A unifying model of genome evolution under parsimony

BACKGROUND: Parsimony and maximum likelihood methods of phylogenetic tree estimation and parsimony methods for genome rearrangements are central to the study of genome evolution yet to date they have largely been pursued in isolation. RESULTS: We present a data structure called a history graph that offers a practical basis for the analysis of genome evolution. It conceptually simplifies the study of parsimonious evolutionary histories by representing both substitutions and double cut and join (DCJ) rearrangements in the presence of duplications. The problem of constructing parsimonious history graphs thus subsumes related maximum parsimony problems in the fields of phylogenetic reconstruction and genome rearrangement. We show that tractable functions can be used to define upper and lower bounds on the minimum number of substitutions and DCJ rearrangements needed to explain any history graph. These bounds become tight for a special type of unambiguous history graph called an ancestral variation graph (AVG), which constrains in its combinatorial structure the number of operations required. We finally demonstrate that for a given history graph G, a finite set of AVGs describe all parsimonious interpretations of G, and this set can be explored with a few sampling moves. CONCLUSION: This theoretical study describes a model in which the inference of genome rearrangements and phylogeny can be unified under parsimony.