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

TL;DR

This paper introduces an exact algorithm for reconstructing ancestral gene orders by combining weighted adjacency data with the SCJ model, improving accuracy and reducing fragmentation in phylogenetic analyses.

Contribution

It presents a novel fixed-parameter tractable algorithm for the weighted small parsimony problem in ancestral genome reconstruction, incorporating adjacency weights from ancient DNA and probabilistic data.

Findings

Including adjacency weights reduces genome fragmentation.

The problem is NP-hard, but solvable with the proposed FPT algorithm.

Application to mammalian and bacterial data demonstrates effectiveness.

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, generally aiming at reducing the fragmentation of the reconstructed ancestral genome. 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. The weights of ancestral gene adjacencies can e.g. be obtained through the recent availability of ancient DNA sequencing data, which provide a direct hint at the genome structure of the considered ancestor, or through probabilistic analysis of gene adjacencies evolution. We show the NP-hardness of our problem variant and propose a Fixed-Parameter Tractable algorithm based on the Sankoff-Rousseau dynamic programming algorithm that also allows to sample co-optimal solutions. We apply our approach to mammalian and bacterial data providing different degrees of complexity. We show that including adjacency weights in the objective has a significant impact in reducing the fragmentation of the reconstructed ancestral gene orders.