Uniqueness, intractability and exact algorithms: reflections on level-k phylogenetic networks
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.
|Keywords||phylogenetic networks, uniqueness, triplets, complexity|
|MSC||Mathematical biology in general (msc 92Bxx)|
|THEME||Life Sciences (theme 5), Energy (theme 4)|
|Journal||Journal of Bioinformatics and Computational Biology|
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.