The Community for Technology Leaders
RSS Icon
Issue No.01 - January-March (2009 vol.6)
pp: 97-102
Stefan Grünewald , CAS-MPG Partner Institute for Computational Biology Max Planck Institute for Mathematics in the Sciences, Shanghai Leipzig
Vincent Moulton , University of East Anglia
With the number of sequenced genomes growing ever larger, it is now common practice to concatenate sequence alignments from several genomic loci as a first step to phylogenetic tree inference. However, as different loci may support different trees due to processes such as gene duplication and lineage sorting, it is important to better understand how commonly used phylogenetic inference methods behave on such "phylogenetic mixtures". Here we shall focus on how parsimony, one of the most popular methods for reconstructing phylogenetic trees, behaves for mixtures of two trees. In particular, we show that (i) the parsimony problem is NP-complete for mixtures of two trees, (ii) there are mixtures of two trees that have exponentially many (in the number of leaves) most parsimonious trees, and (iii) give an explicit description of the most parsimonious tree(s) and scores corresponding to the mixture of a pair of trees related by a single TBR operation.
Applications, Biology and genetics
Stefan Grünewald, Vincent Moulton, "Maximum Parsimony for Tree Mixtures", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.6, no. 1, pp. 97-102, January-March 2009, doi:10.1109/TCBB.2008.75
[1] E. Allman and J. Rhodes, “The Identifiability of Tree Topology for Phylogenetic Models, Including Covarion and Mixture Models,” J.Computational Biology, vol. 13, pp. 1101-1113, 2006.
[2] 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, 1995.
[3] H.-J. Bandelt, Median Hulls as Steiner Hulls in Rectilinear and Molecular Sequence Spaces, A. Brandstädt and V.B. Le, eds., WG 2001, pp. 1-7, 2001.
[4] M. Bordewich and C. Semple, “Computing the Hybridization Number of Two Phylogenetic Trees is Fixed-Parameter Tractable,” IEEE/ACM Trans. Computational Biology and Bioinformatics, to appear.
[5] D. Cieslik, Steiner Minimal Trees. Kluwer Academic, 1998.
[6] W. Day, “Computationally Difficult Parsimony Problems in Phylogenetics Systematics,” J. Theoretical Biology, vol. 103, pp.429-438, 1983.
[7] F. Delsuc, H. Brinkmann, and H. Philippe, “Phylogenomics and the Reconstruction of the Tree of Life,” Nature Rev. Genetics, vol. 6, pp. 361-375, 2005.
[8] J. Felsenstein, Inferring Phylogenies. Sinauer Assoc., 2004.
[9] L. Foulds and R. Graham, “The Steiner Problem in Phylogeny is NP-Complete,” Advances in Applied Math., vol. 3, pp. 43-49, 1982.
[10] M.R. Garey and D.S. Johnson, “The Rectilinear Steiner Tree Problem is NP-Complete,” SIAM J. Applied Math., vol. 32, pp.826-834, 1977.
[11] J. Hein, “Reconstructing Evolution of Sequences Subject to Recombination Using Parsimony,” Math. Biosciences, vol. 98, pp.185-200, 1990.
[12] J. Hein, T. Jiang, L. Wang, and K. Zhang, “On the Complexity of Comparing Evolutionary Trees,” Discrete Applied Math., vol. 71, pp. 153-169, 1996.
[13] M. Hanan, “On Steiner's Problem with Rectilinear Distance,” SIAM J. Applied Math., vol. 14, pp. 255-265, 1966.
[14] S. Klavžar, H.M. Mulder, and R. Škrekovski, “An Euler-Type Formula for Median Graphs,” Discrete Math., vol. 187, pp. 255-258, 1998.
[15] F. Matsen, E. Mossel, and M. Steel, “Mixed-Up Trees: The Structure of Phylogenetic Mixtures,” Bull. of Math. Biology, inpress.
[16] C. Semple and M. Steel, Phylogenetics. Oxford Univ. Press, 2003.
[17] D. Štefankovič and E. Vigoda, “Phylogeny of Mixture Models: Robustness of Maximum Likelihood and Non-Identifiable Distributions,” J. Computational Biology, vol. 14, pp. 156-189, 2007.
[18] R. Tamassia, “On Embedding a Graph in the Grid with the Minimum Number of Bends,” SIAM J. Computing, vol. 16, pp.421-444, 1987.
[19] F.Y. Wu, “Number of Spanning Trees on a Lattice,” J. Physics A: Math. and General, vol. 10, pp. 113-115, 1977.
21 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool