Strongest evidence in compatibility: clique and tree evaluation using apparent phylogenetic signal

Strongest evidence (SE) is an approach to evaluating the support provided by characters for alternative phylogenetic hypotheses (i.e., trees). Although first demonstrated in the context of parsimony, SE is equally applicable to compatibility analysis. In the logic of strongest evidence, a character that is compatible with a phylogenetic hypothesis supports the tree only to the degree at which this compatibility would be improbable under a model of cladistic dissociation between character state distribution and the tree. The support measure derived from this consideration is called the "apparent phylogenetic signal" (APS). The total support for a tree is the sum of the individual character APS values. Tree topology and character structure both affect the chance of "random" compatibility and thus the APS scores. Because a clique of compatible characters implies a specific tree (possibly more than one if the character states are unordered or there are missing data), the evidential strength of a clique may be measured as the SE support for the clique's tree by the clique's characters. Use of this measure is demonstrated on a morphological data set for North American species of Ch[oris (Poaceae). Cliques with the same number of characters vary tremendously in their apparent evidential quality. The strongest clique is nearly 100,000 times less likely to be compatible by chance with the tree it implies than is the weakest clique of the same size. This approach to clique evaluation is compared with character counting and Meacham's clique improbability measure.