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Reconstructing ancestral gene orders in a given phylogeny is a classicalproblem in comparative genomics. Most existing methods compare conservedfeatures in extant genomes in the phylogeny to define potential ancestral geneadjacencies, and either try to reconstruct all ancestral genomes under a globalevolutionary parsimony criterion, or, focusing on a single ancestral genome,use a scaffolding approach to select a subset of ancestral gene adjacencies,generally aiming at reducing the fragmentation of the reconstructed ancestralgenome. In this paper, we describe an exact algorithm for the Small ParsimonyProblem that combines both approaches. We consider that gene adjacencies atinternal nodes of the species phylogeny are weighted, and we introduce anobjective function defined as a convex combination of these weights and theevolutionary cost under the Single-Cut-or-Join (SCJ) model. The weights ofancestral gene adjacencies can e.g. be obtained through the recent availabilityof ancient DNA sequencing data, which provide a direct hint at the genomestructure of the considered ancestor, or through probabilistic analysis of geneadjacencies evolution. We show the NP-hardness of our problem variant andpropose a Fixed-Parameter Tractable algorithm based on the Sankoff-Rousseaudynamic programming algorithm that also allows to sample co-optimal solutions.We apply our approach to mammalian and bacterial data providing differentdegrees of complexity. We show that including adjacency weights in theobjective has a significant impact in reducing the fragmentation of thereconstructed ancestral gene orders.

The SCJ small parsimony problem for weighted gene adjacencies (Extended version)