The Small Parsimony Problem (SPP) aims at finding the gene orders at internal nodes of a given phylogenetic tree such that the overall genome rearrangement distance along the tree branches is minimized. This problem is intractable in most genome rearrangement models, especially when gene duplication and loss are considered. In this work, we describe an Integer Linear Program algorithm to solve the SPP for natural genomes, i.e. genomes that contain conserved, unique, and duplicated markers. The evolutionary model that we consider is the DCJ-indel model that includes the Double-Cut and Join rearrangement operation and the insertion and deletion of genome segments. We evaluate our algorithm on simulated data and show that it is able to reconstruct very efficiently and accurately ancestral gene orders in a very comprehensive evolutionary model.
Keywords: Genome rearrangement; ancestral reconstruction; small parsimony.