Advertisement

Using Colored Petri Nets to Construct Coalescent Hidden Markov Models: Automatic Translation from Demographic Specifications to Efficient Inference Methods

  • Thomas Mailund
  • Anders E. Halager
  • Michael Westergaard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7347)

Abstract

Biotechnological improvements over the last decade has made it economically and technologically feasible to collect large DNA sequence data from many closely related species. This enables us to study the detailed evolutionary history of recent speciation and demographics. Sophisticated statistical methods are needed, however, to extract the information that DNA sequences hold, and a limiting factor in this is dealing with the large state space that the ancestry of large DNA sequences spans. Recently a new analysis method, CoalHMMs, has been developed, that makes it computationally feasible to scan full genome sequences – the complete genetic information of a species – and extract genetic histories from this. Applying this methodology, however, requires that the full state space of ancestral histories can be constructed. This is not feasible to do manually, but by applying formal methods such as Petri nets it is possible to build sophisticated evolutionary histories and automatically derive the analysis models needed. In this paper we describe how to use colored stochastic Petri nets to build CoalHMMs for complex demographic scenarios.

Keywords

State Space Hide Markov Model Rate Matrix Continuous Time Markov Chain Coalescence Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chen, G.K., Marjoram, P., Wall, J.D.: Fast and flexible simulation of DNA sequence data. Genome Res. 19(1), 136–142 (2009)CrossRefGoogle Scholar
  2. 2.
    Chiola, G., Dutheillet, C., Franceshinis, G., Haddad, S.: Stochastic Well-Formed Colored Nets and Symmetric Modeling Applications. IEEE Trans. Computers 42(11), 1343–1360 (1993)CrossRefGoogle Scholar
  3. 3.
    Christensen, S., Kristensen, L.M., Mailund, T.: A Sweep-Line Method for State Space Exploration. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 450–464. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Clarke, E., Emerson, E., Jha, S., Sistla, A.P.: Symmetry Reductions in Model Checking. In: Vardi, M.Y. (ed.) CAV 1998. LNCS, vol. 1427, pp. 147–158. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    Davison, D., Pritchard, J.K., Coop, G.: An approximate likelihood for genetic data under a model with recombination and population splitting. Theoretical Population Biology 75(4), 331–345 (2009)zbMATHCrossRefGoogle Scholar
  6. 6.
    Derisavi, S., Hermanns, H., Sanders, W.H.: Optimal state-space lumping in markov chains. Inf. Process. Lett. 87(6), 309–315 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Durbin, R., Eddy, S.R., Krogh, A., Mitchison, G.: Biological Sequence Analysis. Probabilistic Models of Proteins and Nucleic Acids. Cambridge Univ. Pr. (February 2005)Google Scholar
  8. 8.
    Dutheil, J.Y., Ganapathy, G., Hobolth, A., Mailund, T., Uyenoyama, M.K., Schierup, M.H.: Ancestral population genomics: the coalescent hidden Markov model approach. Genetics 183(1), 259–274 (2009)CrossRefGoogle Scholar
  9. 9.
    Eriksson, A., Mahjani, B., Mehlig, B.: Sequential Markov coalescent algorithms for population models with demographic structure. Theor. Popul. Biol. 76(2), 84–91 (2009)zbMATHCrossRefGoogle Scholar
  10. 10.
    Green, R.E., et al.: A draft sequence of the neandertal genome. Science 328(5979), 710–722 (2010)CrossRefGoogle Scholar
  11. 11.
    Hein, J., Schierup, M.H., Wiuf, C.: Gene genealogies, variation and evolution. a primer in coalescent theory. Oxford University Press, USA (2005)zbMATHGoogle Scholar
  12. 12.
    Hobolth, A., Christensen, O.F., Mailund, T., Schierup, M.H.: Genomic relationships and speciation times of human, chimpanzee, and gorilla inferred from a coalescent hidden Markov model. PLoS Genet 3(2), e7 (2007)CrossRefGoogle Scholar
  13. 13.
    Hobolth, A., Dutheil, J.Y., Hawks, J., Schierup, M.H., Mailund, T.: Incomplete lineage sorting patterns among human, chimpanzee, and orangutan suggest recent orangutan speciation and widespread selection. Genome Res. 21(3), 349–356 (2011)CrossRefGoogle Scholar
  14. 14.
    Jensen, K.: Condensed State Spaces for Symmetrical Coloured Petri Nets. Formal Methods in System Design 9(1/2), 7–40 (1996)CrossRefGoogle Scholar
  15. 15.
    Jensen, K., Kristensen, L.M.: Coloured Petri Nets. Modeling and Validation of Concurrent Systems. Springer-Verlag New York Inc. (June 2009)Google Scholar
  16. 16.
    Li, H., Durbin, R.: Inference of human population history from individual whole-genome sequences. Nature (July 2011)Google Scholar
  17. 17.
    Locke, D.P., et al.: Comparative and demographic analysis of orang-utan genomes. Nature 469(7331), 529–533 (2011)CrossRefGoogle Scholar
  18. 18.
    Mailund, T., Dutheil, J.Y., Hobolth, A., Lunter, G., Schierup, M.H.: Estimating Divergence Time and Ancestral Effective Population Size of Bornean and Sumatran Orangutan Subspecies Using a Coalescent Hidden Markov Model. PLoS Genet. 7(3), e1001319 (2011)CrossRefGoogle Scholar
  19. 19.
    Mailund, T., Schierup, M.H., Pedersen, C.N.S., Mechlenborg, P.J.M., Madsen, J.N., Schauser, L.: CoaSim: a flexible environment for simulating genetic data under coalescent models. BMC Bioinformatics 6, 252 (2005)CrossRefGoogle Scholar
  20. 20.
    Marjoram, P., Wall, J.D.: Fast “coalescent” simulation. BMC Genetics 7, 16 (2006)CrossRefGoogle Scholar
  21. 21.
    Marsan, M.: Stochastic Petri Nets: An Elementary Introduction. In: Rozenberg, G. (ed.) APN 1989. LNCS, vol. 424, pp. 1–29. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  22. 22.
    McVean, G.A.T., Cardin, N.J.: Approximating the coalescent with recombination. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 360(1459), 1387–1393 (2005)CrossRefGoogle Scholar
  23. 23.
    Moler, C., van Loan, C.: Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later. SIAM Review 45(1), 3–49 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Paul, J.S., Steinrucken, M., Song, Y.S.: An Accurate Sequentially Markov Conditional Sampling Distribution for the Coalescent With Recombination. Genetics 187(4), 1115–1128 (2011)CrossRefGoogle Scholar
  25. 25.
    Prüfer, K., et al.: The bonobo genome compared with the genomes of chimpanzee and human, under review at NatureGoogle Scholar
  26. 26.
    Vinter Ratzer, A., Wells, L., Lassen, H.M., Laursen, M., Qvortrup, J.F., Stissing, M.S., Westergaard, M., Christensen, S., Jensen, K.: CPN Tools for Editing, Simulating, and Analysing Coloured Petri Nets. In: van der Aalst, W.M.P., Best, E. (eds.) ICATPN 2003. LNCS, vol. 2679, pp. 450–462. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  27. 27.
    Reich, D., et al.: Genetic history of an archaic hominin group from denisova cave in siberia. Nature 468(7327), 1053–1060 (2010)CrossRefGoogle Scholar
  28. 28.
    Reich, D., et al.: Denisova admixture and the first modern human dispersals into southeast asia and oceania. Am. J. Hum. Genet. 89(4), 516–528 (2011)CrossRefGoogle Scholar
  29. 29.
    Scally, A., et al.: Insights into hominid evolution from the gorilla genome sequence. Nature 483(7388), 169–175 (2012)CrossRefGoogle Scholar
  30. 30.
    Song, Y.S., Lyngso, R., Hein, J.: Counting All Possible Ancestral Configurations of Sample Sequences in Population Genetics. IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB) 3(3), 239 (2006)CrossRefGoogle Scholar
  31. 31.
    Thalmann, O., Fischer, A., Lankester, F., Pääbo, S., Vigilant, L.: The complex evolutionary history of gorillas: insights from genomic data. Mol. Biol. Evol. 24(1), 146–158 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Thomas Mailund
    • 1
  • Anders E. Halager
    • 1
    • 2
  • Michael Westergaard
    • 3
  1. 1.Bioinformatics Research CenterAarhus UniversityDenmark
  2. 2.Department of Computer ScienceAarhus UniversityDenmark
  3. 3.Department of Mathematics and Computer ScienceEindhoven University of TechnologyThe Netherlands

Personalised recommendations