Abstract
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.
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References
Koonin, E.V.: Orthologs, paralogs, and evolutionary genomics. Annual Review of Genetics 39(1), 309–338 (2005)
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)
Chen, K., Durand, D., Farach-Colton, M.: Notung: dating gene duplications using gene family trees. In: RECOMB, pp. 96–106 (2000)
David, L.A., Alm, E.J.: Rapid evolutionary innovation during an archaean genetic expansion. Nature 469, 93–96 (2011)
Durand, D., Halldórsson, B.V., Vernot, B.: A hybrid micro-macroevolutionary approach to gene tree reconstruction. J. Comput. Biol. 13(2), 320–335 (2006)
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)
Scornavacca, C., Jacox, E., Szöllosi, G.J.: Joint amalgamation of most parsimonious reconciled gene trees. Bioinformatics (in press)
Gorbunov, K.Y., Liubetskii, V.A.: Reconstructing genes evolution along a species tree. Molekuliarnaia Biologiia 43(5), 946–958 (2009)
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)
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)
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)
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)
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)
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)
Libeskind-Hadas, R., Wu, Y.C., Bansal, M.S., Kellis, M.: Pareto-optimal phylogenetic tree reconciliation. Bioinformatics 30(12), i87–i95 (2014)
Ovadia, Y., Fielder, D., Conow, C., Libeskind-Hadas, R.: The cophylogeny reconstruction problem is NP-complete. J. Comput. Biol. 18(1), 59–65 (2011)
Libeskind-Hadas, R., Charleston, M.: On the computational complexity of the reticulate cophylogeny reconstruction problem. J. Comput. Biol. 16, 105–117 (2009)
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)
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)
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)
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)
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Kordi, M., Bansal, M.S. (2015). On the Complexity of Duplication-Transfer-Loss Reconciliation with Non-binary Gene Trees. In: Harrison, R., Li, Y., Măndoiu, I. (eds) Bioinformatics Research and Applications. ISBRA 2015. Lecture Notes in Computer Science(), vol 9096. Springer, Cham. https://doi.org/10.1007/978-3-319-19048-8_16
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DOI: https://doi.org/10.1007/978-3-319-19048-8_16
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