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Exact Computation of Coalescent Likelihood under the Infinite Sites Model

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Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 5542))

Abstract

Coalescent likelihood is the probability of observing the given population sequences under the coalescent model. Computation of coalescent likelihood under the infinite sites model is a classic problem in coalescent theory. Existing methods are based on either importance sampling or Markov chain Monte Carlo. In this paper, we develop a simple method that can compute the exact coalescent likelihood for many datasets of moderate size, including a real biological data whose likelihood was previously thought to be difficult to compute exactly. Simulations demonstrate that the practical range of exact coalescent likelihood computation is significantly larger than what was previously believed.

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References

  1. Bahlo, M., Griffiths, R.C.: Inference from Gene Trees in a Subdivided Population. Theoretical Population Biology 57, 79–95 (2000)

    Article  CAS  PubMed  Google Scholar 

  2. Ethier, S.N., Griffiths, R.C.: The Infinitely-Many-Sites Model as a Measure Valued Diffusion. Annals of Probability 15, 515–545 (1987)

    Article  Google Scholar 

  3. Ewens, W.J.: The sampling theory of selectively neutral alleles. Theor. Popul. Biol. 3, 87–112 (1972)

    Article  CAS  PubMed  Google Scholar 

  4. Griffiths, R.C., Tavarè, S.: Simulatiing Probability Distributions in the Coalescent. Theor. Popul. Biol. 46, 131–159 (1994)

    Article  Google Scholar 

  5. Griffiths, R.C., Tavarè, S.: Ancestral inference in population genetics Statistical Science 9, 307–319 (1994)

    Google Scholar 

  6. Griffiths, R.C., Jenkins, P.A., Song, Y.S.: Importance Sampling and Two-Locus Model with Subdivided Population Structure. Adv. Appl. Prob. 40, 473–500 (2008)

    Article  Google Scholar 

  7. Gusfield, D.: Efficient algorithms for inferring evolutionary history. Networks 21, 19–28 (1991)

    Article  Google Scholar 

  8. Hein, J., Schierup, M., Wiuf, C.: Gene Genealogies, Variation and Evolution: A primer in coalescent theory. Oxford University Press, Oxford (2005)

    Google Scholar 

  9. Hobolth, A., Uyenoyama, M.K., Wiuf, C.: Importance Sampling for the Infinite Sites Model. Stat. Appl. Genet. and Mol. Biol. 7 Article 32 (2008)

    Google Scholar 

  10. Hudson, R.: Generating Samples under the Wright-Fisher neutral model of genetic variation. Bioinformatics 18(2), 337–338 (2002)

    Article  CAS  PubMed  Google Scholar 

  11. Kingman, J.F.C.: The coalescent. Stochast. Process. Appl. 13, 235–248 (1982)

    Article  Google Scholar 

  12. Kuhner, M.K., Yamato, J., Felsenstein, J.: Estimating effective population size and mutation rate from sequence data using Metropolis-Hastings sampling. Genetics 140, 1421–1430 (1995)

    CAS  PubMed  PubMed Central  Google Scholar 

  13. Lyngso, R., Song, Y.S., Hein, J.: Accurate Computation of Likelihoods in the Coalescent with Recombination Via Parsimony. In: Vingron, M., Wong, L. (eds.) RECOMB 2008. LNCS (LNBI), vol. 4955, pp. 463–477. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Song, Y.S., Lyngsoe, R., Hein, J.: Counting all possible ancestral configurations of sample sequences in population genetics. IEEE/ACM Transactions on Computational Biology and Bioinformatics 3, 239–251 (2006)

    Article  CAS  PubMed  Google Scholar 

  15. Stephens, M., Donnelly, P.: Inference in molecular population genetics. J. R. Stat. Soc. 62, 605–655 (2000)

    Article  Google Scholar 

  16. Tavarè, S.: Ancestral Inference in Population Genetics. In: Lectures on Probability Theory and Statistics, pages 1931. Springer, Heidelberg (2004)

    Google Scholar 

  17. Wakeley, J.: Coalescent Theory: An Introduction. Roberts and Company Publishers, Greenwood Village (2008)

    Google Scholar 

  18. Ward, R.H., Frazier, B.L., Dew, K., Paabo, S.: Extensive Mitochondria Diversity within a Single Amerindian Tribe. Proc. of the Nat. Academy of Science 88, 8720–8724 (1991)

    Article  CAS  Google Scholar 

  19. Watterson, G.A.: On the number of segregating sites in genetical models without recombination. Theoretical Population Biology 7, 256–276 (1975)

    Article  CAS  PubMed  Google Scholar 

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Wu, Y. (2009). Exact Computation of Coalescent Likelihood under the Infinite Sites Model. In: Măndoiu, I., Narasimhan, G., Zhang, Y. (eds) Bioinformatics Research and Applications. ISBRA 2009. Lecture Notes in Computer Science(), vol 5542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01551-9_21

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  • DOI: https://doi.org/10.1007/978-3-642-01551-9_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01550-2

  • Online ISBN: 978-3-642-01551-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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