An Integer Linear Programming Solution for the Most Parsimonious Reconciliation Problem under the Duplication-Loss-Coalescence Model

Given a gene tree, a species tree, and an association between their leaves, the maximum parsimony reconciliation (MPR) problem seeks to find a mapping of the gene tree to the species tree that explains their incongruity using a biological model of evolutionary events. Unfortunately, when simultaneously accounting for gene duplication, gene loss, and coalescence, the MPR problem is NP-hard. While an exact algorithm exists, it can be problematic to use in practice due to time and memory requirements. In this work, we present an integer linear programming (ILP) formulation for solving the MPR problem when considering duplications, losses, and coalescence. Our experimental results on a simulated data set of 12 Drosophila species shows that our new algorithm is both accurate and scalable. Furthermore, in contrast to the existing exact algorithm, our formulation allows users to limit the maximum runtime and thus trade-off accuracy and scalability, making it an attractive choice for phylogenetic pipelines.