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, charact er independence is a basic assumption of most phylogenetic inference method s, and dependent characters might confound attempts at phylogenetic inferen ce. Previously proposed tests of correlated character evolution require a m odel phylogeny and therefore assume that nonphylogenetic correlation has a negligible effect on initial tree construction. This paper develops "tree-f ree" methods for testing the independence of cladistic characters. These me thods can test the character independence model as a hypothesis before phyl ogeny reconstruction, or can be used simply to test for correlated evolutio n. We first develop an approach for visualizing suites of correlated charac ters by using character compatibility Two characters are compatible if they can be used to construct a tree without homoplasy. The approach is based o n 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. F rom this matrix, an association matrix analogous to a dissimilarity matrix is derived. Eigenvector analyses of this association matrix reveal suites o f 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 compatibili ties, given various criteria from the original data set. These simulated di stributions are then used to test whether the observed amounts of nonphylog enetic correlation in character suites can be attributed to chance alone. W e have applied these methods to published morphological data for caecilian amphibians. The analyses corroborate instances of dependent evolution hypot hesized by previous workers and also identify novel partitions. Phylogeneti c analysis is performed after reducing correlated suites to single characte rs. The resulting cladograrn has greater topological resolution and implies appreciably less change among the remaining characters than does a tree de rived from the raw data matrix.