 0245.92009
[4] Fearnhead, P. and Donnelly, P. (2001). Estimating recombination rates from population genetic data. Genetics 159 , 1299-1318. · Zbl 1206.62171
[5] Golding, G. B. (1984). The sampling distribution of linkage disequilibrium. Genetics 108 , 257-274.
[6] Griffiths, R. C. (1981). Neutral two-locus multiple allele models with recombination. Theoret. Pop. Biol. 19 , 169-186. · Zbl 0512.92012
[7] Griffiths, R. C. and Marjoram, P. (1996). Ancestral inference from samples of DNA sequences with recombination. J. Comput. Biol. 3 , 479-502.
[8] Griffiths, R. C., Jenkins, P. A. and Song, Y. S. (2008). Importance sampling and the two-locus model with subdivided population structure. Adv. Appl. Prob. 40 , 473-500. · Zbl 1144.62092
[9] Hudson, R. R. (1985). The sampling distribution of linkage disequilibrium under an infinite allele model without selection. Genetics 109 , 611-631.
[10] Hudson, R. R. (2001). Two-locus sampling distributions and their application. Genetics 159 , 1805-1817.
[11] Jenkins, P. A. and Song, Y. S. (2009). Closed-form two-locus sampling distributions: accuracy and universality. Genetics 183 , 1087-1103.
[12] Jenkins, P. A. and Song, Y. S. (2010). An asymptotic sampling formula for the coalescent with recombination. Ann. Appl. Prob. 20 , 1005-1028. · Zbl 1193.92077
[13] Jenkins, P. A. and Song, Y. S. (2012). PadĂ© approximants and exact two-locus sampling distributions. Ann. Appl. Prob. 22 , 576-607. · Zbl 1242.65017
[14] Kingman, J. F. C. (1982). The coalescent. Stoch. Process. Appl. 13 , 235-248. · Zbl 0491.60076
[15] Kingman, J. F. C. (1982). On the genealogy of large populations. In Essays in Statistical Science (J. Appl. Prob. Spec. Vol. 19A ), eds J. Gani and E. J. Hannan, Applied Probability Trust, Sheffield, pp. 27-43. · Zbl 0516.92011
[16] Kuhner, M. K., Yamato, J. and Felsenstein, J. (2000). Maximum likelihood estimation of recombination rates from population data. Genetics 156 , 1393-1401.
[17] McVean, G., Awadalla, P. and Fearnhead, P. (2002). A coalescent-based method for detecting and estimating recombination from gene sequences. Genetics 160 , 1231-1241.
[18] McVean, G. A. T. et al. (2004). The fine-scale structure of recombination rate variation in the human genome. Science 304 , 581-584.
[19] Nielsen, R. (2000). Estimation of population parameters and recombination rates from single nucleotide polymorphisms. Genetics 154 , 931-942.
[20] Stephens, M. and Donnelly, P. (2000). Inference in molecular population genetics. J. Roy. Statist. Soc. B 62 , 605-655. · Zbl 0962.62107
[21] Wang, Y. and Rannala, B. (2008). Bayesian inference of fine-scale recombination rates using population genomic data. Phil. Trans. R. Soc. B 363 , 3921-3930.
[22] Wright, S. (1949). Adaptation and selection. In Genetics, Paleontology and Evolution , eds G. L. Jepson, G. G. Simpson and E. Mayr, Princeton University Press, pp. 365-389.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.