Phylogenies inferred from independent data partitions usually differ from one another in topology despite the fact that they are drawn from the same set of organisms (Rodrigo et al., 1993). Some topological differences are due to sampling error or to the use of inappropriate phylogenetic models. These types of topological incongruence do not have their origin in genealogical discordance, i.e., differences between phylogenies underlying the respective data partitions (Baum et al., 1998). Incongruence that is not due to genealogical discordance can often be addressed by modifying the model used in phylogenetic reconstruction (Cunningham, 1997b), and combining data is an appropriate way of dealing with random topological differences that are attributable to sampling error. However, other topological differences, e.g., those arising from lineage sorting (Maddison, 1997; Avise, 2000) and hybridization (Dumolin-Lapègue et al., 1997; Rieseberg, 1997; McKinnon et al., 1999; Avise, 2000), reflect genealogical discordance between the data partitions.