The SCJ small parsimony problem for weighted gene adjacencies

Abstract

Reconstructing ancestral gene orders in a given phylogeny is a classical problem in comparative genomics. Most existing methods compare conserved features in extant genomes in the phylogeny to define potential ancestral gene adjacencies, and either try to reconstruct all ancestral genomes under a global evolutionary parsimony criterion, or, focusing on a single ancestral genome, use a scaffolding approach to select a subset of ancestral gene adjacencies. In this paper, we describe an exact algorithm for the small parsimony problem that combines both approaches. We consider that gene adjacencies at internal nodes of the species phylogeny are weighted, and we introduce an objective function defined as a convex combination of these weights and the evolutionary cost under the Single-Cut-or-Join (SCJ) model. We propose a Fixed- Parameter Tractable algorithm based on the Sankoff-Rousseau dynamic programming algorithm, that also allows to sample co-optimal solutions.