Computing the Hybridization Number of Two Phylogenetic Trees Is Fixed-Parameter Tractable

• Published in: IEEE/ACM transactions on computational biology and bioinformatics Vol. 4; no. 3; pp. 458 - 466
• Main Authors: Bordewich, M., Semple, C.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.07.2007; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: agreement forest; Algorithms; Binary sequences; Bioinformatics; Biological Evolution; Biology computing; Computer Simulation; Evolution (biology); Genetics; Genetics, Population; Genomics; History; hybridization network; Hybridization, Genetic - genetics; Marine animals; Models, Genetic; Phylogeny; Polynomials; reticulate evolution; Rooted phylogenetic tree; subtree prune and regraft
• ISSN: 1545-5963; 1557-9964; 2374-0043; 1557-9964
• DOI: 10.1109/tcbb.2007.1019

Reticulation processes in evolution mean that the ancestral history of certain groups of present-day species is non-tree-like. These processes include hybridization, lateral gene transfer, and recombination. Despite the existence of reticulation, such events are relatively rare and, so, a fundamental problem for biologists is the following: Given a collection of rooted binary phylogenetic trees on sets of species that correctly represent the tree-like evolution of different parts of their genomes, what is the smallest number of "reticulation" vertices in any network that explains the evolution of the species under consideration? It has been previously shown that this problem is NP-hard even when the collection consists of only two rooted binary phylogenetic trees. However, in this paper, we show that the problem is fixed-parameter tractable in the two-tree instance when parameterized by this smallest number of reticulation vertices.