Padé approximants and exact two-locus sampling distributions

Annals of Applied Probability

Volumn 22, Issue 2, 2012, Pages 576-607

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

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Asymptotic expansion; Pad approximants; Population genetics; Recombination; Sampling distribution

Indexed keywords

EID: 84872051158     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AAP780     Document Type: Article

References (24)

1. BAKER, G. A. and GRAVES-MORRIS, P. (1996). Padé Approximants, 2nd ed. Encyclopedia of Mathematics and its Applications 59. Cambridge Univ. Press, Cambridge. MR1383091
2. BUZBAS, E. O., JOYCE, P. and ABDO, Z. (2009). Estimation of selection intensity under overdominance by Bayesian methods. Stat. Appl. Genet. Mol. Biol. 8 Art. 32, 24. MR2533640
3. DINGLE, R. B. (1973). Asymptotic Expansions: Their Derivation and Interpretation. Academic Press, New York. MR0499926
4. ETHIER, S. N. (1979). A limit theorem for two-locus diffusion models in population genetics. J. Appl. Probab. 16 402-408. MR0531773
5. ETHIER, S. N. andGRIFFITHS, R. C. (1990). On the two-locus sampling distribution. J. Math. Biol. 29 131-159. MR1116000
6. ETHIER, S. N. andNAGYLAKI, T. (1989). Diffusion approximations of the two-locus Wright-Fisher model. J. Math. Biol. 27 17-28. MR0984223
7. EWENS, W. J. (1972). The sampling theory of selectively neutral alleles. Theoretical Population Biology 3 87-112.
8. Erratum, ibid. 3 (1972) 240;
9. erratum, ibid. 3 (1972) 376. MR0325177
10. FEARNHEAD, P. (2003). Haplotypes: The joint distribution of alleles at linked loci. J. Appl. Probab. 40 505-512. MR1978106 (Pubitemid 36914122)
11. GOLDING, G. B. (1984). The sampling distribution of linkage disequilibrium. Genetics 108 257- 274. (Pubitemid 14033382)
12. GRIFFITHS, R. C. and TAVARÉ, S. (1994). Simulating probability distributions in the coalescent. Theoretical Population Biology 46 131-159.
13. GROTE, M. N. and SPEED, T. P. (2002). Approximate Ewens formulae for symmetric overdominance selection. Ann. Appl. Probab. 12 637-663. MR1910643 (Pubitemid 37023753)
14. HANDA, K. (2005). Sampling formulae for symmetric selection. Electron. Commun. Probab. 10 223-234. MR2182606 (Pubitemid 41641811)
15. HUDSON, R. R. (2001). Two-locus sampling distributions and their application. Genetics 159 1805- 1817. (Pubitemid 34087616)
16. HUILLET, T. (2007). Ewens sampling formulae with and without selection. J. Comput. Appl. Math. 206 755-773. MR2333711 (Pubitemid 46856039)
17. JENKINS, P. A. and SONG, Y. S. (2009). Closed-form two-locus sampling distributions: Accuracy and universality. Genetics 183 1087-1103.
18. JENKINS, P. A. and SONG, Y. S. (2010). An asymptotic sampling formula for the coalescent with recombination. Ann. Appl. Probab. 20 1005-1028. MR2680556
19. MCVEAN, G., AWADALLA, P. and FEARNHEAD, P. (2002). A coalescent-based method for detecting and estimating recombination from gene sequences. Genetics 160 1231-1241. (Pubitemid 34263482)
20. MCVEAN, G. A. T., MYERS, S. R., HUNT, S., DELOUKAS, P., BENTLEY, D. R. and DONNELLY, P. (2004). The fine-scale structure of recombination rate variation in the human genome. Science 304 581-584. (Pubitemid 38541915)
21. OHTA, T. and KIMURA, M. (1969a). Linkage disequilibrium at steady state determined by random genetic drift and recurrent mutations. Genetics 63 229-238.
22. OHTA, T. and KIMURA, M. (1969b). Linkage disequilibrium due to random genetic drift. Genetical Research 13 47-55.
23. SONG, Y. S. and SONG, J. S. (2007). Analytic computation of the expectation of the linkage disequilibrium coefficient r2. Theoretical Population Biology 71 49-60. (Pubitemid 44751065)
24. WRIGHT, S. (1949). Adaptation and selection. In Genetics, Paleontology and Evolution (G. L. Jepson, E. Mayr and G. G. Simpson, eds.) 365-389. Princeton Univ. Press, Princeton, NJ.