Simple Reconstruction of Binary Near-Perfect Phylogenetic Trees

  • Srinath Sridhar
  • Kedar Dhamdhere
  • Guy E. Blelloch
  • Eran Halperin
  • R. Ravi
  • Russell Schwartz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3992)

Abstract

We consider the problem of reconstructing near-perfect phylogenetic trees using binary character states (referred to as BNPP). A perfect phylogeny assumes that every character mutates at most once in the evolutionary tree, yielding an algorithm for binary character states that is computationally efficient but not robust to imperfections in real data. A near-perfect phylogeny relaxes the perfect phylogeny assumption by allowing at most a constant number q of additional mutations. In this paper, we develop an algorithm for constructing optimal phylogenies and provide empirical evidence of its performance. The algorithm runs in time O((72 κ)qnm + nm2) where n is the number of taxa, m is the number of characters and κ is the number of characters that share four gametes with some other character. This is fixed parameter tractable when q and κ are constants and significantly improves on the previous asymptotic bounds by reducing the exponent to q. Furthermore, the complexity of the previous work makes it impractical and in fact no known implementation of it exists. We implement our algorithm and demonstrate it on a selection of real data sets, showing that it substantially outperforms its worst-case bounds and yields far superior results to a commonly used heuristic method in at least one case. Our results therefore describe the first practical phylogenetic tree reconstruction algorithm that finds guaranteed optimal solutions while being easily implemented and computationally feasible for data sets of biologically meaningful size and complexity.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agarwala, R., Fernandez-Baca, D.: A Polynomial-Time Algorithm for the Perfect Phylogeny Problem when the Number of Character States is Fixed. SIAM Journal on Computing 23 (1994)Google Scholar
  2. 2.
    Bodlaender, H., Fellows, M., Warnow, T.: Two Strikes Against Perfect Phylogeny. In: Proc. ICALP (1992)Google Scholar
  3. 3.
    Damaschke, P.: Parameterized Enumeration, Transversals, and Imperfect Phylogeny Reconstruction. In: Proc. IWPEC (2004)Google Scholar
  4. 4.
    Eskin, E., Halperin, E., Karp, R.M.: Efficient Reconstruction of Haplotype Structure via Perfect Phylogeny. In: JBCB (2003)Google Scholar
  5. 5.
    Felsenstein, J.: PHYLIP version 3.6. Distributed by the author. Department of Genome Sciences. University of Washington, Seattle (2005)Google Scholar
  6. 6.
    Fernandez-Baca, D., Lagergren, J.: A Polynomial-Time Algorithm for Near-Perfect Phylogeny. SIAM Journal on Computing 32 (2003)Google Scholar
  7. 7.
    Foulds, L.R., Graham, R.L.: The Steiner problem in Phylogeny is NP-complete. In: Advances in Applied Mathematics, vol. (3) (1982)Google Scholar
  8. 8.
    Gusfield, D.: Efficient Algorithms for Inferring Evolutionary Trees. Networks 21 (1991)Google Scholar
  9. 9.
    Gusfield, D.: Algorithms on Strings, Trees and Sequences. Cambridge University Press, Cambridge (1999)Google Scholar
  10. 10.
    Gusfield, D., Bansal, V.: A Fundamental Decomposition Theory for Phylogenetic Networks and Incompatible Characters. In: Proc. RECOMB (2005)Google Scholar
  11. 11.
    Gusfield, D., Eddhu, S., Langley, C.: Efficient Reconstruction of Phylogenetic Networks with Constrained Recombination. In: Proc. IEEE CSB (2003)Google Scholar
  12. 12.
    The International HapMap Consortium. The International HapMap Project. Nature 426 (2003)Google Scholar
  13. 13.
    Kannan, S., Warnow, T.: A Fast Algorithm for the Computation and Enumeration of Perfect Phylogenies. SIAM Journal on Computing 26 (1997)Google Scholar
  14. 14.
    Merimaa, M., Liivak, M., Heinaru, E., Truu, J., Heinaru, A.: Functional co-adaption of phenol hydroxylase and catechol 2,3-dioxygenase genes in bacteria possessing different phenol and p-cresol degradation pathways (unpublished)Google Scholar
  15. 15.
    Promel, H.J., Steger, A.: The Steiner Tree Problem: A Tour Through Graphs Algorithms and Complexity. Vieweg Verlag (2002)Google Scholar
  16. 16.
    Semple, C., Steel, M.: Phylogenetics. Oxford University Press, Oxford (2003)MATHGoogle Scholar
  17. 17.
    Steel, M.A.: The Complexity of Reconstructing Trees from Qualitative Characters and Subtrees. J. Classification 9 (1992)Google Scholar
  18. 18.
    Sherry, S.T., Ward, M.H., Kholodov, M., Baker, J., Pham, L., Smigielski, E., Sirotkin, K.: dbSNP: The NCBI Database of Genetic Variation. Nucleic Acids Research 29 (2001)Google Scholar
  19. 19.
    Stone, A.C., Griffiths, R.C., Zegura, S.L., Hammer, M.F.: High levels of Y-chromosome nucleotide diversity in the genus Pan. In: Proceedings of the National Academy of Sciences (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Srinath Sridhar
    • 1
  • Kedar Dhamdhere
    • 2
  • Guy E. Blelloch
    • 1
  • Eran Halperin
    • 3
  • R. Ravi
    • 4
  • Russell Schwartz
    • 5
  1. 1.Computer Science DeptCMUUSA
  2. 2.Google IncMountain View
  3. 3.ICSIUniversity of CaliforniaBerkeley
  4. 4.Tepper School of BusinessCMUUSA
  5. 5.Department of Biological SciencesCMUUSA

Personalised recommendations