Quartet based phylogeny reconstruction with answer set programming

Evolution is an important subarea of study in biological science, where given a set of species, the goal is to reconstruct their evolutionary history, or phylogeny. Many kinds of data associated with the species can be deployed for this task and many reconstruction methods have been proposed and examined in the literature. One very recent approach is to build a local phylogeny for every subset of 4 species, which is called a quartet for these 4 species, and then to assemble a phylogeny for the whole set of species satisfying these predicted quartets. In general, those predicted quartets might not always agree each other; and thus the objective function becomes to satisfy a maximum number of predicted quartets. This is the well-known maximum quartet consistency (MQC) problem, which is studied by a lot of researchers in the last two decades. We present a new equivalent representation for the MQC problem, that is, to search for an ultrametric matrix to satisfy the maximum number of those predicted quartets. We examine a few number of structural properties of the MQC problem in this new representation, through formulating it into answer set programming (ASP), a recent powerful logic programming tool for modeling and solving searching problems. The efficiency and usefulness of our approach are confirmed by our computational experiments on the artificial data as well as two real datasets.