Inferring and testing hypotheses of cladistic character dependence by using character compatibility

The notion that two characters evolve independently is of interest for two reasons. First theories of biological integration often predict that change in one character requires complementary change in another. Second, character independence is a basic assumption of most phylogenetic inference methods, and dependent characters might confound attempts at phylogenetic inference. Previously proposed tests of correlated character evolution require a model phylogeny and therefore assume that nonphylogenetic correlation has a negligible effect on initial tree construction. This paper develops tree-free methods for testing the independence of cladistic characters. These methods can test the character independence model as a hypothesis before phylogeny reconstruction, or can be used simply to test for correlated evolution. We first develop an approach for visualizing suites of correlated characters by using character compatibility Two characters are compatible if they can be used to construct a tree without homoplasy. The approach is based on the examination of mutual compatibilities between characters. The number of times two characters i and j share compatibility with a third character is calculated, and a pairwise shared compatibility matrix is constructed. From this matrix, an association matrix analogous to a dissimilarity matrix is derived. Eigenvector analyses of this association matrix reveal suites of characters with similar compatibility patterns. Apriori character subsets can be tested for significant correlation on these axes. Monte Carlo tests are performed to determine the expected distribution of mutual compatibilities, given various criteria from the original data set. These simulated distributions are then used to test whether the observed amounts of nonphylogenetic correlation in character suites can be attributed to chance alone. We have applied these methods to published morphological data for caecilian amphibians. The analyses corroborate instances of dependent evolution hypothesized by previous workers and also identify novel partitions. Phylogenetic analysis is performed after reducing correlated suites to single characters. The resulting cladograrn has greater topological resolution and implies appreciably less change among the remaining characters than does a tree derived from the raw data matrix.