This Article 
 Bibliographic References 
 Add to: 
Mixed Integer Linear Programming for Maximum-Parsimony Phylogeny Inference
July-September 2008 (vol. 5 no. 3)
pp. 323-331
Reconstruction of phylogenetic trees is a fundamental problem in computational biology. While excellent heuristic methods are available for many variants of this problem, new advances in phylogeny inference will be required if we are to be able to continue to make effective use of the rapidly growing stores of variation data now being gathered. In this paper, we present two integer linear programming (ILP) formulations to find the most parsimonious phylogenetic tree from a set of binary variation data. One method uses a flow-based formulation that can produce exponential numbers of variables and constraints in the worst case. The method has, however, proven extremely efficient in practice on datasets that are well beyond the reach of the available provably efficient methods, solving several large mtDNA and Y-chromosome instances within a few seconds and giving provably optimal results in times competitive with fast heuristics than cannot guarantee optimality. An alternative formulation establishes that the problem can be solved with a polynomial-sized ILP. We further present a web server developed based on the exponential-sized ILP that performs fast maximum parsimony inferences and serves as a front end to a database of precomputed phylogenies spanning the human genome.

[1] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman & Co., 1979.
[2] Int'l HapMap Consortium, “The International HapMap Project,” Nature, vol. 426, pp. 789-796, , 2005.
[3] E.M. Smigielski, K. Sirotkin, M. Ward, and S.T. Sherry, “dbSNP: A Database of Single Nucleotide Polymorphisms,” Nucleic Acids Research, vol. 28, no. 1, pp. 352-355, 2000.
[4] Chimpanzee Sequencing and Analysis Consortium, “Initial Sequence of the Chimpanzee Genome and Comparison with the Human Genome,” Nature, vol. 437, no. 7055, pp. 69-87, , 2005.
[5] K. Linblad-Toh, E. Winchester, M.J. Daly, D.G. Wang, J.N. Hirschhorn, J.P. Laviolette, K. Ardlie, D.E. Reich, E. Robinson, P. Sklar, N. Shah, D. Thomas, J.B. Fan, T. Gingeras, J. Warrington, N. Patil, T.J. Hudson, and E.S. Lander, “Large-Scale Discovery and Genotyping of Single-Nucleotide Polymorphisms in the Mouse,” Nature Genetics, vol. 24, no. 4, pp. 381-386, 2000.
[6] K. Linblad-Toh, C.M. Wade, T.S. Mikkelsen, E.K. Karlsson, D.B. Jaffe, M. Kamal, M. Clamp, J.L. Chang, E.J. Kulbokas, M.C. Zody, E. Mauceli, X. Xie, M. Breen, R.K. Wayne, E.A. Ostrander, C.P. Ponting, F. Galibert, D.R. Smith, P.J. deJong, E. Kirkness, P. Alvarez, T. Biagi, W. Brockman, J. Butler, C.-W. Chin, A. Cook, J. Cuff, M.J. Daly, D. DeCaprio, S. Gnerre, M. Grabherr, M. Kellis, M. Kleber, C. Bardeleben, L. Goodstadt, A. Heger, C. Hitte, L. Kim, K.-P. Kopfli, H.G. Parker, J.P. Pollinger, S.M.J. Searle, N.B. Sutter, R. Thomas, C. Webber, and E.S. Lander, “Genome Sequence, Comparative Analysis and Haplotype Structure of the Domestic Dog,” Nature, vol. 438, no. 7069, pp. 803-819, , 2005.
[7] ENCODE Project Consortium, “The ENCODE (ENCyclopedia of DNA Elements) Project,” Science, vol. 306, no. 5696, pp. 636-640, 2004.
[8] R. Agarwala and D. Fernandez-Baca, “A Polynomial-Time Algorithm for the Perfect Phylogeny Problem When the Number of Character States Is Fixed,” SIAM J. Computing, vol. 23, pp. 1216-1224, 1994.
[9] D. Gusfield, “Efficient Algorithms for Inferring Evolutionary Trees,” Networks, vol. 21, pp. 19-28, 1991.
[10] S. Kannan and T. Warnow, “A Fast Algorithm for the Computation and Enumeration of Perfect Phylogenies,” SIAM J. Computing, vol. 26, pp. 1749-1763, 1997.
[11] H.J. Bandelt, P. Forster, B.C. Sykes, and M.B. Richards, “Mitochondrial Portraits of Human Populations Using Median Networks,” Genetics, vol. 141, pp. 743-753, 1989.
[12] J. Felsenstein, “PHYLIP (Phylogeny Inference Package) Version3.6,” distributed by the author, Dept. of Genome Sciences, Univ. of Washington, 2005.
[13] N. Saitou and M. Nei, “The Neighbor-Joining Method: A New Method for Reconstructing Phylogenetic Trees,” Molecular Biology and Evolution, vol. 4, no. 4, pp. 406-425, 1987.
[14] G.E. Blelloch, K. Dhamdhere, E. Halperin, R. Ravi, R. Schwartz, and S. Sridhar, “Fixed Parameter Tractability of Binary Near-Perfect Phylogenetic Tree Reconstruction,” Proc. 33rd Int'l Colloquium Automata, Languages and Programming (ICALP '06), pp.667-689, 2006.
[15] D. Fernandez-Baca and J. Lagergren, “A Polynomial-Time Algorithm for Near-Perfect Phylogeny,” SIAM J. Computing, vol. 32, pp.1115-1127, 2003.
[16] S. Sridhar, G.E. Blelloch, R. Ravi, and R. Schwartz, “Optimal Imperfect Phylogeny Reconstruction and Haplotyping,” Proc. Computational Systems Bioinformatics Conf. (CSB '06), pp. 199-210, 2006.
[17] S. Sridhar, K. Dhamdhere, G.E. Blelloch, E. Halperin, R. Ravi, and R. Schwartz, “Simple Reconstruction of Binary Near-Perfect Phylogenetic Trees,” Proc. Int'l Workshop Bioinformatics Research and Applications (IWBRA), 2006.
[18] D. Gusfield, “Haplotyping by Pure Parsimony,” Proc. 14th Symp. Combinatorial Pattern Matching (CPM '03), pp. 144-155, 2003.
[19] Steiner Trees in Industry, X. Cheng and D.Z. Zu, eds., Springer, 2002.
[20] F.K. Hwang, D.S. Richards, and P. Winter, “The Steiner Minimum Tree Problems,” Annals of Discrete Math., vol. 53, 1992.
[21] L.R. Foulds and R.L. Graham, “The Steiner Problem in Phylogeny Is NP-Complete,” Advances in Applied Math., vol. 3, 1982.
[22] P. Buneman, “The Recovery of Trees from Measures of Dissimilarity,” Math. in the Archeological and Historical Sciences, F. Hodson et al., eds., pp. 387-395, 1971.
[23] J. Barthélemy, “From Copair Hypergraphs to Median Graphs with Latent Vertices,” Discrete Math, vol. 76, pp. 9-28, 1989.
[24] C. Semple and M. Steel, Phylogenetics. Oxford Univ. Press, 2003.
[25] V. Bafna, D. Gusfield, G. Lancia, and S. Yooseph, “Haplotyping as Perfect Phylogeny: A Direct Approach,” J. Computational Biology, vol. 10, pp. 323-340, 2003.
[26] D. Gusfield and V. Bansal, “A Fundamental Decomposition Theory for Phylogenetic Networks and Incompatible Characters,” Proc. Ninth Int'l Conf. Research in Computational Molecular Biology (RECOMB '05), pp. 217-232, 2005.
[27] J. Beasley, “An Algorithm for the Steiner Problem in Graphs,” Networks, vol. 14, pp. 147-159, 1984.
[28] N. Maculan, “The Steiner Problem in Graphs,” Annals of Discrete Math., vol. 31, pp. 185-212, 1987.
[29] R. Wong, “A Dual Ascent Approach for Steiner Tree Problems on a Directed Graph,” Math. Programming, vol. 28, pp. 271-287, 1984.
[30] A.C. Stone, R.C. Griffiths, S.L. Zegura, and M.F. Hammer, “High Levels of Y-Chromosome Nucleotide Diversity in the Genus Pan,” Proc. Nat'l Academy of Sciences, vol. 99, pp. 43-48, 2002.
[31] T. Wirth, X. Wang, B. Linz, R.P. Novick, J.K. Lum, M. Blaser, G. Morelli, D. Falush, and M. Achtman, “Distinguishing Human Ethnic Groups by Means of Sequences from Helicobacter Pylori: Lessons from Ladakh,” Proc. Nat'l Academy of Sciences, vol. 101, no. 14, pp. 4746-4751, 2004.
[32] S. Sharma, A. Saha, E. Rai, A. Bhat, and R. Bamezai, “Human mtDNA Hypervariable Regions, HVR I and II, Hint at Deep Common Maternal Founder and Subsequent Maternal Gene Flow in Indian Population Groups,” Am. J. Human Genetics, vol. 50, pp.497-506, 2005.
[33] C.J. Lewis, R. Tito, B. Lizarraga, and A. Stone, “Land, Language, and Loci: mtDNA in Native Americans and the Genetic History of Peru,” Am. J. Physical Anthropology, vol. 127, pp. 351-360, 2005.
[34] A. Helgason, G. Palsson, H.S. Pedersen, E. Angulalik, E.D. Gunnarsdottir, B. Yngvadottir, and K. Stefansson, “mtDNA Variation in Inuit Populations of Greenland and Canada: Migration History and Population Structure,” Am. J. Physical Anthropology, vol. 130, pp. 123-134, 2006.
[35] M. Merimaa, M. Liivak, E. Heinaru, J. Truu, and A. Heinaru, “Functional Co-Adaption of Phenol Hydroxylase and Catechol 2,3-Dioxygenase Genes in Bacteria Possessing Different Phenol and p-Cresol Degradation Pathways,” Proc. Eighth Symp. Bacterial Genetics and Ecology (BAGECO '05), vol. 31, pp. 185-212, 2005.
[36] S. Sridhar, F. Lam, G. Blelloch, R. Ravi, and R. Schwartz, “Efficiently Finding the Most Parsimonious Phylogenetic Tree via Linear Programming,” Proc. Int'l Symp. Bioinformatics Research and Applications (ISBRA '07), pp. 37-48, 2007.

Index Terms:
Computational Biology, Algorithms, Integer Linear Programming, Steiner tree problem, Phylogenetic tree reconstruction, Maximum parsimony
Srinath Sridhar, Fumei Lam, Guy E. Blelloch, R. Ravi, Russell Schwartz, "Mixed Integer Linear Programming for Maximum-Parsimony Phylogeny Inference," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 5, no. 3, pp. 323-331, July-Sept. 2008, doi:10.1109/TCBB.2008.26
Usage of this product signifies your acceptance of the Terms of Use.