Phylogenetic networks provide a way to describe and visualize evolutionary histories that have undergone so-called reticulate evolutionary events such as recombination, hybridization or horizontal gene transfer. The level k of a network determines how non-treelike the evolution can be, with level-0 networks being trees. We study the problem of constructing level-k phylogenetic networks from triplets, i.e. phylogenetic trees for three leaves (taxa). We give, for each k, a level-k network that is uniquely defined by its triplets. We demonstrate the applicability of this result by using it to prove that (1) for all k of at least one it is NP-hard to construct a level-k network consistent with all input triplets, and (2) for all k it is NP-hard to construct a level-k network consistent with a maximum number of input triplets, even when the input is dense. As a response to this intractability we give an exact algorithm for constructing level-1 networks consistent with a maximum number of input triplets.
Additional Metadata
Keywords phylogenetic networks, uniqueness, triplets, complexity
MSC Mathematical biology in general (msc 92Bxx)
THEME Life Sciences (theme 5), Energy (theme 4)
Publisher World Scientific
Journal Journal of Bioinformatics and Computational Biology
Citation
van Iersel, L.J.J, Kelk, S.M, & Mnich, M. (2009). Uniqueness, intractability and exact algorithms: reflections on level-k phylogenetic networks. Journal of Bioinformatics and Computational Biology.