Abstract
We present efficient sensitivity-analysis algorithms for two problems involving Markov models of sequence evolution: ancestral reconstruction in evolutionary trees and local ungapped alignment under log-odds scoring. Our algorithms generate complete descriptions of the optimum solutions for all possible values of the evolutionary distance. The running time for the parametric ancestral reconstruction problem under the Kimura 2-parameter model is O(kn + kn 2/3 log k), where n is the number of sequences and k is their length, assuming all edges have the same length. For the parametric gapless alignment problem under the Jukes-Cantor model, the running time is O(mn + mn 2/3 log m), where m and n are the sequence lengths and n ≤ m.
Research partially supported by grants CCR-9988348 and EF-0334832 from the National Science Foundation.
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References
Agarwal, P., States, D.: A Bayesian evolutionary distance for parametrically aligned sequences. Journal of Computational Biology 3, 1–17 (1996)
Agarwal, P.K., Sharir, M.: Davenport-Schinzel Sequences and their Geometric Applications. Cambridge University Press, Cambridge (1995)
Chor, B., Khetan, A., Snir, S.: Maximum likelihood on four taxa phylogenetic trees: analytic solutions. In: RECOMB 2003: Proceedings of the seventh annual international conference on Computational molecular biology, pp. 76–83. ACM Press, New York (2003)
Cohen, R.F., Tamassia, R.: Dynamic expression trees. Algorithmica 13(3), 245–265 (1995)
Dayhoff, M., Schwartz, R., Orcutt, B.: A model of evolutionary change in proteins. Atlas of Protein Sequence and Structure 5, 345–352 (1978)
Durbin, R., Eddy, S., Krogh, A., Mitchison, G.: Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. Cambridge University Press, Cambridge (1998)
Felsenstein, J.: Inferring Phylogenies. Sinauer Assoc., Sunderland (2003)
Fernández-Baca, D., Seppäläinen, T., Slutzki, G.: Parametric multiple sequence alignment and phylogeny construction. Journal of Discrete Algorithms 2, 271–287 (2004); Special issue on Combinatorial Pattern Matching, Giancarlo R., Sankoff, D. (eds.)
Fernández-Baca, D., Slutzki, G.: Optimal parametric search on graphs of bounded treewidth. Journal of Algorithms 22, 212–240 (1997)
Fitch, W.M., Smith, T.F.: Optimal sequence alignments. Proc. Natl. Acad. Sci. USA 80, 1382–1386 (1983)
Gusfield, D., Balasubramanian, K., Naor, D.: Parametric optimization of sequence alignment. Algorithmica 12, 312–326 (1994)
Pachter, L., Sturmfels, B.: Parametric inference for biological sequence analysis. Proc. Natl. Acad. Sci. USA 101(46), 16138–16143 (2004)
Pachter, L., Sturmfels, B.: Tropical geometry of statistical models. Proc. Natl. Acad. Sci. USA 101(46), 16132–16137 (2004)
Semple, C., Steel, M.: Phylogenetics. Oxford Lecture Series in Mathematics. Oxford University Press, Oxford (2003)
States, D., Gish, W., Altschul, S.: Improved sensitivity of nucleic acid database searches using application-specific scoring matrices. Methods in Enzymology 3, 66–70 (1991)
Steel, M.A.: The maximum likelihood point for a phylogenetic tree is not unique. Syst. Biology 43(4), 560–564 (1994)
Steel, M.A., Penny, D.: Parsimony, likelihood, and the role of models in molecular phylogenetics. Molecular Biology and Evolution 17, 839–850 (2000)
Waterman, M.S., Eggert, M., Lander, E.: Parametric sequence comparisons. Proc. Natl. Acad. Sci. USA 89, 6090–6093 (1992)
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Fernández-Baca, D., Venkatachalam, B. (2005). Parametric Analysis for Ungapped Markov Models of Evolution. In: Apostolico, A., Crochemore, M., Park, K. (eds) Combinatorial Pattern Matching. CPM 2005. Lecture Notes in Computer Science, vol 3537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496656_34
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DOI: https://doi.org/10.1007/11496656_34
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