Estimating true evolutionary distances under the DCJ model

Motivation: Modern techniques can yield the ordering and strandedness of genes on each chromosome of a genome; such data already exists for hundreds of organisms. The evolutionary mechanisms through which the set of the genes of an organism is altered and reordered are of great interest to systematists, evolutionary biologists, comparative genomicists and biomedical researchers. Perhaps the most basic concept in this area is that of evolutionary distance between two genomes: under a given model of genomic evolution, how many events most likely took place to account for the difference between the two genomes? Results: We present a method to estimate the true evolutionary distance between two genomes under the 'double-cut-and-join' (DCJ) model of genome rearrangement, a model under which a single multichromosomal operation accounts for all genomic rearrangement events: inversion, transposition, translocation, block interchange and chromosomal fusion and fission. Our method relies on a simple structural characterization of a genome pair and is both analytically and computationally tractable. We provide analytical results to describe the asymptotic behavior of genomes under the DCJ model, as well as experimental results on a wide variety of genome structures to exemplify the very high accuracy (and low variance) of our estimator. Our results provide a tool for accurate phylogenetic reconstruction from multichromosomal gene rearrangement data as well as a theoretical basis for refinements of the DCJ model to account for biological constraints.