Robustness of Greedy Type Minimum Evolution Algorithms

  • Takeya Shigezumi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3992)


For a phylogeny reconstruction problem, Desper and Gascuel [2] proposed Greedy Minimum Evolution algorithm (in short, GME) and Balanced Minimum Evolution algorithm (in short, BME). Both of them are faster than the current major algorithm, Neighbor Joining (in short, NJ); however, less accurate when an input distance matrix has errors. In this paper, we prove that BME has the same optimal robustness to such errors as NJ but GME does not. Precisely, we prove that if the maximum distance error is less than a half of the minimum edge length of the target tree, then BME reconstruct it correctly. On the other hand, there is some distance matrix such that maximum distance error is less than \(\frac{2}{\sqrt{n}}\) of the minimum edge length of the target tree, for which GME fails to reconstruct the target tree.


Ordinary Little Square Distance Matrix Target Tree Minimum Evolution Phylogeny Reconstruction 
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  1. 1.
    Desper, R., Gascuel, O.: Theoretical Foundation of the Balanced Minimum Evolution Method of Phylogenetic Inference and Its Relationship to Weighted Least-Squares Tree Fitting. J. of Mol. Biol. Evol. 21(3), 587–598 (2004)CrossRefGoogle Scholar
  2. 2.
    Desper, R., Gascuel, R.: Fast and accurate phylogeny reconstruction algorithms based on the minimum evolution principle. J. Comp. Biol. 9, 687–705 (2002)CrossRefGoogle Scholar
  3. 3.
    Pauplin, Y.: Direct calculation of a tree length using a distance matrix. J. Mol. Evol. 51(1), 41–47 (2000)Google Scholar
  4. 4.
    Saitou, N., Nei, M.: The Neighbor-Joining Method: a New Method for Reconstructing Phylogenetic Trees. Mol. Biol. Evol. 4(4), 406–425 (1987)Google Scholar
  5. 5.
    Gascuel, O.: BIONJ: an Improved Version of the NJ Algorithm Based on a Simple Model of Sequence Data. Mol. Biol. Evol. 14(7), 685–695 (1997)Google Scholar
  6. 6.
    Bruno, W.J., Socci, N.D., Halpern, A.: Weighted Neighbor Joining: a Likelihood-Based Approach to Distance-Based Phylogeny Reconstruction. Mol. Biol. Evol. 17(1), 189–197 (2000)Google Scholar
  7. 7.
    Atteson, K.: The Performance of Neighbor-Joining Algorithms of Phylogeny Reconstruction. In: Jiang, T., Lee, D.T. (eds.) COCOON 1997. LNCS, vol. 1276, pp. 101–110. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  8. 8.
    Day, W., Sankoff, D.: Computational Complexity of Inferring Phylogenies by Compatibility. Systematic Zoology 35(2), 224–229 (1986)CrossRefGoogle Scholar
  9. 9.
    Felsenstein, J.: An Alternating Least Squares Approach to Inferring Phylogenies from Pairwise Distances. Systematic Biology 46(1), 101–111 (1997)CrossRefGoogle Scholar
  10. 10.
    Benedetto, D., Caglioti, E., Loreto, V.: Language Trees and Zipping. Physical Review Letters 88(4), 048702-1–04872-4 (2002)Google Scholar
  11. 11.
    Cilibrasi, R., Vitányi, P.: Clustering by Compression. IEEE Transactions on Information Theory 51(4), 1523–1545 (2005)CrossRefGoogle Scholar
  12. 12.
    Shigezumi, T.: Robustness of Greedy Type Minimum Evolution Algorithms. Dept. of Math. and Comp. Sciences Tokyo Institute of Technology Research Reports (Series C), C-218 (2005),

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Takeya Shigezumi
    • 1
  1. 1.c/o Prof. O. Watanabe, Dept. of Mathematical and Computing SciencesTokyo Institute of TechnologyJapan

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