Issue No.01 - January-March (2008 vol.5)
pp: 136-145
The Maximum Parsimony problem aims at reconstructing a phylogenetic tree from DNA sequences while minimizing the number of genetic transformations. To solve this NP-complete problem, heuristic methods have been developed, often based on local search. In this article, we focus on the influence of the neighborhood relations. After analyzing the advantages and drawbacks of the well-known NNI, SPR and TBR neighborhoods, we introduce the concept of Progressive Neighborhood which consists in constraining progressively the size of the neighborhood as the search advances. We empirically show that applied to the Maximum Parsimony problem, this progressive neighborhood turns out to be more efficient and robust than the classic neighborhoods using a descent algorithm. Indeed, it allows to find better solutions with a smaller number of iterations or trees evaluated.
optimization, combinatorial algorithms, phylogeny reconstruction, maximum parsimony
Adrien Go?ffon, Jean-Michel Richer, Jin-Kao Hao, "Progressive Tree Neighborhood Applied to the Maximum Parsimony Problem", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.5, no. 1, pp. 136-145, January-March 2008, doi:10.1109/TCBB.2007.1065
[1] A.A. Andreatta and C.C. Ribeiro, “Heuristics for the Phylogeny Problem,” J. Heuristics, vol. 8, pp. 429-447, 2002.
[2] B.L. Allen and M. Steel, “Subtree Transfer Operations and Their Induced Metrics on Evolutionary Trees,” Annals of Combinatorics, vol. 5, no. 1, pp. 1-15, 2000.
[3] O.R.P. Bininda-Emonds, “Phylogenetic Supertrees: Combining Information to Reveal the Tree of Life,” Computational Biology, vol. 4, Kluwer Academic Publishers, 2004.
[4] L.L. Cavalli-Sforza and A.W.F. Edwards, “Phylogenetic Analysis: Models and Estimation Procedures,” Evolution, vol. 32, pp. 550-570, 1967.
[5] I. Charon and O. Hudry, “The Noising Methods: A Generalization of Some Metaheuristics,” European J. Operational Research, vol. 135, pp. 86-101, 2001.
[6] M.W. Chase et al., “Phylogenetics of Seed Plants: An Analysis of Nucleotide-Sequences from the Plastid Gene rbcL,” Annals of the Missouri Botanical Garden, vol. 80, pp. 528-580, 1993.
[7] A.W.F. Edwards and L.L. Cavalli-Sforza, “The Reconstruction of Evolution,” Annals of Human Genetics, vol. 27, pp. 105-106, 1963.
[8] J. Felsenstein, “Evolutionary Trees from DNA Sequences: A Maximum Likelihood Approach,” J. Molecular Evolution, vol. 17, pp. 368-376, 1981.
[9] J. Felsenstein, Inferring Phylogenies. Sinauer Assoc., 2003.
[10] T.A. Feo and M.G.C. Resende, “Greedy Randomized Adaptative Search Procedures,” J. Global Optimization, vol. 6, pp. 109-133, 1995.
[11] W. Fitch, “Towards Defining Course of Evolution: Minimum Change for a Specified Tree Topology,” Systematic Zoology, vol. 20, pp. 406-416, 1971.
[12] W.M. Fitch and E. Margoliash, “Construction of Phylogenetic Trees,” Science, vol. 155, pp. 279-284, 1967.
[13] L.R. Foulds and R.L. Graham, “The Steiner Problem in Phylogeny Is NP-Complete,” Advances in Applied Math., vol. 3, pp. 43-49, 1982.
[14] G. Ganapathy, V. Ramachandran, and T. Warnow, “On Contract-and-Refine Transformations between Phylogenetic Trees,” Proc. ACM-SIAM Symp. Discrete Algorithms (SODA '04), pp. 900-909, 2004.
[15] O. Gascuel, “On the Optimization Principle in Phylogenetic Analysis and the Minimum Evolution Criterion,” Biology and Evolution, vol. 17, pp. 401-405, 2000.
[16] A. Goëffon, J.-M. Richer, and J.-K. Hao, “Local Search for the Maximum Parsimony Problem,” Lecture Notes in Computer Science, vol. 3612, pp. 678-683, Springer, 2005.
[17] A. Goëffon, J.-M. Richer, and J.-K. Hao, “A Distance-Based Information Preservation Tree Crossover for the Maximum Parsimony Problem,” Lecture Notes in Computer Science, vol. 4193, pp. 761-770, Springer, 2006.
[18] P.A. Goloboff, “Character Optimisation and Calculation of Tree Lengths,” Cladistics, vol. 9, pp. 433-436, 1993.
[19] P.A. Goloboff, “Analyzing Large Data Sets in Reasonable Times: Solutions for Composite Optima,” Cladistics, vol. 15, pp. 415-428, 1999.
[20] P.A. Goloboff, J.S. Farris, and K. Nixon, “TNT: Tree Analysis Using New Technology,” http://www.cladistics.comaboutTNT.html, 2003.
[21] P. Hansen and N. Mladenovic, “An Introduction to Variable Neighborhood Search,” Metaheuristics, Advances and Trends in Local Search Paradigms for Optimization, S. Voss et al., eds., pp. 433-458, Kluwer Academic Publishers, 1999.
[22] D. Hillis, C. Moritz, and B. Mable, Molecular Systematics. Sinauer, 1996.
[23] H.H. Hoos and T. Stützle, Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, 2005.
[24] M. Kimura, “A Simple Model for Estimating Evolutionary Rates of Base of Base Substitutions through Comparative Studies of Nucleotide Sequence,” J. Molecular Evolution, vol. 16, pp. 111-120, 1980.
[25] M.K. Kuhner and J. Felsenstein, “A Simulation Comparison of Phylogeny Algorithms under Equal and Unequal Evolutionary Rates,” Molecular Biology and Evolution, vol. 11, pp. 459-468, 1994, (Erratum 12:525).
[26] M. Luckow and R.A. Pimentel, “An Empirical Comparison of Numerical Wagner Computer Programs,” Cladistics, vol. 1, pp. 47-66, 1985.
[27] D.R. Maddison, “The Discovery and Importance of Multiple Islands of Most-Parsimonious Trees,” Systematic Zoology, vol. 43, no. 3, pp. 315-328, 1991.
[28] K.C. Nixon, “The Parsimony Ratchet, A New Method for Rapid Parsimony Analysis,” Cladistics, vol. 15, pp. 407-414, 1999.
[29] C.C. Ribeiro and D.S. Vianna, “A GRASP/VND Heuristic for the Phylogeny Problem Using a New Neighborhood Structure,” Int'l Trans. Operational Research, vol. 12, pp. 1-14, 2005.
[30] D.F. Robinson, “Comparison of Labeled Trees with Valency Three,” J. Combinatorial Theory, vol. 11, pp. 105-119, 1971.
[31] N. Saitou and M. Nei, “The Neighbor-Joining Method: A New Method for Reconstructing Phylogenetic Trees,” Molecular Biology and Evolution, vol. 4, pp. 406-425, 1987.
[32] E. Schröder, “Vier Kombinatorische Probleme,” Zeitschrift fur Mathematik und Physik, vol. 15, pp. 361-376, 1870.
[33] R.R. Sokal and C.D. Michener, A Statistical Method for Evaluating Systemaic Relationships, vol. 38, Univ. of Kansas Science Bull., pp.1409-1438, 1958.
[34] R.R. Sokal and P.H.A. Sneath, Principles of Numerical Taxonomy. W.H. Freeman, 1963.
[35] D.L. Swofford and G.J. Olsen, “Phylogeny Reconstruction,” Molecular Systematics, D.M. Hillis and C. Moritz, eds., chapter11, pp. 411-501, 1990.
[36] D.L. Swofford, “PAUP*: Phylogenetic Analysis Using Parsimony 4.0 Beta, 2002,” Molecular Systematics, chapter 11, pp. 411-501, 1990.
[37] M.S. Waterman and T.F. Smith, “On the Similarity of Dendograms,” J. Theoretical Biology, vol. 73, pp. 789-800, 1978.