Computing consensus networks for collections of 1-nested phylogenetic networks

. An important and well-studied problem in phylogenetics is to compute a consensus tree so as to summarize the common features within a collection of rooted phylogenetic trees, all whose leaf-sets are bijectively labeled by the same set X of species. More recently, however, it has become of interest to find a consensus for a collection of more general, rooted directed acyclic graphs all of whose sink-sets are bijec-tively labeled by X , so called rooted phylogenetic networks . These networks are used to analyze the evolution of species that cross with one another, such as plants and viruses. In this paper, we introduce an algorithm for computing a consensus for a collection of so-called 1-nested phylogenetic networks. Our approach builds on a previous result by Rosell´o et al. that describes an encoding for any 1-nested phylogenetic network in terms of a collection of ordered pairs of subsets of X . More specifically, we characterize those collections of ordered pairs that arise as the encoding of some 1-nested phylogenetic network, and then use this characterization to compute a consensus network for a collection of t ≥ 1 1-nested networks in O ( t | X | 2 + | X | 3 ) time. Applying our algorithm to a collection of phylogenetic trees yields the well-known majority rule consensus tree. Our approach leads to several new directions for future work, and we expect that it should provide a useful new tool to help understand complex evolutionary scenarios.