On the Complexity of Duplication-Transfer-Loss Reconciliation with Non-binary Gene Trees

  • Misagh Kordi
  • Mukul S. Bansal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9096)


Duplication-Transfer-Loss (DTL) reconciliation has emerged as a powerful technique for studying gene family evolution in the presence of horizontal gene transfer. DTL reconciliation takes as input a gene family phylogeny and the corresponding species phylogeny, and reconciles the two by postulating speciation, gene duplication, horizontal gene transfer, and gene loss events. Efficient algorithms exist for finding optimal DTL reconciliations when the gene tree is binary. However, gene trees are frequently non-binary. With such non-binary gene trees, the reconciliation problem seeks to find a binary resolution of the gene tree that minimizes the reconciliation cost. Given the prevalence of non-binary gene trees, many efficient algorithms have been developed for this problem in the context of the simpler Duplication-Loss (DL) reconciliation model. Yet, no efficient algorithms exist for DTL reconciliation with non-binary gene trees and the complexity of the problem remains unknown. In this work, we resolve this open question by showing that the problem is, in fact, NP-hard. Our reduction applies to both the dated and undated formulations of DTL reconciliation. By resolving this long-standing open problem, this work will spur the development of both exact and heuristic algorithms for this important problem.


Species Tree Gene Tree Horizontal Gene Transfer Internal Node Binary Resolution 
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.


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  1. 1.
    Koonin, E.V.: Orthologs, paralogs, and evolutionary genomics. Annual Review of Genetics 39(1), 309–338 (2005)CrossRefGoogle Scholar
  2. 2.
    Vilella, A.J., Severin, J., Ureta-Vidal, A., Heng, L., Durbin, R., Birney, E.: Ensemblcompara genetrees: Complete, duplication-aware phylogenetic trees in vertebrates. Genome Research 19(2), 327–335 (2009)CrossRefGoogle Scholar
  3. 3.
    Chen, K., Durand, D., Farach-Colton, M.: Notung: dating gene duplications using gene family trees. In: RECOMB, pp. 96–106 (2000)Google Scholar
  4. 4.
    David, L.A., Alm, E.J.: Rapid evolutionary innovation during an archaean genetic expansion. Nature 469, 93–96 (2011)CrossRefGoogle Scholar
  5. 5.
    Durand, D., Halldórsson, B.V., Vernot, B.: A hybrid micro-macroevolutionary approach to gene tree reconstruction. J. Comput. Biol. 13(2), 320–335 (2006)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Burleigh, J.G., Bansal, M.S., Eulenstein, O., Hartmann, S., Wehe, A., Vision, T.J.: Genome-scale phylogenetics: Inferring the plant tree of life from 18,896 gene trees. Syst. Biol. 60(2), 117–125 (2011)CrossRefGoogle Scholar
  7. 7.
    Scornavacca, C., Jacox, E., Szöllosi, G.J.: Joint amalgamation of most parsimonious reconciled gene trees. Bioinformatics (in press)Google Scholar
  8. 8.
    Gorbunov, K.Y., Liubetskii, V.A.: Reconstructing genes evolution along a species tree. Molekuliarnaia Biologiia 43(5), 946–958 (2009)Google Scholar
  9. 9.
    Doyon, J.-P., Scornavacca, C., Gorbunov, K.Y., Szöllősi, G.J., Ranwez, V., Berry, V.: An efficient algorithm for gene/species trees parsimonious reconciliation with losses, duplications and transfers. In: Tannier, E. (ed.) RECOMB-CG 2010. LNCS, vol. 6398, pp. 93–108. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Tofigh, A., Hallett, M.T., Lagergren, J.: Simultaneous identification of duplications and lateral gene transfers. IEEE/ACM Trans. Comput. Biology Bioinform. 8(2), 517–535 (2011)CrossRefGoogle Scholar
  11. 11.
    Bansal, M.S., Alm, E.J., Kellis, M.: Efficient algorithms for the reconciliation problem with gene duplication, horizontal transfer and loss. Bioinformatics 28(12), 283–291 (2012)CrossRefGoogle Scholar
  12. 12.
    Stolzer, M., Lai, H., Xu, M., Sathaye, D., Vernot, B., Durand, D.: Inferring duplications, losses, transfers and incomplete lineage sorting with nonbinary species trees. Bioinformatics 28(18), 409–415 (2012)CrossRefGoogle Scholar
  13. 13.
    Bansal, M.S., Alm, E.J., Kellis, M.: Reconciliation revisited: Handling multiple optima when reconciling with duplication, transfer, and loss. J. Comput. Biol. 20(10), 738–754 (2013)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Scornavacca, C., Paprotny, W., Berry, V., Ranwez, V.: Representing a set of reconciliations in a compact way. J. Bioinform. Comput. Biol. 11(02), 1250025 (2013)CrossRefGoogle Scholar
  15. 15.
    Libeskind-Hadas, R., Wu, Y.C., Bansal, M.S., Kellis, M.: Pareto-optimal phylogenetic tree reconciliation. Bioinformatics 30(12), i87–i95 (2014)Google Scholar
  16. 16.
    Ovadia, Y., Fielder, D., Conow, C., Libeskind-Hadas, R.: The cophylogeny reconstruction problem is NP-complete. J. Comput. Biol. 18(1), 59–65 (2011)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Libeskind-Hadas, R., Charleston, M.: On the computational complexity of the reticulate cophylogeny reconstruction problem. J. Comput. Biol. 16, 105–117 (2009)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Chang, W.-C., Eulenstein, O.: Reconciling gene trees with apparent polytomies. In: Chen, D.Z., Lee, D.T. (eds.) COCOON 2006. LNCS, vol. 4112, pp. 235–244. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Lafond, M., Swenson, K.M., El-Mabrouk, N.: An optimal reconciliation algorithm for gene trees with polytomies. In: Raphael, B., Tang, J. (eds.) WABI 2012. LNCS, vol. 7534, pp. 106–122. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  20. 20.
    Zheng, Y., Zhang, L.: Reconciliation with non-binary gene trees revisited. In: Sharan, R. (ed.) RECOMB 2014. LNCS, vol. 8394, pp. 418–432. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  21. 21.
    Karp, R.M.: Reducibility among combinatorial problems. In: Proceedings of a Symposium on the Complexity of Computer Computations, held March 20-22, 1972, at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York, pp. 85–103 (1972)Google Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringUniversity of ConnecticutStorrsUSA
  2. 2.Institute for Systems GenomicsUniversity of ConnecticutStorrsUSA

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