A Statistically Fair Comparison of Ancestral Genome Reconstructions, Based on Breakpoint and Rearrangement Distances

We introduce a way of evaluating two mathematically different optimization approaches to the same problem, namely how good or bad each is with respect to the other's criterion. We illustrate this in a comparison of breakpoint and rearrangement distances between the endpoints of a branch, where total branch-length is minimized in reconstructing ancestral genomes at the nodes of a given phylogeny. We apply this to mammalian genome evolution and simulations under various hypotheses about breakpoint re-use. Reconstructions based on rearrangement distance are superior in terms of branch length and dispersion of the multiple optimal reconstructions, but simulations show that both sets of reconstructions are equally close to the simulated ancestors.