Efficient Computation of the Joint Sample Frequency Spectra for Multiple Populations

Journal of Computational and Graphical Statistics

Volumn 26, Issue 1, 2017, Pages 182-194

  Kamm, John A ^a   Terhorst, Jonathan ^a   Song, Yun S ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Coalescent; Demographic inference; Population genetics; Sum product algorithm

Indexed keywords

EID: 85013082995     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.2016.1159212     Document Type: Article

References (43)

1. Al-Mohy, A.H., and Higham, N.J., (2011), “Computing the Action of the Matrix Exponential, With an Application to Exponential Integrators,” SIAM Journal on Scientific Computing, 33, 488–511.
2. Aldous, D.J., (1985), “Exchangeability and Related Topics,” in École d’Été de Probabilités de Saint-Flour XIII—1983, ed. Hennequin, P., Berlin:Springer, Vol. 1117 of Lecture Notes in Mathematics, pp. 1–198.
3. Beaumont, M.A., and Nichols, R.A., (1996), “Evaluating Loci for Use in the Genetic Analysis of Population Structure,” Proceedings of the Royal Society of London, Series B:Biological Sciences, 263, 1619–1626.
4. Bhaskar, A., Kamm, J.A., and Song, Y.S., (2012), “Approximate Sampling Formulae for General Finite-Alleles Models of Mutation,” Advances in Applied Probability, 44, 408–428 (PMC3953561).
5. Bhaskar, A., and Song, Y.S., (2014), “Descartes’ Rule of Signs and the Identifiability of Population Demographic Models From Genomic Variation Data,” Annals of Statistics, 42, 2469–2493.
6. Bhaskar, A., Wang, Y. X.R., and Song, Y.S., (2015), “Efficient Inference of Population Size Histories and Locus-Specific Mutation Rates From Large-Sample Genomic Variation Data,” Genome Research, 25, 268–279.
7. Boyko, A.R., Williamson, S.H., Indap, A.R., Degenhardt, J.D., Hernandez, R.D., Lohmueller, K.E., Adams, M.D., Schmidt, S., Sninsky, J.J., Sunyaev, S.R., et al. (2008), “Assessing the Evolutionary Impact of Amino Acid Mutations in the Human Genome,” PLoS Genetics, 4, e1000083.
8. Bryant, D., Bouckaert, R., Felsenstein, J., Rosenberg, N.A., and RoyChoudhury, A., (2012), “Inferring Species Trees Directly From Biallelic Genetic Markers:Bypassing Gene Trees in a Full Coalescent Analysis,” Molecular Biology and Evolution, 29, 1917–1932.
9. Chen, H., (2012), “The Joint Allele Frequency Spectrum of Multiple Populations:A Coalescent Theory Approach,” Theoretical Population Biology, 81, 179–195.
10. ——— (2013), “Intercoalescence Time Distribution of Incomplete Gene Genealogies in Temporally Varying Populations, and Applications in Population Genetic Inference,” Annals of Human Genetics, 77, 158–173.
11. Cooley, J.W., and Tukey, J.W., (1965), “An Algorithm for the Machine Calculation of Complex Fourier Series,” Mathematics of Computation, 19, 297–301.
12. Coventry, A., Bull-Otterson, L.M., Liu, X., Clark, A.G., Maxwell, T.J., Crosby, J., Hixson, J.E., Rea, T.J., Muzny, D.M., Lewis, L.R., et al. (2010), “Deep Resequencing Reveals Excess Rare Recent Variants Consistent With Explosive Population Growth,” Nature Communications, 1, 131.
13. De Maio, N., Schlötterer, C., and Kosiol, C., (2013), “Linking Great Apes Genome Evolution Across Time Scales Using Polymorphism-Aware Phylogenetic Models,” Molecular Biology and Evolution, 30, 2249–2262.
14. Durrett, R., (2008), Probability Models for DNA Sequence Evolution (2nd ed.), New York:Springer.
15. Ewens, W.J., (2004), Mathematical Population Genetics:I. Theoretical Introduction, New York:Springer Science+Business Media, Inc.
16. Excoffier, L., Dupanloup, I., Huerta-Sánchez, E., Sousa, V.C., and Foll, M., (2013), “Robust Demographic Inference from Genomic and SNP Data,” PLoS Genetics, 9, e1003905.
17. Felsenstein, J., (1981), “Evolutionary Trees From DNA Sequences:A Maximum Likelihood Approach,” Journal of Molecular Evolution, 17, 368–376.
18. Gazave, E., Ma, L., Chang, D., Coventry, A., Gao, F., Muzny, D., Boerwinkle, E., Gibbs, R.A., Sing, C.F., Clark, A.G., et al. (2014), “Neutral Genomic Regions Refine Models of Recent Rapid Human Population Growth,” Proceedings of the National Academy of Sciences, 111, 757–762.
19. Gravel, S., Henn, B.M., Gutenkunst, R.N., Indap, A.R., Marth, G.T., Clark, A.G., Yu, F., Gibbs, R.A., Bustamante, C.D., Altshuler, D.L., et al. (2011), “Demographic History and Rare Allele Sharing Among Human Populations,” Proceedings of the National Academy of Sciences, 108, 11983–11988.
20. Griffiths, R., and Tavaré, S., (1998), “The Age of a Mutation in a General Coalescent Tree,” Communications in Statistics—Stochastic Models, 14, 273–295.
21. Gutenkunst, R.N., Hernandez, R.D., Williamson, S.H., and Bustamante, C.D., (2009), “Inferring the Joint Demographic History of Multiple Populations from Multidimensional SNP Frequency Data,” PLoS Genetics, 5, e1000695.
22. Higham, N.J., (2002), Accuracy and Stability of Numerical Algorithms (2nd ed.), SIAM:Society for Industrial and Applied Mathematics.
23. Hoppe, F., (1984), “Pólya-like Urns and the Ewens’ Sampling Formula,” Journal of Mathematical Biology, 20, 91–94.
24. Jenkins, P.A., Mueller, J.W., and Song, Y.S., (2014), “General Triallelic Frequency Spectrum Under Demographic Models With Variable Population Size,” Genetics, 196, 295–311 (PMC3872192).
25. Jenkins, P.A., and Song, Y.S., (2011), “The Effect of Recurrent Mutation on the Frequency Spectrum of a Segregating Site and the Age of an Allele,” Theoretical Population Biology, 80, 158–173 (PMC3143209).
26. Johnson, N.L., and Kotz, S., (1977), Urn Models and Their Application:An Approach to Modern Discrete Probability Theory, New York:Wiley.
27. Kimura, M., (1969), “The Number of Heterozygous Nucleotide Sites Maintained in a Finite Population Due to Steady Flux of Mutations,” Genetics, 61, 893.
28. Kingman, J. F.C., (1982a), “The Coalescent,” Stochastic Processes and their Applications, 13, 235–248.
29. ——— (1982b), “Exchangeability and the Evolution of Large Populations,” in Exchangeability in Probability and Statistics, eds. Koch, G., and Spizzichino, F., Amsterdam:North-Holland Publishing Company, pp. 97–112.
30. ——— (1982c), “On the Genealogy of Large Populations,” Journal of Applied Probability, 19A, 27–43.
31. Lauritzen, S.L., and Spiegelhalter, D.J., (1988), “Local Computations With Probabilities on Graphical Structures and Their Application to Expert Systems,” Journal of the Royal Statistical Society, Series B, 50, 157–224.
32. Lukić, S., and Hey, J., (2012), “Demographic Inference Using Spectral Methods on SNP Data, With an Analysis of the Human Out-of-Africa Expansion,” Genetics, 192, 619–639.
33. Moler, C., and Van Loan, C., (2003), “Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later,” SIAM Review, 45, 3–49.
34. Moran, P., (1958), “Random Processes in Genetics,” Mathematical Proceedings of the Cambridge Philosophical Society, 54, 60–71.
35. Myers, S., Fefferman, C., and Patterson, N., (2008), “Can One Learn History From the Allelic Spectrum?” Theoretical Population Biology, 73, 342–348.
36. Nelson, M.R., Wegmann, D., Ehm, M.G., Kessner, D., Jean, P.S., Verzilli, C., Shen, J., Tang, Z., Bacanu, S.-A., Fraser, D., et al. (2012), “An Abundance of Rare Functional Variants in 202 Drug Target Genes Sequenced in 14, 002 People,” Science, 337, 100–104.
37. Nielsen, R., (2000), “Estimation of Population Parameters and Recombination Rates From Single Nucleotide Polymorphisms,” Genetics, 154, 931–942.
38. Pearl, J., (1982), “Reverend Bayes on Inference Engines:A Distributed Hierarchical Approach,” in Proceedings of the National Conference on Artificial Intelligence, pp. 133–136.
39. Polanski, A., and Kimmel, M., (2003), “New Explicit Expressions for Relative Frequencies of Single-Nucleotide Polymorphisms With Application to Statistical Inference on Population Growth,” Genetics, 165, 427–436.
40. Schaffner, S.F., Foo, C., Gabriel, S., Reich, D., Daly, W.J., and Altshuler, D., (2005), “Calibrating a Coalescent Simulation of Human Genome Sequence Variation,” Genome Research, 15, 1576–1583.
41. Staab, P.R., Zhu, S., Metzler, D., and Lunter, G., (2015), “Scrm:Efficiently Simulating Long Sequences Using the Approximated Coalescent With Recombination,” Bioinformatics, 31, 1680–1682.
42. Tavaré, S., (1984), “Line-of-Descent and Genealogical Processes, and Their Applications in Population Genetics Models,” Theoretical Population Biology, 26, 119–164.
43. Wakeley, J., and Hey, J., (1997), “Estimating Ancestral Population Parameters,” Genetics, 145, 847–855.