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

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Abstract

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.

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References

  • Cavender, J. A. 1978. Taxonomy with confidence.Mathematical Biosci. 40, 270–280.

    MathSciNet  Google Scholar 

  • Chang, J. T. 1996. Inconsistency of evolutionary tree topology reconstruction methods when substitution rates vary across characters.Mathematical Biosci. 134, 189–215.

    Article  MATH  Google Scholar 

  • Edwards, A. W. F. 1972.Likelihood. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Erdős, P. L. and L. A. Székely. 1993. Counting bichromatic evolutionary trees.Discrete Appl. Math. 47, 1–8.

    Article  MathSciNet  Google Scholar 

  • Erdős, P. L. and L. A. Székely. 1994. On weighted multiway cuts in trees.Mathematical Programming 65, 93–105.

    Article  MathSciNet  Google Scholar 

  • Farris, J. S. 1973. A probability model for inferring evolutionary trees.Systematic Zoology 22, 250–256.

    Article  Google Scholar 

  • Felsenstein, J. 1978. Cases in which parsimony or compatibility will be positively misleading.Systematic Zoology 27, 401–410.

    Article  Google Scholar 

  • 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 

  • Fitch, W. M. 1971. Toward defining the course of evolution: minimum change for a specific tree topology.Systematic Zoology 20, 406–416.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Harary, F. 1969.Graph Theory. Series in Mathematics. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Hendy, M. D. and D. Penny 1989. A framework for the qualitative study of evolutionary trees.Systematic Zoology 38, 297–309.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Maddison, W. P. 1995. Calculating the probability distributions of ancestral states reconstructed by parsimony on phylogenetic trees.Systematic Biol. 44, 474–481.

    Article  Google Scholar 

  • 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 

  • 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 

  • Steel, M. A. 1993a. Decompositions of leaf-colored binary trees.Advances in Appl. Math. 14, 1–24.

    Article  MATH  MathSciNet  Google Scholar 

  • Steel, M. A. 1993b. Distributions on bicoloured binary trees arising from the principle of parsimony.Discrete Appl. Math. 41, 245–261.

    Article  MATH  MathSciNet  Google Scholar 

  • Steel, M. A. 1994. The maximum likelihood point for a phylogenetic tree is not unique.Systematic Biol. 43, 560–564.

    Article  Google Scholar 

  • 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.

  • Tillier, E. R. M. 1994. Maximum likelihood with multiparameter models of substitution.J. Molecular Evolution 39, 409–417.

    Article  Google Scholar 

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Tuffley, C., Steel, M. Links between maximum likelihood and maximum parsimony under a simple model of site substitution. Bltn Mathcal Biology 59, 581–607 (1997). https://doi.org/10.1007/BF02459467

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  • DOI: https://doi.org/10.1007/BF02459467

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