TY - JOUR

T1 - Uniqueness, intractability and exact algorithms: Reflections on level-k phylogenetic networks

AU - van Iersel, Leo

AU - Kelk, Steven

AU - Mnich, Matthias

PY - 2009

Y1 - 2009

N2 - 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 > or = 1 it is NP-hard to construct a level-k network consistent with all input triplets, and (2) for all k > or = 0 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.

AB - 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 > or = 1 it is NP-hard to construct a level-k network consistent with all input triplets, and (2) for all k > or = 0 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.

U2 - 10.1142/S0219720009004308

DO - 10.1142/S0219720009004308

M3 - Article

SN - 0219-7200

VL - 7

SP - 597

EP - 623

JO - Journal of Bioinformatics and Computational Biology

JF - Journal of Bioinformatics and Computational Biology

IS - 4

ER -