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

M. Bordewich, C. Semple
2007 IEEE/ACM Transactions on Computational Biology & Bioinformatics  
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
more » ... 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.
doi:10.1109/tcbb.2007.1019 pmid:17666765 fatcat:2z6ny3tyyzezxbxqajso2jly7i