An asymptotic sampling formula for the coalescent with recombination

Annals of Applied Probability

Volumn 20, Issue 3, 2010, Pages 1005-1028

  Jenkins, Paul A ^a   Song, Yun S ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Coalescent theory; Ewens sampling formula; Infinite alleles model; Recombination; Two locus model

Indexed keywords

EID: 77953815370     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/09-AAP646     Document Type: Article

References (30)

1. Arratia,A., Barbour,A.D. and TavarÉ, S. (2003). Logarithmic Combinatorial Structures: A Probabilistic Approach. European Mathematical Society Publishing House, Switzerland. MR2032426
2. De Iorio,M. and Griffiths, R. C. (2004a). Importance sampling on coalescent histories. I. Adv. n Appl. Probab. 36 417-433. MR2058143
3. De Iorio,M.andGriffiths, R. C. (2004b). Importance sampling on coalescent histories. II. Adv. nAppl. Probab. 36 434-454. MR2058144
4. Ethier,S. N. and Griffiths, R. C. (1990). On the two-locus sampling distribution. J. Math. Biol. 9 131-159. MR1116000
5. Ewens, W. J. (1972). The sampling theory of selectively neutral alleles. Theor. Popul. Biol. 3 87-112. MR0325177
6. Fearnhead,P. and Donnelly, P. (2001). Estimating recombination rates from population genetic data. Genetics 159 1299-1318.
7. Golding, G. B. (1984). The sampling distribution of linkage disequilibrium. Genetics 108 257-274.
8. Griffiths, R. C. (1981). Neutral two-locus multiple allele models with recombination. Theor. opul. Biol. 19 169-186. MR630871
9. Griffiths, R. C. (1991). The two-locus ancestral graph. In Selected Proceedings of the Sheffield ymposium on Applied Probability. IMS Lecture Notes-Monograph Series (I. V. Basawa and R. L. Taylor, eds.) 18 100-117. IMS, Hayward, CA. MR1193063
10. Griffiths,R.C., Jenkins,P.A. and Song, Y. S. (2008). Importance sampling and the two-locus model with subdivided population structure. Adv. in Appl. Probab. 40 473-500. MR2433706
11. Griffiths,R.C. and Lessard, S. (2005). Ewens' sampling formula and related formulae: Combinatorial proofs, extensions to variable population size and applications to ages of alleles. Theor. Popul. Biol. 68 167-177.
12. Griffiths,R.C. and Marjoram, P. (1996). Ancestral inference from samples of DNA sequences with recombination. J. Comput. Biol. 3 479-502.
13. Hoppe, F. (1984). Pólya-like urns and the Ewens' sampling formula. /. Math. Biol. 20 91-94. MR758915
14. Hudson, R. R. (1985). The sampling distribution of linkage disequilibrium under an infinite allele model without selection. Genetics 109 611-631.
15. Hudson, R. R. (2001). Two-locus sampling distributions and their application. Genetics 159 1805-1817.
16. JENKINS,P.A.andSONG, Y. S. (2009). Closed-form two-locus sampling distributions: Accuracy and universality. Genetics 183 1087-1103.
17. Kingman, J. F. C. (1982a). The coalescent. Stochastic Process. Appl. 13 235-248. MR671034
18. Kingman, J. F. C. (1982b). On the genealogy of large populations. J. Appl. Probab. 19 27-43. MR633178
19. KUHNER,M.K.,YAMATO,J.andFELSENSTEIN, J. (2000). Maximum likelihood estimation of recombination rates from population data. Genetics 156 1393-1401.
20. Mcvean,G.A.T.,Myers,S.,Hunt,S.,Deloukas,P.,Bentley,D.R.andDonnellY,P. (2004). The ?ne-scale structure of recombination rate variation in the human genome. Science 304 581-584.
21. Myers,S., Bottolo,L., Freeman,C., McVean,G. and Donnelly, P. (2005). A fine-scale map of recombination rates and hotspots across the human genome. Science 310 321-324.
22. Nielsen, R. (2000). Estimation of population parameters and recombination rates from single nucleotide polymorphisms. Genetics 154 931-942.
23. Pitman, J. (1992). The two-parameter generalization of Ewens' random partition structure. Technical Report 345, Dept. Statistics, Univ. California, Berkeley.
24. Pitma n, J. (1995). Exchangeable and partially exchangeable random partitions. Probab. Theory elated Fields 102 145-158. MR1337249
25. Slatkin, M. (1994). An exact test for neutrality based on the Ewens sampling distribution. Genet. Res. 64 71-74.
26. Slatkin, M. (1996). A correction to an exact test based on the Ewens sampling distribution. Genet. Res. 68 259-260.
27. Stephens, M. (2001). Inference under the coalescent. In Handbook of Statistical Genetics (D. Balding, M. Bishop and C. Cannings, eds.) 213-238.Wiley, Chichester, UK.
28. Stephens,M. and Donnelly, P. (2000). Inference in molecular population genetics. J. R. Stat. Soc. Ser. BStat. Methodol. 62 605-655. MR1796282
29. Wang,Y. and Rannala, B. (2008). Bayesian inference of fine-scale recombination rates using population genomic data. Philos. Trans. R. Soc. 363 3921-3930.
30. Watterson, G. A. (1977). Heterosis or neutrality? Genetics 85 789-814. MR0504021