Reconstructing k-Reticulated Phylogenetic Network from a Set of Gene Trees

  • Hoa Vu
  • Francis Chin
  • W. K. Hon
  • Henry Leung
  • K. Sadakane
  • Ken W. K. Sung
  • Siu-Ming Yiu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7875)


The time complexity of existing algorithms for reconstructing a level-x phylogenetic network increases exponentially in x. In this paper, we propose a new classification of phylogenetic networks called k-reticulated network. A k-reticulated network can model all level-k networks and some level-x networks with x > k. We design algorithms for reconstructing k-reticulated network (k = 1 or 2) with minimum number of hybrid nodes from a set of m binary trees, each with n leaves in O(mn 2) time. The implication is that some level-x networks with x > k can now be reconstructed in a faster way. We implemented our algorithm (ARTNET) and compared it with CMPT. We show that ARTNET outperforms CMPT in terms of running time and accuracy. We also consider the case when there does not exist a 2-reticulated network for the input trees. We present an algorithm computing a maximum subset of the species set so that a new set of subtrees can be combined into a 2-reticulated network.


Gene Tree Leaf Node Binary Tree Phylogenetic Network Input Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Lam, T.W., Sung, W.K., Ting, H.F.: Computing the unrooted maximum agreement subtree in sub-quadratic time. Nordic Journal of Computing 3(4), 295–322 (1996)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Farach, M., Thorup, M.: Sparse dynamic programming for evolutionary-tree comparison. SIAM Journal on Computing 26(1), 210–230 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Steel, M., Warnow, T.J.: Kaikoura tree theorems: Computing the maximum agreement subtree. Information Processing Letters 48, 77–82 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Ford Doolittle, W.: Phylogenetic classification and the universal tree. Science 284(5423), 2124–2128 (1999)CrossRefGoogle Scholar
  5. 5.
    Gusfield, D., Bansal, V.: A fundamental decomposition theory for phylogenetic networks and incompatible characters. In: Miyano, S., Mesirov, J., Kasif, S., Istrail, S., Pevzner, P.A., Waterman, M. (eds.) RECOMB 2005. LNCS (LNBI), vol. 3500, pp. 217–232. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Nakhleh, L., Warnow, T., Linder, C.R.: Reconstructing reticulate evolution in species – theory and practice. In: Proceedings of the 8th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2004), pp. 337–346 (2004)Google Scholar
  7. 7.
    Lee, W.-H., Sung, W.-K.: RB-finder: An improved distance-based sliding window method to detect recombination breakpoints. In: Speed, T., Huang, H. (eds.) RECOMB 2007. LNCS (LNBI), vol. 4453, pp. 518–532. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Falush, D., Torpdahl, M., Didelot, X., Conrad, D.F., Wilson, D.J., Achtman, M.: Mismatch induced speciation in salmonella: model and data. Philos. Trans. R Soc. Lond. B Biol. Sci. 361(1475), 2045–2053 (2006)CrossRefGoogle Scholar
  9. 9.
    Majewski, J.: Sexual isolation in bacteria. FEMS Microbiol. Lett. 199(2), 161–169 (2001)CrossRefGoogle Scholar
  10. 10.
    Fraser, C., Hanage, W.P., Spratt, B.G.: Recombination and the nature of bacterial speciation. Science 315(5811), 476–480 (2007)CrossRefGoogle Scholar
  11. 11.
    van Iersel, L., Keijsper, J., Kelk, S., Stougie, L., Hagen, F., Boekhout, T.: Constructing level-2 phylogenetic networks from triplets. In: Vingron, M., Wong, L. (eds.) RECOMB 2008. LNCS (LNBI), vol. 4955, pp. 450–462. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Huynh, T.N.D., Jansson, J., Nguyen, N.B., Sung, W.-K.: Constructing a smallest refining galled phylogenetic network. In: Miyano, S., Mesirov, J., Kasif, S., Istrail, S., Pevzner, P.A., Waterman, M. (eds.) RECOMB 2005. LNCS (LNBI), vol. 3500, pp. 265–280. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Zhi-Zhong, C., Lusheng, W.: Algorithms for Reticulate Networks of Multiple Phylogenetic Trees. IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB) 9(2), 372–384 (2012)CrossRefGoogle Scholar
  14. 14.
    Huson, D.H., Klöpper, T.H.: Beyond galled trees - decomposition and computation of galled networks. In: Speed, T., Huang, H. (eds.) RECOMB 2007. LNCS (LNBI), vol. 4453, pp. 211–225. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Jansson, J., Nguyen, N.B., Sung, W.-K.: Algorithms for combining rooted triplets into a galled phylogenetic network. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 349–358 (2005)Google Scholar
  16. 16.
    Habib, M., To, T.-H.: Constructing a minimum phylogenetic network from a dense triplet set. J. Bioinformatics and Computational Biology 10(05) (2012)Google Scholar
  17. 17.
    Gambette, P., Berry, V., Paul, C.: Quartets and Unrooted Phylogenetic Networks. Journal of Bioinformatics and Computational Biology (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hoa Vu
    • 1
  • Francis Chin
    • 1
  • W. K. Hon
    • 2
  • Henry Leung
    • 1
  • K. Sadakane
    • 3
  • Ken W. K. Sung
    • 4
  • Siu-Ming Yiu
    • 1
  1. 1.Department of Computer ScienceThe University of Hong KongHong Kong
  2. 2.Department of Computer ScienceNational Tsinghua UniversityTaiwan
  3. 3.Informatics Research DivisionNational Institute of InformaticsJapan
  4. 4.Department of Computer ScienceNational University of SingaporeSingapore

Personalised recommendations