Fast Algorithms for Computing the Tripartition-Based Distance Between Phylogenetic Networks

Consider two phylogenetic networks N and N′ of size n. The tripartition-based distance finds the proportion of tripartitions which are not shared by N and N′. This distance is proposed by Moret et al (2004) and is a generalization of Robinson-Foulds distance, which is orginally used to compare two phylogenetic trees. This paper gives an O(min{kn log n, n log n+hn})-time algorithm to compute this distance, where h is the number of hybrid nodes in N and N′ while k is the maximum number of hybrid nodes among all biconnected components in N and N′. Note that k << h << n in a phylogenetic network. In addition, we propose algorithms for comparing galled-trees, which are an important, biological meaningful special case of phylogenetic network. We give an O(n)-time algorithm for comparing two galled-trees. We also give an O(n + kh)-time algorithm for comparing a galled-tree with another general network, where h and k are the number of hybrid nodes in the latter network and its biggest biconnected component respectively.

[1]  Daniel H. Huson,et al.  Reconstruction of Reticulate Networks from Gene Trees , 2005, RECOMB.

[2]  V. Moulton,et al.  Neighbor-net: an agglomerative method for the construction of phylogenetic networks. , 2002, Molecular biology and evolution.

[3]  Kunihiko Sadakane,et al.  Computing the Maximum Agreement of Phylogenetic Networks , 2004, CATS.

[4]  Wing-Kin Sung,et al.  The Maximum Agreement of Two Nested Phylogenetic Networks , 2004, ISAAC.

[5]  Dan Gusfield,et al.  A Fundamental Decomposition Theory for Phylogenetic Networks and Incompatible Characters , 2005, RECOMB.

[6]  Kaizhong Zhang,et al.  Perfect Phylogenetic Networks with Recombination , 2001, J. Comput. Biol..

[7]  Robert E. Tarjan,et al.  Fast Algorithms for Finding Nearest Common Ancestors , 1984, SIAM J. Comput..

[8]  Wing-Kin Sung,et al.  Constructing a Smallest Refining Galled Phylogenetic Network , 2005, RECOMB.

[9]  Tandy J. Warnow,et al.  Phylogenetic networks: modeling, reconstructibility, and accuracy , 2004, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[10]  D. Robinson,et al.  Comparison of phylogenetic trees , 1981 .

[11]  Siu-Ming Yiu,et al.  Non-shared edges and nearest neighbor interchanges revisited , 2004, Inf. Process. Lett..

[12]  Tandy J. Warnow,et al.  Towards the Development of Computational Tools for Evaluating Phylogenetic Network Reconstruction Methods , 2002, Pacific Symposium on Biocomputing.

[13]  Doolittle Wf.  Phylogenetic Classification and the Universal Tree , 1999 .

[14]  J. Hein.  Reconstructing evolution of sequences subject to recombination using parsimony. , 1990, Mathematical biosciences.

[15]  Dan Gusfield,et al.  Efficient reconstruction of phylogenetic networks with constrained recombination , 2003, Computational Systems Bioinformatics. CSB2003. Proceedings of the 2003 IEEE Bioinformatics Conference. CSB2003.

[16]  K. Crandall,et al.  Intraspecific gene genealogies: trees grafting into networks. , 2001, Trends in ecology & evolution.

[17]  Tandy J. Warnow,et al.  Reconstructing Reticulate Evolution in SpeciesTheory and Practice , 2005, J. Comput. Biol..

[18]  Daniel H. Huson,et al.  Phylogenetic super-networks from partial trees , 2004, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[19]  Tandy J. Warnow,et al.  Reconstructing reticulate evolution in species: theory and practice , 2004, RECOMB.

[20]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[21]  Wing-Kin Sung,et al.  Inferring a level-1 phylogenetic network from a dense set of rooted triplets , 2006, Theor. Comput. Sci..

[22]  Wing-Kin Sung,et al.  Algorithms for combining rooted triplets into a galled phylogenetic network , 2005, SODA '05.