Figure 3

Taxon coverage patterns and decisiveness. A. Trivially decisive for all trees because one locus contains all taxa and thus by itself satisfies the required four-way partition property. B. Not decisive for all trees. For two loci only two quartets are induced by any tree, and although two are necessary to define a tree, these two do not suffice. We also know that all triples must be present as a necessary condition for decisiveness for all trees, but the triple {C, D, E} is not present in any column. C. Decisive for all trees because there is a reference taxon and every quadruple of taxa containing the reference pattern is seen among the loci, which satisfies a sufficient condition.