The Community for Technology Leaders
RSS Icon
Issue No.01 - Jan.-Feb. (2013 vol.10)
pp: 61-72
Cuong V. Than , Dept. of Comput. Sci., Univ. of Tuebingen, Tubingen, Germany
Noah A. Rosenberg , Dept. of Biol., Stanford Univ., Stanford, CA, USA
In the minimizing-deep-coalescences (MDC) approach for species tree inference, a tree that has the minimal deep coalescence cost for reconciling a collection of gene trees is taken as an estimate of the species tree topology. The MDC method possesses the desirable Pareto property, and in practice it is quite accurate and computationally efficient. Here, in order to better understand the MDC method, we investigate some properties of the deep coalescence cost. We prove that the unit neighborhood of either a rooted species tree or a rooted gene tree under the deep coalescence cost is exactly the same as the tree's unit neighborhood under the rooted nearest-neighbor interchange (NNI) distance. Next, for a fixed species tree, we obtain the maximum deep coalescence cost across all gene trees as well as the number of gene trees that achieve the maximum cost. We also study corresponding problems for a fixed gene tree.
Vegetation, Topology, Computational biology, Bioinformatics, Upper bound, Sorting, Transforms,nearest-neighbor interchange, Deep coalescence, gene tree reconcilation, incomplete lineage sorting, maximal subtrees
Cuong V. Than, Noah A. Rosenberg, "Mathematical Properties of the Deep Coalescence Cost", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.10, no. 1, pp. 61-72, Jan.-Feb. 2013, doi:10.1109/TCBB.2012.133
[1] W.P. Maddison, “Gene Trees in Species Trees,” Systematic Biology, vol. 46, pp. 523-536, 1997.
[2] W.P. Maddison and L.L. Knowles, “Inferring Phylogeny Despite Incomplete Lineage Sorting,” Systematic Biology, vol. 55, pp. 21-30, 2006.
[3] C. Than and L. Nakhleh, “Species Tree Inference by Minimizing Deep Coalescences,” PLoS Computational Biology, vol. 5, article e1000501, 2009.
[4] M.S. Bansal, J.G. Burleigh, and O. Eulenstein, “Efficient Genome-Scale Phylogenetic Analysis under the Duplication-Loss and Deep Coalescence Cost Models,” BMC Bioinformatics, vol. 11, article S42, 2010.
[5] H.T. Lin, J.G. Burleigh, and O. Eulenstein, “The Deep Coalescence Consensus Tree Problem is Pareto on Clusters,” Proc. Seventh Int'l Symp. Bioinformatics Research and Applications, Lecture Notes in Computer Science, vol. 6674, pp. 172-183, 2011.
[6] L. Zhang, “From Gene Trees to Species Trees II: Species Tree Inference by Minimizing Deep Coalescence Events,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 8, no. 6, pp. 1685-1691, Nov./Dec. 2011.
[7] T. Wu and L. Zhang, “Structural Properties of the Reconciliation Space and Their Applications in Enumerating Nearly-Optimal Reconcilations between a Gene Tree and a Species Tree,” BMC Bioinformatics, vol. 12, article S7, 2012.
[8] J.H. Degnan and N.A. Rosenberg, “Gene Tree Discordance, Phylogenetic Inference and the Multispecies Coalescent,” Trends in Ecology and Evolution, vol. 24, pp. 332-340, 2009.
[9] C.V. Than and N.A. Rosenberg, “Consistency Properties of Species Tree Inference by Minimizing Deep Coalescences,” J. Computational Biology, vol. 18, pp. 1-15, 2011.
[10] D.F. Robinson, “Comparison of Labeled Trees with Valency Three,” J. Combinatorial Theory, vol. 11, pp. 105-119, 1971.
[11] B. Allen and M. Steel, “Subtree Transfer Operations and Their Induced Metrics On Evolutionary Trees,” Annals of Combinatorics, vol. 5, pp. 1-13, 2001.
[12] F.A. Matsen, “A Geometric Approach to Tree Shape Statistics,” Systematic Biology, vol. 55, pp. 652-661, 2006.
[13] R. Nichols, “Gene Trees and Species Trees Are Not the Same,” Trends in Ecology and Evolution, vol. 16, pp. 358-364, 2001.
[14] J.S. Rogers, “Central Moments and Probability Distributions of three Measures of Phylogenetic Tree Imbalance,” Systematic Biology, vol. 45, pp. 99-110, 1996.
[15] M.G.B. Blum and O. Francois, “Minimal Clade Size and External Branch Length under the Neutral Coalescent,” Advances in Applied Probability, vol. 37, pp. 647-662, 2005.
[16] R. Klein and D. Wood, “On the Path Length of Binary Trees,” J. Assoc. Computing Machinery, vol. 36, pp. 280-289, 1989.
[17] D.E. Knuth, The Art of Computer Programming: Fundamental Algorithms, third ed., vol. 1, Addison-Wesley, 1997.
[18] P.W. Diaconis and S.P. Holmes, “Matchings and Phylogenetic Trees,” Proc. Nat'l Academy of Sciences USA, vol. 95, pp. 14600-14602, 1998.
[19] G.W. Furnas, “The Generation of Random, Binary Unordered Trees,” J. Classification, vol. 1, pp. 187-233, 1984.
[20] M. Kirkpatrick and M. Slatkin, “Searching for Evolutionary Patterns in the Shape of a Phylogenetic Tree,” Evolution, vol. 47, pp. 1171-1181, 1993.
[21] C. Semple and M. Steel, Phylogenetics, Oxford Lecture Series in Mathematics and Its Applications, vol. 24, Oxford Univ. Press, 2003.
240 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool