Real evolutionary data often contain a number of different and sometimes conflicting phylogenetic signals, and thus do not always clearly support a unique tree. To address this problem, Bandelt and Dress (Adv. Math., 92, 47-05, 1992) developed the method of split decomposition. For ideal data, this method gives rise to a tree, whereas less ideal data are represented by a tree-like network that may indicate evidence for different and conflicting phylogenies.