Higher-Order Homoplasy Tests

The Le Quesne test of character compatibility uses pairwise comparisons of characters to detect homoplasy in phylogenetic character data. If a pair of characters fails this test we can conclude that a minimum of a single extra step is required by the pair of characters. The rationale of the Le Quesne test is extended to comparisons of triplets of characters. The triplet homoplasy test can reveal that that there is a minimum of four extra steps across a triplet of characters and thus that there are at least two extra steps associated with one of the characters. The triplet homoplasy test can thus detect higher orders of homoplasy than can be detected by the pairwise Le Quesne test. The possibility of quartet and other higher-order homoplasy tests is discussed. The utility of higher-order homoplasy tests is discussed. It is suggested higher-order homoplasy tests have potential uses analogous to the uses of the Le Quesne test, particularly with respect to data exploration.