Reconciling taxonomy and phylogenetic inference: formalism and algorithms for describing discord and inferring taxonomic roots

Background: Although taxonomy is often used informally to evaluate the results of phylogenetic inference and the root of phylogenetic trees, algorithmic methods to do so are lacking. Results: In this paper we formalize these procedures and develop algorithms to solve the relevant problems. In particular, we introduce a new algorithm that solves a subcoloring problem to express the difference between a taxonomy and a phylogeny at a given rank. This algorithm improves upon the current best algorithm in terms of asymptotic complexity for the parameter regime of interest; we also describe a branch-and-bound algorithm that saves orders of magnitude in computation on real data sets. We also develop a formalism and an algorithm for rooting phylogenetic trees according to a taxonomy. Conclusions: The algorithms in this paper, and the associated freely-available software, will help biologists better use and understand taxonomically labeled phylogenetic trees.