A Simple Fixed Parameter Tractable Algorithm for Computing the Hybridization Number of Two (Not Necessarily Binary) Trees

Here, we present a new fixed parameter tractable algorithm to compute the hybridization number r of two rooted, not necessarily binary phylogenetic trees on taxon set X in time (6rr!) · poly(n), where n = |X|. The novelty of this approach is its use of terminals, which are maximal elements of a natural partial order on X, and several insights from the softwired clusters literature. This yields a surprisingly simple and practical bounded-search algorithm and offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem.

[1]  Daniel H. Huson,et al.  Phylogenetic Networks - Concepts, Algorithms and Applications , 2011 .

[2]  Naren Ramakrishnan,et al.  Problem Solving Handbook in Computational Biology and Bioinformatics , 2010 .

[3]  Steven Kelk,et al.  Towards the fixed parameter tractability of constructing minimal phylogenetic networks from arbitrary sets of nonbinary trees , 2012, ArXiv.

[4]  D. Huson,et al.  Dendroscope 3: an interactive tool for rooted phylogenetic trees and networks. , 2012, Systematic biology.

[5]  Daniel H. Huson,et al.  Phylogenetic Networks: Contents , 2010 .

[6]  D. Huson,et al.  A Survey of Combinatorial Methods for Phylogenetic Networks , 2010, Genome biology and evolution.

[7]  Leo van Iersel,et al.  Cycle Killer...Qu'est-ce que c'est? On the Comparative Approximability of Hybridization Number and Directed Feedback Vertex Set , 2011, SIAM J. Discret. Math..

[8]  Olivier Gascuel,et al.  Mathematics of Evolution and Phylogeny , 2005 .

[9]  Zhi-Zhong Chen,et al.  HybridNET: a tool for constructing hybridization networks , 2010, Bioinform..

[10]  Jörg Flum,et al.  Parameterized Complexity Theory , 2006, Texts in Theoretical Computer Science. An EATCS Series.

[11]  Simone Linz,et al.  Hybridization in Non-Binary Trees , 2008 .

[12]  L. Nakhleh.  Evolutionary Phylogenetic Networks: Models and Issues , 2010 .

[13]  Steven Kelk,et al.  When two trees go to war. , 2010, Journal of theoretical biology.

[14]  Charles Semple,et al.  HYBRIDIZATION NETWORKS , 2014 .

[15]  Jörg Flum,et al.  Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series) , 2006 .

[16]  Charles Semple,et al.  A Framework for Representing Reticulate Evolution , 2005 .

[17]  Charles Semple,et al.  Computing the minimum number of hybridization events for a consistent evolutionary history , 2007, Discret. Appl. Math..

[18]  Simone Linz,et al.  A Reduction Algorithm for Computing The Hybridization Number of Two Trees , 2007, Evolutionary bioinformatics online.

[19]  Norbert Zeh,et al.  Fixed-Parameter and Approximation Algorithms for Maximum Agreement Forests of Multifurcating Trees , 2013, Algorithmica.

[20]  Daniel H. Huson,et al.  Computing galled networks from real data , 2009, Bioinform..

[21]  J. Davenport.  Editor , 1960 .

[22]  Leo van Iersel,et al.  A quadratic kernel for computing the hybridization number of multiple trees , 2012, Inf. Process. Lett..

[23]  Steven Kelk,et al.  Constructing Minimal Phylogenetic Networks from Softwired Clusters is Fixed Parameter Tractable , 2012, Algorithmica.

[24]  V. Moulton,et al.  Bounding the Number of Hybridisation Events for a Consistent Evolutionary History , 2005, Journal of mathematical biology.

[25]  Leo van Iersel,et al.  Phylogenetic networks do not need to be complex: using fewer reticulations to represent conflicting clusters , 2009, Bioinform..

[26]  Simone Linz,et al.  Quantifying Hybridization in Realistic Time , 2011, J. Comput. Biol..

[27]  Leo van Iersel,et al.  On the Elusiveness of Clusters , 2011, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[28]  L. Segal.  John , 2013, The Messianic Secret.

[29]  Olivier Gascuel,et al.  Reconstructing evolution : new mathematical and computational advances , 2007 .

[30]  Daniel H. Huson,et al.  Fast computation of minimum hybridization networks , 2012, Bioinform..

[31]  C. Semple,et al.  Hybridization in Nonbinary Trees , 2009, IEEE/ACM Transactions on Computational Biology and Bioinformatics.