Maximum likelihood on four taxa phylogenetic trees: Analytic solutions

Proceedings of the Annual International Conference on Computational Molecular Biology, RECOMB

Volumn , Issue , 2003, Pages 76-83

  Chor, Benny ^a   Khetan, Amit ^b   Snir, Sagi ^c  

^a TEL AVIV UNIVERSITY   (Israel)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

2 state model; Constrained optimization; Groebner bases; Hadamard conjugation; Maximum likelihood; Molecular clock; Phylogenetic trees; Saturation; Symbolic algebra

Indexed keywords

ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; OPTIMIZATION; TOPOLOGY;

PHYLOGENETIC TREES;

GENETIC ENGINEERING;

EID: 0038716206     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (28)

1. A. Aho, Y. Sagiv, T. Szymanski, and J. Ullman. Inferring a tree from lowest common ancestors with an application to the optimization of relational expressions. SIAM Journal of Computing, 10(3):405-421, 1981.
2. H.-J. Bandelt and A. Dress. Reconstructing the shape of a tree from observed dissimilarity data. Advances in Applied Mathematics, 7:309-343, 1986.
3. A. Ben-Dor, B. Chor, D. Graur, R. Ophir, and D. Pelleg. Constructing phylogenies from quarbcgoptets: Elucidation of eutherian superordinal relationships. Jour. of Comput. Biology, 5(3):377-390, 1998.
4. B. Chor, M. Hendy, B. Holland, and D. Penny. Multiple maxima of likelihood in phylogenetic trees: An analytic approach. MBE, 17(10):1529-1541, 2000. Earlier version appeared in RECOMB 2000.
5. B. Chor, M. Hendy, and D. Penny. Analytic solutions for three taxon mlmc trees with variable rates across sites. In WABI 2001, 2001.
6. J. Felsenstein. PHYLIP - phylogenetic inference package, (version 3.2), Cladistics, 5:164-166, 1989.
7. K. Fukami and Y. Tateno. On the uniqueness of the maximum likelihood method for estimating molecular trees: Uniqueness of the likelihood point. J. Mol. Evol., 28:460-464, 1989.
8. I. Gelfand, M. Kapranov, and A. Zelevinsky. Discriminants, Resultants and Multidimensional Determinants. Birkhauser, Boston. 1994.
9. D. Graur and W. Li. Fundamentals of Molecular Evolution. Sinauer Assoc., 2000.
10. M. D. Hendy and D. Penny. Spectral analysis of phylogenetic data. J. Classif., 10:5-24, 1993.
11. M. D. Hendy, D. Penny, and M. Steel. Discrete fourier analysis for evolutionary trees. Proc. Natl. Acad. Sci. USA., 91:3339-3343, 1994.
12. T. Jiang, P. Kearney, and M. Li. Orchestrating quartets: approximation and data correction. In IEEE Symp. Foundation of Computer Science (FOCS), pages 416-425, Palo Alto, California, November 1998.
13. K. S. John, T. Warnow. B. M. E. Moret, and L. Vawter. Performance study of phylogenetic methods: (unweighted) quartet methods and neighbor-joining. In Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, 2001.
14. T. Jukes and C. Cantor. Evolution of protein molecules. In H. Munro, editor, Mammalian Protein Metabolism, pages 21-132. Academic Press, New York, 1969.
15. P. Kearney. The ordinal quartet method. In RECOMB98, the Second Annual International Conference on Computational Molecular Biology, New York, 1998. ACM.
16. M. Kimura. The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge, 1983.
17. J. Neymann. Molecular studies of evolution: A source of novel statistical problems. In S. Gupta and Y. Jackel, editors. Statistical Decision Theory and Related Topics, pages 1-27. Academic Press, New York, 1971.
18. R. Page. Modified mincut supertrees. In R. Guigo and D Gusfield (Eds): WABI 2002, LNCS 2452, 2002.
19. V. Ranwez and O. Gascuel. Quartet-based phylogenetic inference: Improvements and limits. Molecular Biology and Evolution, 18:1103-1116, 2001.
20. M. Ruvolo. Molecular phylogeny of the hominoids: Inferences from multiple independent dna sequence data sets. Molecular Biology and Evolution, 14(7):248-265, 1997.
21. C. Semple and M. Steel. A supertree method for rooted trees. Discrete Applied Mathematics, 103:147-158, 2000.
22. M. Steel. The complexity of reconstructing trees from qualitative characters and subtress. Journal of Classification, 9(1):91-116, 1992.
23. M. Steel. The maximum likelihood point for a phylogenetic tree is not unique. Syst. Biology, 43(4):560-564, 1994.
24. M. Steel, A. Dress, and S. Boker. Simple but fundamental limitations on supertree and consensus tree methods. Systematic Biology, 49:363-368, 2000.
25. K. Strimmer and A. von Haeseler. Quartet puzzling: A quartet maximum-likelihood method for reconstructing tree topologies. Molecular Biology and Evolution, 13(7):964-969, 1996. Software available at ftp://ftp.ebi.ac.uk/pub/software/unix/puzzle/.
26. J. Thompson, D. Higgins, and T. Gibson. CLUSTAL W: Improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalty and weight matrix choice. Nucleic Acids Research, 22:4673-4780, 1994.
27. E. Tillier. Maximum likelihood with multiparameter models of substitution. J. Mol. Evol., 39:409-417, 1994.
28. Z. Yang. Complexity of the simplest phylogenetic estimation problem. Proc. R. Soc. Lond. B, 267:109-119, 2000.