Phylogenetic Reconstruction Algorithms Based on Weighted 4-Trees

  • Vincent Ranwez
  • Olivier Gascuel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2066)


Quartet methods first compute 4-taxon trees (or 4-trees) then use a combinatorial algorithm to infer a phylogeny that closely respects the inferred 4-trees. This article focuses on the special case involving weighted 4-trees. The sum of the weights of the 4-trees induced by the inferred phylogeny is a natural measurement of the fit between this phylogeny and the 4-tree set. In order to measure the fit of each edge of the inferred tree, we propose a new criterion that takes the weights of the 4-trees along with the way they are grouped into account. However, finding the tree that optimizes the natural criterion is NP-hard [10], and optimizing our new criterion is likely not easier. We then describe two greedy heuristic algorithms that are experimentally efficient in optimizing these criteria and have an O(n 4) time complexity (where n is the number of studied taxa). We use computer simulations to show that these two algorithms have better topological accuracy than QUARTET PUZZLING [12], which is one of the few quartet methods able to take 4-trees weighting into account, and seems to be widely used.


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  1. [1]
    J. P. Barth lemy and A. Gu noche. Trees and Proximity Representation. John Wiley & sons, 1990.Google Scholar
  2. [2]
    V. Berry. M thodes et algorithmes pour reconstruire les arbres de l’ volut ion. PhD thesis, Univ. Montpellier II, d cembre 1997.Google Scholar
  3. [3]
    V. Berry and O. Gascuel. Inferring evolutionary trees with strong combinatorial evidence. Theoretical Computer Science, 240:271–298, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    J. Felsenstein. Evolutionary trees from DNA sequences: a maximum likelihood approach. J. Mol. Evol., 17:368–376, 1981.CrossRefGoogle Scholar
  5. [5]
    J. Felsenstein. Phylogeny inference package (version 3.2). Cladistics, 5, 1989.Google Scholar
  6. [6]
    O. Gascuel. BIONJ: An improved version of the nj algorithm based on a simple model of sequence data. Mol. Biol. Evol., 14:685–695, 1997.Google Scholar
  7. [7]
    S. Kumar. A stepwise algorithm for finding minimum evolution trees. Mol. Biol. Evol., 1996.Google Scholar
  8. [8]
    T. Margush and F.R. McMorris. Consensus n-trees. Bulletin of Math. Biol., 43(2):239–244, 1981.zbMATHMathSciNetGoogle Scholar
  9. [9]
    A. Rambaut and N.C. Grassly. Seq-gen: An application for the monte carlo simulation of dna sequence evolution along phylogenetic trees. Comput. Appl. Biosci., 1997.Google Scholar
  10. [10]
    M. Steel. The complexity of reconstructing trees from qualitative characters and subtrees. J. of Classification, 9:91–116, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    K. Strimmer, N. Goldman, and A. von Haeseler. Baysian probabilities and quartet puzzling. Mol. Biol. Evol., 14:210–211, 1997.Google Scholar
  12. [12]
    K. Strimmer and A. von Haeseler. Quartet puzzling: a quartet maximum-likelihood method for reconstructing tree topologies. Mol. Biol. Evol., 13(7):964–969, 1996.Google Scholar
  13. [13]
    S. J. Willson. Building phylogenetic trees from quartets by using local inconsistency measure. Mol. Biol. Evol., 16:685–693, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Vincent Ranwez
    • 1
  • Olivier Gascuel
    • 1

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