Abstract
Tractability results are rare in the comparison of gene orders for more than two genomes. Here we present a linear-time algorithm for the small parsimony problem (inferring ancestral genomes given a phylogeny on an arbitrary number of genomes) in the case gene orders are permutations, that evolve by inversions not breaking common gene intervals, and these intervals are organised in a linear structure. We present two examples where this allows to reconstruct the ancestral gene orders in phylogenies of several γ-Proteobacteria species and Burkholderia strains, respectively. We prove in addition that the large parsimony problem (where the phylogeny is output) remains NP-complete.
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References
Belda, E., Moya, A., Silva, F.J.: Genome rearrangement distances and gene order phylogeny in γ-proteobacteria. Mol. Biol. Evol. 22, 1456–1467 (2005)
Bérard, S., Bergeron, A., Chauve, C., Paul, C.: Perfect sorting by reversals is not always difficult. IEEE/ACM Trans. Comput. Biol. Bioinf. 4, 4–16 (2007)
Bérard, S., Chauve, C., Paul, C.: A more efficient algorithm for perfect sorting by reversals. Inform. Process. Lett. 106, 90–95 (2008)
Bergeron, A., Chauve, C., de Montgolfier, F., Raffinot, M.: Computing common intervals of k permutations, with applications to modular decomposition of graphs. SIAM J. Discrete Math. 22, 1022–1039 (2008)
Bernt, M.: Gene Order Rearrangement Methods for the Reconstruction of Phylogeny. PhD thesis, Universität Leipzig (2010)
Bernt, M., Merkle, D., Middendorf, M.: Solving the preserving reversal median problem. IEEE/ACM Trans. Comput. Biol. Bioinf. 5, 332–347 (2008)
Bernt, M., Merkle, D., Ramsch, K., Fritzsch, G., Perseke, M., Bernhard, D., Schlegel, M., Stadler, P.F., Middendorf, M.: CREx: inferring genomic rearrangements based on common intervals. Bioinformatics 23, 2957–2958 (2007)
Booth, K., Lueker, G.: Testing for the consecutive ones property, interval graphs and graph planarity using PQ-tree algorithms. J. Comput. Syst. Sci. 13, 335–339 (1976)
Bouvel, M., Chauve, C., Mishna, M., Rossin, D.: Average-Case Analysis of Perfect Sorting by Reversals. In: Kucherov, G., Ukkonen, E. (eds.) CPM 2009. LNCS, vol. 5577, pp. 314–325. Springer, Heidelberg (2009)
Day, W.H.E., Sankoff, D.: Computational complexity of inferring phylogenies by compatibility. Syst. Zool. 35, 224–229 (1986)
Dutheil, J., Gaillard, S., Bazin, E., Glemin, S., Ranwez, V., Galtier, N., Belkhir, K.: Bio++: a set of C++ libraries for sequence analysis, phylogenetics, molecular evolution and population genetics. BMC Bioinformatics 7(1), 188 (2006)
Feijao, P., Meidanis, J.: SCJ: A breakpoint-like distance that simplifies several rearrangement problems. IEEE/ACM Trans. Comput. Biol. Bioinf. 8, 1318–1329 (2011)
Fertin, G., Labarre, A., Rusu, I., Tannier, E., Vialette, S.: Combinatorics of Genome Rearrangements. MIT Press (2009)
Figeac, M., Varré, J.-S.: Sorting by Reversals with Common Intervals. In: Jonassen, I., Kim, J. (eds.) WABI 2004. LNCS (LNBI), vol. 3240, pp. 26–37. Springer, Heidelberg (2004)
Fitch, W.: Toward defining the course of evolution: minimum change for a specified tree topology. Syst. Zool. 20, 406–416 (1971)
Foulds, L.R., Graham, R.L.: The Steiner problem in phylogeny is NP-complete. Adv. Appl. Math. 3, 43–49 (1982)
Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. In: ACM Symposium on Theory of Computing, pp. 178–189 (1995)
Heber, S., Stoye, J.: Finding All Common Intervals of k Permutations. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, pp. 207–218. Springer, Heidelberg (2001)
Penel, S., Arigon, A.M., Dufayard, J.F., Sertier, A.S., Daubin, V., Duret, L., Gouy, M., Perrière, G.: Databases of homologous gene families for comparative genomics. BMC Bioinformatics 10, S3 (2009)
Sankoff, D.: Edit Distance for Genome Comparison Based on Non-Local Operations. In: Apostolico, A., Galil, Z., Manber, U., Crochemore, M. (eds.) CPM 1992. LNCS, vol. 644, pp. 121–135. Springer, Heidelberg (1992)
Tannier, E., Zheng, C., Sankoff, D.: Multichromosomal median and halving problems under different genomic distances. BMC Bioinformatics 10, 120 (2009)
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Bernt, M., Chao, KM., Kao, JW., Middendorf, M., Tannier, E. (2012). Preserving Inversion Phylogeny Reconstruction. In: Raphael, B., Tang, J. (eds) Algorithms in Bioinformatics. WABI 2012. Lecture Notes in Computer Science(), vol 7534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33122-0_1
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DOI: https://doi.org/10.1007/978-3-642-33122-0_1
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