Skip to main content

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

  • Conference paper
Application and Theory of Petri Nets (PETRI NETS 2012)

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chen, G.K., Marjoram, P., Wall, J.D.: Fast and flexible simulation of DNA sequence data. Genome Res. 19(1), 136–142 (2009)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  6. Derisavi, S., Hermanns, H., Sanders, W.H.: Optimal state-space lumping in markov chains. Inf. Process. Lett. 87(6), 309–315 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  10. Green, R.E., et al.: A draft sequence of the neandertal genome. Science 328(5979), 710–722 (2010)

    Article  Google Scholar 

  11. Hein, J., Schierup, M.H., Wiuf, C.: Gene genealogies, variation and evolution. a primer in coalescent theory. Oxford University Press, USA (2005)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  14. Jensen, K.: Condensed State Spaces for Symmetrical Coloured Petri Nets. Formal Methods in System Design 9(1/2), 7–40 (1996)

    Article  Google Scholar 

  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. Li, H., Durbin, R.: Inference of human population history from individual whole-genome sequences. Nature (July 2011)

    Google Scholar 

  17. Locke, D.P., et al.: Comparative and demographic analysis of orang-utan genomes. Nature 469(7331), 529–533 (2011)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  20. Marjoram, P., Wall, J.D.: Fast “coalescent” simulation. BMC Genetics 7, 16 (2006)

    Article  Google Scholar 

  21. Marsan, M.: Stochastic Petri Nets: An Elementary Introduction. In: Rozenberg, G. (ed.) APN 1989. LNCS, vol. 424, pp. 1–29. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  25. Prüfer, K., et al.: The bonobo genome compared with the genomes of chimpanzee and human, under review at Nature

    Google Scholar 

  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)

    Chapter  Google Scholar 

  27. Reich, D., et al.: Genetic history of an archaic hominin group from denisova cave in siberia. Nature 468(7327), 1053–1060 (2010)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  29. Scally, A., et al.: Insights into hominid evolution from the gorilla genome sequence. Nature 483(7388), 169–175 (2012)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mailund, T., Halager, A.E., Westergaard, M. (2012). Using Colored Petri Nets to Construct Coalescent Hidden Markov Models: Automatic Translation from Demographic Specifications to Efficient Inference Methods. In: Haddad, S., Pomello, L. (eds) Application and Theory of Petri Nets. PETRI NETS 2012. Lecture Notes in Computer Science, vol 7347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31131-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31131-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31130-7

  • Online ISBN: 978-3-642-31131-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics