Bulletin of Mathematical Biology

, Volume 59, Issue 3, pp 581–607 | Cite as

Links between maximum likelihood and maximum parsimony under a simple model of site substitution

  • Chris Tuffley
  • Mike Steel


Stochastic models of nucleotide substitution are playing an increasingly important role in phylogenetic reconstruction through such methods as maximum likelihood. Here, we examine the behaviour of a simple substitution model, and establish some links between the methods of maximum parsimony and maximum likelihood under this model.


Maximum Parsimony Binary Tree Mutation Probability Symmetric Model Internal Vertex 
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. Cavender, J. A. 1978. Taxonomy with confidence.Mathematical Biosci. 40, 270–280.MathSciNetGoogle Scholar
  2. Chang, J. T. 1996. Inconsistency of evolutionary tree topology reconstruction methods when substitution rates vary across characters.Mathematical Biosci. 134, 189–215.zbMATHCrossRefGoogle Scholar
  3. Edwards, A. W. F. 1972.Likelihood. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  4. Erdős, P. L. and L. A. Székely. 1993. Counting bichromatic evolutionary trees.Discrete Appl. Math. 47, 1–8.MathSciNetCrossRefGoogle Scholar
  5. Erdős, P. L. and L. A. Székely. 1994. On weighted multiway cuts in trees.Mathematical Programming 65, 93–105.MathSciNetCrossRefGoogle Scholar
  6. Farris, J. S. 1973. A probability model for inferring evolutionary trees.Systematic Zoology 22, 250–256.CrossRefGoogle Scholar
  7. Felsenstein, J. 1978. Cases in which parsimony or compatibility will be positively misleading.Systematic Zoology 27, 401–410.CrossRefGoogle Scholar
  8. Felsenstein, J. 1981. A likelihood approach to character weighting and what it tells us about parsimony and compatibility.Biological J. Linnean Soc. 16, 183–196.Google Scholar
  9. Fitch, W. M. 1971. Toward defining the course of evolution: minimum change for a specific tree topology.Systematic Zoology 20, 406–416.CrossRefGoogle Scholar
  10. Fukami, K. and Y. Tateno. 1989. On the maximum likelihood method for estimating molecular trees: uniqueness of the likelihood point.J. Molecular Evolution 28, 460–464.Google Scholar
  11. Goldman, N. 1990. Maximum likelihood inference of phylogenetic trees, with special reference to a Poisson process model of DNA substitution and to parsimony analyses.Systematic Zoology 39, 345–361.CrossRefGoogle Scholar
  12. Harary, F. 1969.Graph Theory. Series in Mathematics. Reading, MA: Addison-Wesley.Google Scholar
  13. Hendy, M. D. and D. Penny 1989. A framework for the qualitative study of evolutionary trees.Systematic Zoology 38, 297–309.CrossRefGoogle Scholar
  14. Jukes, T. H. and C. R. Cantor 1969. Evolution of protein molecules. InMammalian Protein Metabolism, H. N. Munro (Ed), pp. 21–132. New York: Academic Press.Google Scholar
  15. Lockhart, P. J., A. W. D. Larkum, M. A. Steel, P. J. Waddell and D. Penny. 1996. Evolution of chlorophyll and bacteriochlorophyll: the problem of invariant sites in sequence analysis.Proc. Natl. Acad. Sci. USA 93, 1930–1934.CrossRefGoogle Scholar
  16. Maddison, W. P. 1995. Calculating the probability distributions of ancestral states reconstructed by parsimony on phylogenetic trees.Systematic Biol. 44, 474–481.CrossRefGoogle Scholar
  17. Neyman, J. 1971. Molecular studies of evolution: A source of novel statistical problems. InStatistical Decision Theory and Related Topics, S. S. Gupta and J. Yackel (Eds), pp. 1–27. New York: Academic Press.Google Scholar
  18. Penny, D., P. J. Lockhart, M. A. Steel and M. D. Hendy. 1994. The role of models in reconstructing evolutionary trees. InModels in Phylogeny Reconstruction, R. W. Scotland, D. J. Siebert and D. M. Williams (Eds), Systematic Association Special Vol. 52, pp. 211–230. Oxford: Clarendon Press.Google Scholar
  19. Steel, M. A. 1993a. Decompositions of leaf-colored binary trees.Advances in Appl. Math. 14, 1–24.zbMATHMathSciNetCrossRefGoogle Scholar
  20. Steel, M. A. 1993b. Distributions on bicoloured binary trees arising from the principle of parsimony.Discrete Appl. Math. 41, 245–261.zbMATHMathSciNetCrossRefGoogle Scholar
  21. Steel, M. A. 1994. The maximum likelihood point for a phylogenetic tree is not unique.Systematic Biol. 43, 560–564.CrossRefGoogle Scholar
  22. Swofford, D. L., G. J. Olsen, P. J. Waddell and D. M. Hillis. 1996. Phylogenetic inference. InMolecular Systematics, 2nd ed., D. M. Hillis, C. Moritz and B. K. Marble (Eds), ch. 11, pp. 407–514. Sinauer Associates.Google Scholar
  23. Tillier, E. R. M. 1994. Maximum likelihood with multiparameter models of substitution.J. Molecular Evolution 39, 409–417.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1997

Authors and Affiliations

  • Chris Tuffley
    • 1
  • Mike Steel
    • 1
  1. 1.Biomathematics Research Centre, Department of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand

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