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 rst 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. A priori character subsets can be tested for signicant 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 cladogram has greater topological resolution and implies appreciably less change among the remaining characters than does a tree derived from the raw data matrix. [Character independence; character weighting; compatibility; correlated character evolution; similarity coefcient. ] A hypothesis of correlated character evolution, that is, that change in one character depends on conditions of another character, is of interest for both theoretical and methodological reasons. Theories from developmental (Wake, 1989), functional (Wainwright et al., 1975), architectural (Raup, 1966), and molecular (Huelsenbeck and Nielsen, 1999) biology all predict that correlated change should be common. However, phylogenetic inference methods such as parsimony (Edwards and Cavalli-Sforza, 1964; Kluge and Farris, 1969)and simple maximum likelihood (Felsenstein, 1973) assume independent character change. Thus, workers have long recognized that character correlation (also termed lack of character independence or character oversplitting) is a central issue in character selection (Sneath and Sokal, 1973). If characters evolve in a correlated manner, the characters in the correlated suite are effectively overweighted (de Queiroz, 1993; Chippindale and Wiens, 1994). Simulations indicate that parsimony tree topologies and tree lengths are less accurate when character evolution is correlated rather than independent (Wagner, 1998; Huelsenbeck and Nielsen, 1999). Correlated character evolution might also exaggerate bootstrap and Bremer support values for some nodes by inating apparent numbers of synapomorphies. Sneath and Sokal (1973) give two reasons why characters might be correlated: simple logical correlation arising from the definitions of the characters themselves, and correlation arising from the biology of the organisms under study. Judicious character selection can eliminate logical correlations among characters. Biological correlations are more difcult to identify but have been suggested for many groups of organisms (see Emerson and Hastings [1998] for a review and discussion). Examples include 657 Downloaded from https://academic.oup. com/sysbio/article-abstract/50/5/657/1645352