Quartets in maximal weakly compatible split systems

Abstract

Weakly compatible split systems are a generalization of unrooted evolutionary trees and are commonly used to display reticulate evolution or ambiguity in biological data. They are collections of bipartitions of a finite set X of taxa (e.g. species) with the property that, for every four taxa, at least one of the three bipartitions into two pairs (quartets) is not induced by any of the X-splits. We characterize all split systems where exactly two quartets from every quadruple are induced by some split: On the other hand, we construct maximal weakly compatible split systems where the number of induced quartets per quadruple tends to 0 with the number of taxa going to infinity. (C) 2009 Elsevier Ltd. All rights reserved.