A matrix representation of phylogenetic trees

  • Sanzheng Qiao
  • W. S-Y Wang
Session 8: Computational Biology II
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1276)


In this paper we begin by describing two currently used methods for evaluating phylogenetic trees, one proposed by Fitch and Margoliash [5] and the other proposed by Saitou and Nei [7]. Both methods are heuristic in the sense that not all possible trees are tested to ensure that the best solution has been reached. We develop a matrix representation of unrooted binary trees. The problem of evaluating phylogenetic trees is then transformed into the standard linear least squares problem. Then we propose a matrix decomposition method for evaluating phylogenetic trees.


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  1. 1.
    Cavalli-Sforsza, L.L. and A.W.F. Edwards. 1967. Phylogenetic Analysis Models and Estimation Procedures. Evolution, 32, pp.550–570 (also published in Amer. J. Hum. Genet. 19, pp.233–257).Google Scholar
  2. 2.
    Cavalli-Sforsza, L.L. and W. S-Y. Wang. 1986. Spatial Distance and Lexical Replacement. Language, 62, pp.38–55.Google Scholar
  3. 3.
    Day, W.H.E. 1987. Computational-Complexity of Inferring Phylogenies from Dissimilarity Matrices. Bulletin of Mathematical Biology, 49, pp.46–467.Google Scholar
  4. 4.
    Felsenstein, J. An Alternating Least Squares Approach to Inferring Phylogenies from Pairwise Distances, Manuscript.Google Scholar
  5. 5.
    Fitch, W. and E. Margoliash. 1967. Construction of Phylogenetic Trees. Science, Vol. 155, No. 3760, pp.279–284.Google Scholar
  6. 6.
    Garey, M.R. and D.S. Johnson. 1979. Computers and Intractability: a Guide to the Theory of NP-Completeness, W.H. Freeman, New York.Google Scholar
  7. 7.
    Saitou, N. and M. Nei. 1987. The Neighbor-joining Method: A New Method for Reconstructing Phylogenetic Trees. Molecular Biology and Evolution, 4(4), pp.406–425.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Sanzheng Qiao
    • 1
  • W. S-Y Wang
    • 2
  1. 1.Department of Computer Science and SystemsMcMaster UniversityHamiltonCanada
  2. 2.Department of Electronic EngineeringCity University of Hong KongKowloonHong Kong

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