Methods for the Comparative Analysis of Variation Patterns

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Abstract
Although comparisons of variation patterns with theoretical expectations and across species are playing an increasingly important role in systematics, there has been a lack of appropriate procedures for statistically testing the proposed hypotheses. We present a series of statistical tests for hypotheses of morphological integration and for interspecific comparison, along with examples of their application. These tests are based on various randomization and resampling procedures, such as Mantel's test with its recent extensions and bootstrapping. They have the advantage of avoiding the specific and strict distributional assumptions invoked by analytically-based statistics. The statistical procedures described include one for testing the fit of observed correlation matrices to hypotheses of morphological integration and a related test for significant differences in the fit of two alternative hypotheses of morphological integration to the observed correlation structure. Tests for significant similarity in the patterns and magnitudes of variance and correlation among species are also provided.