Advertisement

Online Consensus and Agreement of Phylogenetic Trees

  • Tanya Y. Berger-Wolf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3240)

Abstract

Computational heuristics are the primary methods for reconstruction of phylogenetic trees on large datasets. Most large-scale phylogenetic analyses produce numerous trees that are equivalent for some optimization criteria. Even using the best heuristics, it takes significant amount of time to obtain optimal trees in simulation experiments. When biological data are used, the score of the optimal tree is not known. As a result, the heuristics are either run for a fixed (long) period of time, or until some measure of a lack of improvement is achieved. It is unclear, though, what is a good criterion for measuring this lack of improvement. However, often it is useful to represent the collection of best trees so far in a compact way to allow scientists to monitor the reconstruction progress. Consensus and agreement trees are common such representations. Using existing static algorithms to produce these trees increases an already lengthy computational time substantially. In this paper we present efficient online algorithms for computing strict and majority consensi and the maximum agreement subtree.

Keywords

Binary Tree Consensus Tree Online Algorithm Mast Problem Depth First Search 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Amir, A., Keselman, D.: Maximum agreement subtree in a set of evolutionary trees - metrics and efficient algorithms. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 758–769 (1994)Google Scholar
  2. 2.
    Barthélemy, J.P., McMorris, F.R.: The median procedure for n-trees. Journal of Classification 3, 329–334 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Berbee, M.L.: The phylogeny of plant and animal pathogens in the Ascomycota. Physiological and Molecular Plant Pathology (2001)Google Scholar
  4. 4.
    Bryant, D.: Building trees, hunting for trees, and comparing trees: Theory and methods in phylogenetic analysis. PhD thesis, University of Canterbury (1997)Google Scholar
  5. 5.
    Buneman, P.: The recovery of trees from measures of dissimilarity. In: Hodson, F.R., Kendall, D.G., Tautu, P. (eds.) Mathematics in the Archeological and Historical Sciences, pp. 387–395. Edinburgh University Press, Edinburgh (1971)Google Scholar
  6. 6.
    Bush, R.M., Fitch, W.M., Bender, C.A., Co, N.J.: Positive selection on the H3 hemagglutinin gene of human influenza virus A. Molecular Biology and Evolution 16, 1457–1465 (1999)Google Scholar
  7. 7.
    Chase, M.W., Soltis, D.E., Olmstead, R.G., Morgan, D., Les, D.H., Mishler, B.D., Duvall, M.R., Price, R.A., Hills, H.G., Qiu, Y.L., Kron, K.A., Rettig, J.H., Conti, E., Palmer, J.D., Manhart, J.R., Sytsma, K.J., Michaels, H.J., Kress, W.J., Karol, K.G., Clark, W.D., Hedren, M., Gaut, B.S., Jansen, R.K., Kim, K.J., Wimpee, C.F., Smith, J.F., Furnier, G.R., Strauss, S.H., Xiang, Q.Y., Plunkett, G.M., Soltis, P.S., Swensen, S.M., Williams, S.E., Gadek, P.A., Quinn, C.J., Eguiarte, L.E., Golenberg, E., Learn Jr., G.H., Graham, S.W., Barrett, S.C.H., Dayanandan, S., Albert, V.A.: Phylogenetics of seed plants: an analysis of nucleotide sequences from the plastid gene rbcL. Annals of the Missouri Botanical Garden 80, 528–580 (1993)CrossRefGoogle Scholar
  8. 8.
    Cole, R., Farach-Colton, M., Hariharan, R., Przytycka, T.M., Thorup, M.: An O(n log n) algorithm for the maximum agreement subtree problem for binary trees. SIAM Journal of Computing 30(5), 1385–1404 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Day, W.H.E.: Optimal algorithms for comparing trees with labeled leaves. Journal of Classification 2, 7–28 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Estabrook Jr., G.F., Johnson, C.S., McMorris, F.R.: An algebraic analysis of cladistic characters. Discrete Mathematics 16, 141–147 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Estabrook, G.F., McMorris, F.R.: When is one estimate of evolutionary history a refinement of another? Mathematical Biology 10, 367–373 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Farach, M., Przytycka, T., Thorup, M.: On the agreement of many trees. Information. Processing Letters 55, 297–301 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Finden, C.R., Gordon, A.D.: Obtaining common pruned trees. Journal of Classification 2, 255–276 (1985)CrossRefGoogle Scholar
  14. 14.
    Goddard, W., Kubicka, E., Kubicki, G., McMorris, F.R.: The agreement metric for labelled binary trees. Mathematical Biosciences 123, 215–226 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Gusfield, D.: Efficient algorithms for inferring evolutionary trees. Networks 21, 12–28 (1991)Google Scholar
  16. 16.
    Källersjö, M., Farris, J.S., Chase, M.W., Bremer, B., Fay, M.F., Humphries, C.J., Pedersen, G., Seberg, O., Bremer, K.: Simultaneous parsimony jackknife analysis of 2538 rbcl DNA sequences reveals support for major clades of green plants, land plants, seed plants and flowering plants. Plant Systematics and Evolution 213, 259–287 (1998)CrossRefGoogle Scholar
  17. 17.
    Kubicka, E., Kubicki, G., McMorris, F.R.: On agreement subtrees of two binary trees. Congressus Numerantium 88, 217–224 (1992)MathSciNetGoogle Scholar
  18. 18.
    Margush, T., McMorris, F.R.: Consensus n-trees. Bulletin of Mathematical Biology 43(2), 239–244 (1981)zbMATHMathSciNetGoogle Scholar
  19. 19.
    McMorris, F.R., Meronik, D.B., Neumann, D.A.: A view of some consensus methods for trees. In: Felsenstein, J. (ed.) Numerical Taxonomy, pp. 122–125. Springer, Heidelberg (1983)Google Scholar
  20. 20.
    McMorris, F.R.: On the compatibility of binary qualitive taxonomic characters. Bulletin of Mathematical Biology 39, 133–138 (1977)zbMATHMathSciNetGoogle Scholar
  21. 21.
    John, K.S., Amenta, N., Clarke, F.: A linear-time majority tree algorithm. In: Benson, G., Page, R.D.M. (eds.) WABI 2003. LNCS (LNBI), vol. 2812, pp. 216–227. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  22. 22.
    Savolainen, V., Chase, M.W., Hoot, S.B., Morton, C.M., Soltis, D.E., Bayer, C., Fay, M.F., De Bruijn, A.Y., Sullivan, S., Qiu, Y.L.: Phylogenetics of flowering plants based on combined analysis of plastid atpB and rbcL gene sequences. Systematic Biology 49, 306–362 (2000)CrossRefGoogle Scholar
  23. 23.
    Soltis, P.S., Soltis, D.E., Chase, M.W.: Angiosperm phylogeny inferred from multiple genes as a tool for comparative biology. Nature 402, 402–404 (1999)CrossRefGoogle Scholar
  24. 24.
    Steel, M., Warnow, T.: Kaikoura tree theorems: Computing the maximum agreement subtree. Information Processing Letters 48(2), 77–82 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Amir, A., Keselman, D.: Maximum agreement subtree in a set of evolutionary trees - metrics and efficient algorithms. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 758–769 (1994)Google Scholar
  26. 26.
    Van de Peer, Y., De Wachter, R.: Evolutionary relationships among the eukaryotic crown taxa taking into account site-to-site rate variation in 18S rRNA. Journal of molecular evolution 45, 619–630 (1997)CrossRefGoogle Scholar
  27. 27.
    Warnow, T.J.: Three compatibility and inferring evolutionary history. Journal of Algorithms 16, 388–407 (1991)CrossRefMathSciNetGoogle Scholar
  28. 28.
    Williams, T.L., Berger-Wolf, T.Y., Moret, B.M.E., Roshan, U., Warnow, T.J.: The relationship between maximum parsimony scores and phylogenetic tree topologies. Technical Report TR-CS-2004-04, University of New Mexico (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Tanya Y. Berger-Wolf
    • 1
  1. 1.Department of Computer ScienceUniversity of New MexicoAlbuquerqueUSA

Personalised recommendations