Better Hill-Climbing Searches for Parsimony

  • Ganeshkumar Ganapathy
  • Vijaya Ramachandran
  • Tandy Warnow
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2812)


The reconstruction of evolutionary trees is a major problem in biology, and many evolutionary trees are estimated using heuristics for the NP-hard optimization problem Maximum Parsimony. The current heuristics for searching through tree space use a particular technique, called “tree-bisection and reconnection”, or TBR, to transform one tree into another tree; other less-frequently used transformations, such as SPR and NNI, are special cases of TBR. In this paper, we describe a new tree-rearrangement operation which we call the p-ECR move, for p-Edge-Contract-and-Refine. Our results include an efficient algorithm for computing the best 2-ECR neighbors of a given tree, based upon a simple data structure which also allows us to efficiently calculate the best neighbors under NNI, SPR, and TBR operations (as well as efficiently running the greedy sequence addition technique for maximum parsimony). More significantly, we show that the 2-ECR neighborhood of a given tree is incomparable to the neighborhood defined by TBR, and properly contains all trees within two NNI moves. Hence, the use of the 2-ECR move, in conjunction with TBR and/or NNI moves, may be a more effective technique for exploring tree space than TBR alone.


Maximum Parsimony Binary Tree Internal Node Parsimony Score Near Neighbor Interchange 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Allen, B., Steel, M.: Subtree Transfer Operations and their Induced Metrics on Evolutionary Trees. Annals of Combinatorics 5, 1–15 (2001)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Bonet, M., Steel, M., Warnow, T., Yooseph, S.: Better Methods for Solving Parsimony and Compatibility. Journal of Computational Biology 5(3), 409–422 (1998)CrossRefGoogle Scholar
  3. 3.
    Buneman, P.: The Recovery of Trees from Measures of Dissimilarity. Mathematics in the Archaelogical and Historical Sciences, pp. 387–395 (1971)Google Scholar
  4. 4.
    Dasgupta, B., He, X., Jiang, T., Li, M., Tromp, J., Zhang, L.: On the Distances Between Phylogenetic Trees. In: Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 427–436. ACM-SIAM (1997)Google Scholar
  5. 5.
    Foulds, L.R., Graham, R.L.: The Steiner problem in Phylogeny is NP-complete. Advances in Applied Mathematics 3, 43–49 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Fitch, W.: Toward Defining Course of Evolution: Minimum Change for a Specified Tree Topology. Systematic Zoology 20, 406–416 (1971)CrossRefGoogle Scholar
  7. 7.
    Goloboff, P.A.: Character Optimization and Calculation of Tree Lengths. Cladistics 9, 433–436 (1994)CrossRefGoogle Scholar
  8. 8.
    Goloboff, P.A.: Methods for Faster Parsimony Analysis. Cladistics 12, 199–220 (1996)CrossRefGoogle Scholar
  9. 9.
    Goloboff, P.A.: Analyzing Large Datasets in Reasonable Times: Solutions for Composite Optima. Cladistics 15, 415–428 (1999)CrossRefGoogle Scholar
  10. 10.
    Hein, J., Jiang, T., Wang, L., Zhang, K.: On the Complexity of Comparing Evolutionary trees. Discrete Applied Mathematics 71, 153–169 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Li, M., Tromp, J., Zhang, L.: On the Nearest Neighbour Interchange Distance Between Evolutionary Trees. Journal of Theoretical Biology 182, 463–467 (1996)CrossRefGoogle Scholar
  12. 12.
    Maddison, D.R.: The Discovery and Importance of Multiple Islands of Most Parsimonious Trees. Systematic Zoology 43(3), 315–328 (1991)CrossRefGoogle Scholar
  13. 13.
    Robinson, D.F., Foulds, L.R.: Comparison of Phylogenetic Trees. Mathematical Biosciences 53, 131–147 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Robinson, D.F.: Comparison of Labeled Trees with Valency Three. Journal of Combinatorial Theory 11, 105–119 (1971)CrossRefGoogle Scholar
  15. 15.
    Swofford, D., Olson, G.J., Waddell, P.J., Hillis, D.M.: Molecular Systematics, 2nd edn. ch. Phylogenetic Inference, pp. 407–425. Sinauer Associates, Sunderland (1996)Google Scholar
  16. 16.
    Swofford, D.L.: Studies in Numerical Cladistics: Phylogentic Inference Under the Principle of Maximum Parsimony. PhD thesis, University of Illinois at Urbana-Champaign (1986)Google Scholar
  17. 17.
    Warnow, T.: Tree Compatibility and Inferring Evolutionary History. Journal of Algorithms 16, 388–407 (1994)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ganeshkumar Ganapathy
    • 1
  • Vijaya Ramachandran
    • 1
  • Tandy Warnow
    • 1
  1. 1.Department of Computer SciencesUniversity of TexasAustinUSA

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