Advertisement

Inferring evolutionary trees with strong combinatorial evidence

  • Vincent Berry
  • Olivier Gascuel
Session 4: Computational Biology I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1276)

Abstract

We consider the problem of inferring the evolutionary tree of a set of n species. We propose a quartet reconstruction method which specifically produces trees whose edges have strong combinatorial evidence. For this purpose we use the Q* relation [3], defined as the maximum subset of resolved quartets which is equivalent to a tree. We further investigate the properties of this variation of the NP-hard quartet consistency problem, first providing a polynomial time, O(n4), algorithm. Moreover, we show that the convergence rate of the method is polynomial for realistic conditions, under the Cavender-Farris model of evolution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Agarwala, V. Bafna, M. Farach, B. Narayanan, M. Paterson, and M. Thorup. On the approximability of numerical taxonomy: Fitting distances by tree metrics. In Proc. of the 7th ACM-SIAM SODA, 1996.Google Scholar
  2. 2.
    N. Alon and J.H. Spencer. The Probabilistic Method. John Wiley and Sons, 1992.Google Scholar
  3. 3.
    H-J. Bandelt and A. Dress. Reconstructing the shape of a tree from observed dissimilarity data. Adv. in appl. math., 7:309–343, 1986.Google Scholar
  4. 4.
    H.-J. Bandelt and A. Dress. A canonical decomposition theory for metrics on a finite set. Advances Math, 92:47–105, 1992.Google Scholar
  5. 5.
    V. Berry and O. Gascuel. On the interpretation of bootstrap trees: appropriate threshold of clade selection and induced gain. Mol. Biol. Evol. 13(7), 1996.Google Scholar
  6. 6.
    P. Buneman. Mathematics in Archeological and Historical Sciences, chapter The recovery of trees from measures of dissimilarity, pages 387–395. Edhinburgh University Press, 1971.Google Scholar
  7. 7.
    J. A. Cavender. Taxonomy with confidence. Math. Biosci., 40:271–280, 1978.Google Scholar
  8. 8.
    P.L. Erdös, M.A. Steel, L.A. Székely, and T.J. Warnow. Constructing big trees from short sequences. In ICALP, 1997.Google Scholar
  9. 9.
    M. Farach and S. Karman. Efficient algorithms for inverting evolution. In Proceedings of the 7th ACM SODA, 1996.Google Scholar
  10. 10.
    J. Felsenstein. Phylogenies from molecular sequences: inference and reliability. Annu. Rev. Genet., 22:521–565, 1988.Google Scholar
  11. 11.
    W. M. Fitch. A non-sequential method for constructing trees and hierarchical classifications. J. Mol. Evol., 18:30–37, 1981.Google Scholar
  12. 12.
    O. Gascuel and D. Levy. A reduction for approximating a (non-metric) dissimilarity by a tree distance. J. of Classification, 1996.Google Scholar
  13. 13.
    D. Gusfield. Efficient algorithms for inferring evolutionnary trees. Networks, 21:19–28, 1991.Google Scholar
  14. 14.
    G. Lecointre, H. Philippe, H.L.V. Lé, and H. Le Guyader. Species sampling has a major impact on phylogenetic inference. Mol. Phylogenet. Evol., 2:205–224, 1993.Google Scholar
  15. 15.
    M. Nei. Relative efficiencies of different tree-making methods for molecular data. In M.M. Miyamoto and J. Cracraft, editors, Phylogenetic analysis of DNA sequences. Oxford Univ. Press, 1991.Google Scholar
  16. 16.
    D. Penny, M.D. Hendy, and M.A. Steel. Testing the theory of descent. In M. M. Miyamoto and J. Cracraft, editors, Phylogenetic analysis of DNA sequences, pages 155–183. 1991.Google Scholar
  17. 17.
    N. Saitou and M. Nei. The neighbor-joining method: A new method for reconstruction phylogenetic trees. Mol. Biol. Evol., 4(4):406–425, 1987.Google Scholar
  18. 18.
    S. Sattah and A. Tversky. Additive similarity trees. Psychom., 42:319–345, 1977.Google Scholar
  19. 19.
    M. Steel. The complexity of reconstructing trees from qualitative characters and subtrees. J. of Classification, 9:91–116, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Vincent Berry
    • 1
  • Olivier Gascuel
    • 2
  1. 1.Département d'Informatique Fondamentale, LIRMMUniversité de Montpellier IIFrance
  2. 2.GERADMontreal (Quebec)Canada

Personalised recommendations