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Issue No.03 - May/June (2011 vol.8)
pp: 848-850
Mukul S. Bansal , Tel-Aviv University, Tel Aviv
Ron Shamir , Tel-Aviv University, Tel Aviv
The NP-hard gene-duplication problem takes as input a collection of gene trees and seeks a species tree that requires the fewest number of gene duplications to reconcile the input gene trees. An oft-cited, decade-old result by Stege states that the gene-duplication problem is fixed parameter tractable when parameterized by the number of gene duplications necessary for the reconciliation. Here, we uncover an error in this fixed parameter algorithm and show that this error cannot be corrected without sacrificing the fixed parameter tractability of the algorithm. Furthermore, we show a link between the gene-duplication problem and the minimum rooted triplets inconsistency problem which implies that the gene-duplication problem is 1) W[2]-hard when parameterized by the number of gene duplications necessary for the reconciliation and 2) hard to approximate to better than a logarithmic factor.
Phylogenetics, gene duplication, algorithms, fixed parameter tractability, approximability.
Mukul S. Bansal, Ron Shamir, "A Note on the Fixed Parameter Tractability of the Gene-Duplication Problem", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.8, no. 3, pp. 848-850, May/June 2011, doi:10.1109/TCBB.2010.74
[1] M. Goodman, J. Czelusniak, G.W. Moore, A.E. Romero-Herrera, and G. Matsuda, "Fitting the Gene Lineage into Its Species Lineage, a Parsimony Strategy Illustrated by Cladograms Constructed from Globin Sequences," Systematic Zoology, vol. 28, pp. 132-163, 1979.
[2] B. Ma, M. Li, and L. Zhang, "From Gene Trees to Species Trees," SIAM J. Computing, vol. 30, no. 3, pp. 729-752, 2000.
[3] R.D.M. Page, "Maps between Trees and Cladistic Analysis of Historical Associations among Genes, Organisms, and Areas," Systematic Biology, vol. 43, no. 1, pp. 58-77, 1994.
[4] R. Guigó, I. Muchnik, and T.F. Smith, "Reconstruction of Ancient Molecular Phylogeny," Molecular Phylogenetics and Evolution, vol. 6, no. 2, pp. 189-213, 1996.
[5] B. Mirkin, I. Muchnik, and T.F. Smith, "A Biologically Consistent Model for Comparing Molecular Phylogenies," J. Computational Biology, vol. 2, no. 4, pp. 493-507, 1995.
[6] O. Eulenstein and M. Vingron, "On the Equivalence of Two Tree Mapping Measures," Discrete Applied Math., vol. 88, pp. 101-126, 1998.
[7] L. Zhang, "On a Mirkin-Muchnik-Smith Conjecture for Comparing Molecular Phylogenies," J. Computational Biology, vol. 4, no. 2, pp. 177-187, 1997.
[8] M.T. Hallett and J. Lagergren, "New Algorithms for the Duplication-Loss Model," RECOMB '00: Proc. Fourth Ann. Int'l Conf. Computational Molecular Biology, pp. 138-146, , 2000.
[9] K. Chen, D. Durand, and M. Farach-Colton, "Notung: A Program for Dating Gene Duplications and Optimizing Gene Family Trees," J. Computational Biology, vol. 7, pp. 429-447, 2000.
[10] P. Bonizzoni, G.D. Vedova, and R. Dondi, "Reconciling a Gene Tree to a Species Tree under the Duplication Cost Model," Theoretical Computer Science, vol. 347, nos. 1/2, pp. 36-53, 2005.
[11] P. Górecki and J. Tiuryn, "Dls-Trees: A Model of Evolutionary Scenarios," Theoretical Computer Science, vol. 359, nos. 1-3, pp. 378-399, 2006.
[12] C. Chauve, J.-P. Doyon, and N. El-Mabrouk, "Gene Family Evolution by Duplication, Speciation, and Loss," J. Computational Biology, vol. 15, no. 8, pp. 1043-1062, 2008.
[13] M.S. Bansal, O. Eulenstein, and A. Wehe, "The Gene-Duplication Problem: Near-Linear Time Algorithms for NNI-Based Local Searches," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 6, no. 2, pp. 221-231, Apr.-June 2009.
[14] U. Stege, "Gene Trees and Species Trees: The Gene-Duplication Problem Is Fixed-Parameter Tractable," Proc. Int'l Workshop Algorithms and Data Structures (WADS), pp. 288-293, 1999.
[15] U. Stege, "Resolving Conflicts in Problems from Computational Biology," PhD dissertation, Swiss Fed. Inst. of Technology (ETH), 1999.
[16] D. Bryant, "Hunting for Trees, Building Trees and Comparing Trees: Theory and Method in Phylogeneticanalysis," PhD dissertation, Dept. of Math., Univ. of Canterbury, 1997.
[17] B.Y. Wu, "Constructing the Maximum Consensus Tree from Rooted Triples," J. Combinatorial Optimization, vol. 8, no. 1, pp. 29-39, 2004.
[18] S. Snir and S. Rao, "Using Max Cut to Enhance Rooted Trees Consistency," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 3, no. 4, pp. 323-333, Oct.-Dec. 2006.
[19] J. Byrka, S. Guillemot, and J. Jansson, "New Results on Optimizing Rooted Triplets Consistency," Discrete Applied Math., vol. 158, pp. 1136-1147, 2010.
[20] 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, Suppl 1, S42, 2010.
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