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Issue No.02 - March/April (2012 vol.9)
pp: 372-384
Zhi-Zhong Chen , Div. of Inf. Syst. Design, Tokyo Denki Univ., Saitama, Japan
Lusheng Wang , Dept. of Comput. Sci., City Univ. of Hong Kong, Kowloon, China
A reticulate network N of multiple phylogenetic trees may have nodes with two or more parents (called reticulation nodes). There are two ways to define the reticulation number of N. One way is to define it as the number of reticulation nodes in N in this case, a reticulate network with the smallest reticulation number is called an optimal type-I reticulate network of the trees. The better way is to define it as the total number of parents of reticulation nodes in N minus the number of reticulation nodes in N ; in this case, a reticulate network with the smallest reticulation number is called an optimal type-II reticulate network of the trees. In this paper, we first present a fast fixed-parameter algorithm for constructing one or all optimal type-I reticulate networks of multiple phylogenetic trees. We then use the algorithm together with other ideas to obtain an algorithm for estimating a lower bound on the reticulation number of an optimal type-II reticulate network of the input trees. To our knowledge, these are the first fixed-parameter algorithms for the problems. We have implemented the algorithms in ANSI C, obtaining programs CMPT and MaafB. Our experimental data show that CMPT can construct optimal type-I reticulate networks rapidly and MaafB can compute better lower bounds for optimal type-II reticulate networks within shorter time than the previously best program PIRN designed by Wu.
Phylogeny, Vegetation, Algorithm design and analysis, Bioinformatics, Computational biology, Materials,lower bounds of reticulate numbers., Phylogenetic trees, reticulate networks
Zhi-Zhong Chen, Lusheng Wang, "Algorithms for Reticulate Networks of Multiple Phylogenetic Trees", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.9, no. 2, pp. 372-384, March/April 2012, doi:10.1109/TCBB.2011.137
[1] R.G. Beiko and N. Hamilton, “Phylogenetic Identification of Lateral Genetic Transfer Events,” BMC Evolutionary Biology, vol. 6, pp. 159-169, 2006.
[2] M. Bordewich and C. Semple, “On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance,” Annals of Combinatorics, vol. 8, pp. 409-423, 2005.
[3] M. Bordewich and C. Semple, “Computing the Minimum Number of Hybridization Events for a Consistent Evolutionary History,” Discrete Applied Math., vol. 155, pp. 914-928, 2007.
[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, vol. 4, no. 3, pp. 458-466, July 2007.
[5] Z.-Z. Chen and L. Wang, “HybridNet: A Tool for Constructing Hybridization Networks,” Bioinformatics, vol. 26, pp. 2912-2913, or Hnnotess2.pdf), 2010.
[6] L. Collins, S. Linz, and C. Semple, “Quantifying Hybridization in Realistic Time,” J. Computational Biology, vol. 18, pp. 1305-1318, software.shtml], 2011.
[7] N.P. Barker et al., “Phylogeny and Subfamilial Classification of the Grasses (Poaceae),” Annals of the Missouri Botanical Garden, vol. 88, pp. 373-457, 2001.
[8] J. Hein, T. Jing, L. Wang, and K. Zhang, “On the Complexity of Comparing Evolutionary Trees,” Discrete Applied Math., vol. 71, pp. 153-169, 1996.
[9] T. Hill, K.J. Nordström, M. Thollesson, T.M. Säfström, A.K. Vernersson, R. Fredriksson, and H.B. Schiöth, “SPRIT: Identifying Horizontal Gene Transfer in Rooted Phylogenetic Trees,” BMC Evolutionary Biology, vol. 10, article 42, 2010.
[10] R. Hudson, “Generating Samples under the Wright-Fisher Neutral Model of Genetic Variation,” Bioinformatics, vol. 18, pp. 337-338, 2002.
[11] H.A. Schmidt, “Phylogenetic Trees from Large Data Sets,” PhD thesis, Heinrich-Heine-Universitat, Dusseldorf, 2003.
[12] B. Schieber and U. Vishkin, “On Finding Lowest Common Ancestors: Simplification and Parallelization,” SIAM J. Computing, vol. 17, pp. 1253-1262, 1988.
[13] C. Semple, “Reticulate Evolution,” , 2005.
[14] C. Semple, “Hybridization Networks,” Reconstructing Evolution: New Mathematical and Computational Advances, O. Gascuel and M. Steel, eds., pp. 277-314, Oxford Univ. Press, 2007.
[15] J. Wang and Y. Wu, “Fast Computation of the Exact Hybridization Number of Two Phylogenetic Trees,” Proc. Int'l Symp. Bioinformatics Research and Applications (ISBRA '10), pp. 203-214, 2010.
[16] C. Whidden, R.G. Beiko, and N. Zeh, “Fast FPT Algorithms for Computing Rooted Agreement Forest: Theory and Experiments,” Proc. Int'l Symp. Experimental Algorithms, pp. 141-153, 2010.
[17] Y. Wu, “A Practical Method for Exact Computation of Subtree Prune and Regraft Distance,” Bioinformatics, vol. 25, pp. 190-196, 2009.
[18] Y. Wu, “Close Lower and Upper Bounds for the Minimum Reticulate Network of Multiple Phylogenetic Trees,” Bioinformatics, vol. 26, pp. 140-148, 2010.
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