Minimum Leaf Removal for Reconciliation: Complexity and Algorithms
Reconciliation is a well-known method for studying the evolution of a gene family through speciation, duplication, and loss. Unfortunately, the inferred history strongly depends on the considered gene tree for the gene family, as a few misplaced leaves can lead to a completely different history, possibly with significantly more duplications and losses. It is therefore essential to develop methods that are able to preprocess and correct gene trees prior to reconciliation. In this paper, we consider a combinatorial problem, known as the Minimum Leaf Removal problem, that has been proposed to remove errors from a gene tree by deleting some of its leaves. We prove that the problem is APX-hard, even in the restricted case of a gene family with at most two copies per genome. On the positive side, we present fixed-parameter algorithms where the parameters are the size of the solution (minimum number of leaf removals) and the number of genomes containing multiple gene copies.
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- 2.Altschul, S., Gish, W., Miller, W., Myers, E., Lipman, D.: Basic local alignment search tool. J. Mol. Biol. 215(3), 403–410 (1990)Google Scholar
- 5.Blomme, T., Vandepoele, K., Bodt, S.D., Silmillion, C., Maere, S., van de Peer, Y.: The gain and loss of genes during 600 millions years of vertebrate evolution. Genome Biology 7, R43 (2006)Google Scholar
- 11.Demuth, J., Bie, T.D., Stajich, J., Cristianini, N., Hahn, M.: The evolution of mammalian gene families. PLoS ONE 1, e85 (2006)Google Scholar
- 19.Hahn, M.: Bias in phylogenetic tree reconciliation methods: implications for vertebrate genome evolution. Genome Biology 8(R141) (2007)Google Scholar
- 20.Hahn, M., Han, M., Han, S.G.: Gene family evolution across 12 drosophilia genomes. PLoS Genetics 3, e197 (2007)Google Scholar
- 24.Ohno, S.: Evolution by gene duplication. Springer, Berlin (1970)Google Scholar
- 25.Page, R.: Maps between trees and cladistic analysis of historical associations among genes, organisms, and areas. Systematic Biology 43, 58–77 (1994)Google Scholar
- 28.Page, R., Cotton, J.: Vertebrate phylogenomics: reconciled trees and gene duplications. In: Pacific Symposium on Biocomputing, pp. 536–547 (2002)Google Scholar
- 29.Sanderson, M., McMahon, M.: Inferring angiosperm phylogeny from EST data with widespread gene duplication. BMC Evolutionary Biology 7, S3 (2007)Google Scholar