An Approximation Algorithm for Computing a Parsimonious First Speciation in the Gene Duplication Model

  • Aïda Ouangraoua
  • Krister M. Swenson
  • Cedric Chauve
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6398)


We consider the following problem: given a forest of gene family trees on a set of genomes, find a first speciation which splits these genomes into two subsets and minimizes the number of gene duplications that happened before this speciation. We call this problem the Minimum Duplication Bipartition Problem. Using a generalization of the Minimum Edge-Cut Problem, known as Submodular Function Minimization, we propose a polynomial time and space 2-approximation algorithm for the Minimum Duplication Bipartition Problem. We illustrate the potential of this algorithm on both synthetic and real data.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bansal, M.S., et al.: Heuristics for the gene-duplication problem: A Θ(n) speed-up for the local search. In: Speed, T., Huang, H. (eds.) RECOMB 2007. LNCS (LNBI), vol. 4453, pp. 238–252. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Bansal, M.S., Shamir, R.: A Note on the Fixed Parameter Tractability of the Gene-Duplication Problem (submitted, 2010)Google Scholar
  3. 3.
    Blomme, T., van de Peer, Y., et al.: The gain and loss of genes during 600 millions years of vertebrate evolution. Genome Biol. 7, R43 (2006)Google Scholar
  4. 4.
    Bryant, D.: Hunting for trees, building trees and comparing trees: theory and methods in phylogenetic analysis. Ph.D. thesis, Dept. of Math., Univ. of Canterbury, New Zealand (1997)Google Scholar
  5. 5.
    Burleig, J.G., et al.: Genome-scale phylogenetics: Inferring the plant tree of life from 18,896 discordant gene trees Systematic Biology (in press, 2010)Google Scholar
  6. 6.
    Byrka, J., Guillemot, S., Jansson, J.: New Results on Optimizing Rooted Triplets Consistency. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 484–495. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Chauve, C., El-Mabrouk, N.: New perspectives on gene family evolution: losses in reconciliation and a link with supertrees. In: Batzoglou, S. (ed.) RECOMB 2009. LNCS, vol. 5541, pp. 46–58. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Chauve, C., Ouangraoua, A.: A 3-approximation algorithm for computing a parsimonious first speciation in the gene duplication model. arXiv:0904.1645v2 (2009)Google Scholar
  9. 9.
    De Bie, T., et al.: CAFE: a computational tool for the study of gene family evolution. Bioinformatics 22, 1269–1271 (2006)CrossRefPubMedGoogle Scholar
  10. 10.
    Fujishige, S.: Submodular Functions and Optimization, 2nd edn. Annals of Discrete Math., vol. 58. Elsevier, Amsterdam (2005)Google Scholar
  11. 11.
    Górecki, P., Tiuryn, J.: DLS-trees: a model of evolutionary scenarios. Theoret. Comput. Sci. 359, 378–399 (2006)CrossRefGoogle Scholar
  12. 12.
    Guillemot, S.: Approches combinatoires pour le consensus d’arbres et de séquences. Ph.D. thesis, Univ. Montpellier II, France (2008)Google Scholar
  13. 13.
    Hallett, M.T., Lagergren, J.: New algorithms for the duplication-loss model. In: RECOMB 2000, pp. 138–146. ACM Press, New York (2000)Google Scholar
  14. 14.
    Iwata, S., Orlin, J.B.: Simple combinatorial algorithm for submodular function minimization. In: SODA 2009, pp. 1230–1237. SIAM, Philadelphia (2009)Google Scholar
  15. 15.
    Hahn, M.W., Han, M.V., Han, S.-G.: Gene family evolution across 12 Drosophilia genomes. PLoS Genet. 3, e197 (2007)Google Scholar
  16. 16.
    Ma, B., Li, M., Zhang, L.: From gene trees to species trees. SIAM J. Comput. 30, 729–752 (2000)CrossRefGoogle Scholar
  17. 17.
    Mak, W.-K.: Faster Min-Cut Computation in Unweighted Hypergraphs/Circuit Netlists. In: VLSI Design, Automation and Test, 2005 (VLSI-TSA-DAT), pp. 67–70. IEEE, Los Alamitos (2005)Google Scholar
  18. 18.
    Page, R.D.M.: Modified mincut supertrees. In: Guigó, R., Gusfield, D. (eds.) WABI 2002. LNCS, vol. 2452, pp. 537–551. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    Sanderson, M.J., McMahon, M.M.: Inferring angiosperm phylogeny from EST data with widespread gene duplication. BMC Evol. Biol. 7, S3 (2007)Google Scholar
  20. 20.
    Scornavacca, C., Berry, V., Ranwez, V.: From gene trees to species trees through a supertree approach. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds.) LATA 2009. LNCS, vol. 5457, pp. 702–714. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  21. 21.
    Semple, C., Steel, M.: A supertree method for rooted trees. Discrete Appl. Math. 105, 147–158 (2000)CrossRefGoogle Scholar
  22. 22.
    Stege, U.: Gene Trees and Species Trees: The Gene-Duplication Problem in Fixed-Parameter Tractable. In: Dehne, F., Gupta, A., Sack, J.-R., Tamassia, R. (eds.) WADS 1999. LNCS, vol. 1663, pp. 288–293. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  23. 23.
    Wapinski, I., et al.: Natural history and evolutionary principles of gene duplication in fungi. Nature 449, 54–61 (2007)CrossRefPubMedGoogle Scholar
  24. 24.
    Li, H., et al.: Treefam: a curated database of phylogenetic trees of animal gene families. Nucleic Acids Res. 34, 572–580 (2006)CrossRefGoogle Scholar
  25. 25.
    Wehe, A., et al.: DupTree: a program for large-scale phylogenetic analyses using gene tree parsimony. Bioinformatics 24, 1540–1541 (2008)CrossRefPubMedGoogle Scholar
  26. 26.
    Zhou, X., Lin, Z., Ma, H.: Phylogenetic detection of numerous gene duplications shared by animals, fungi and plants Genome Biol., 11, R38 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Aïda Ouangraoua
    • 1
    • 2
    • 3
  • Krister M. Swenson
    • 2
    • 4
  • Cedric Chauve
    • 1
    • 2
  1. 1.Department of MathematicsSFUBurnabyCanada
  2. 2.LacimUniversité du Québec à MontréalMontréalCanada
  3. 3.INRIA LNE, LIFLUniversité Lille 1France
  4. 4.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

Personalised recommendations