Advertisement

Tree Reconstruction via a Closure Operation on Partial Splits

  • Charles Semple
  • Mike Steel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2066)

Abstract

A fundamental problem in biological classiffication is the reconstruction of phylogenetic trees for a set X of species from a collection of either subtrees or qualitative characters. This task is equivalent to tree reconstruction from a set of partial X-splits (bipartitions of subsets of X). In this paper, we define and analyse a “closure” operation for partial X-splits that was informally proposed by Meacham [5]. In particular, we establish a sufficient condition for such an operation to reconstruct a tree when there is essentially only one tree that displays the partial X-splits. This result exploits a recent combinatorial result from [2].

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Böcker, S., Bryant, D., Dress, A. W. M., and Steel, M. A.: Algorithmic aspects of tree amalgamation. To appear in Journal of Algorithms.Google Scholar
  2. [2]
    Böcker, S., Dress, A. W. M., and Steel, M.: Patching up X-trees. Annals of Combinatorics 3 (1999) 1–12.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Bodlaender, H. L., Fellows, M. R., and Warnow, T. J.: Two strikes against perfect phylogeny. In Proceedings of the International Colloquium on Automata, Languages and Programming, Vol. 623 of Lecture Notes in Computer Science, Springer-Verlag, Berlin (1993) 273–283.Google Scholar
  4. [4]
    Buneman, P.: The recovery of trees from measures of dissimilarity. In F. R. Hodson, D. G. Kendall, and P. Tautu (eds.): Mathematics in the Archaeological and Historical Sciences, Edinburgh University Press (1971) 387–395.Google Scholar
  5. [5]
    Meacham, C. A.: Theoretical and computational considerations of the compatibility of qualitative taxonomic characters. In J. Felsenstein (ed.): Numerical Taxonomy, NATO ASI Series Vol. G1, Springer-Verlag (1983) 304–314.Google Scholar
  6. [6]
    Steel, M.: The complexity of reconstructing trees from qualitative characters and subtrees. Journal of Classification 9(1) (1992) 91–116.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Charles Semple
    • 1
  • Mike Steel
    • 1
  1. 1.Biomathematics Research Centre Department of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand

Personalised recommendations