Abstract. One of the simplest evolutionary models has molecular sequences evolving from a common ancestor down a bifurcating phylogenetic tree, experiencing point-mutations along the way. However, empirical analyses of different genes indicate that the evolution of genomes is often more complex than can be represented by such a model. Thus, the following problem is of significant interest in molecular evolution: Given a set of molecular sequences, compute a reticulate network that explains the data using a minimal number of reticulations. This paper makes four contributions toward solving this problem. First, it shows that there exists a one-to-one correspondence between the tangles in a reticulate network, the connected components of the associated incompatibility graph and the netted components of the associated splits graph. Second, it provides an algorithm that computes a most parsimonious reticulate network in polynomial time, if the reticulations contained in any tangle have a ce...
Daniel H. Huson, Tobias H. Klöpper, Pete J. L