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Keywords:

  • Assignment statistics;
  • Morphological integration;
  • Taxonomy;
  • Land snails;
  • Arianta;
  • Shell characters

Abstract

Taxa can be characterized by character coupling represented in similarity matrices. The customary methods of testing equality of variance-covariance matrices are based upon the multinormality assumption which is, however, frequently unacceptable in reality. Quadratic assignment procedures (QAP) have proved to be an alternative. They represent a type of computer-based test and utilize a random-permutation strategy to discover significant pattern correspondences between matrices. A comparison of the applicability of both testing methods requires an example with underlying multinormality. The samples of two species of land snails (Pulmonata, Helicidae), i. e. Arianta arbustorum (n = 104) and Arianta chamaeleon (n = 36), fulfil this requirement. Four parameters of shape and two parameters of spiral change were determined in each shell. The data serve as the basis for similarity matrices (variance-covariance, product-moment and rank order correlations).

The inspection of methods reveals that QAP are suitable for correlation matrices, but can be applied for variance-covariance matrices with limitations only. Nevertheless, they are recommended procedures in taxonomy and evolutionary biology. Straightforward application, independence from distributional assumptions, and the possibility to test hypotheses of character coupling are advantageous features.

The snail species are significantly discriminated by character coupling. Also, their parameters of shape and spiral change are morphologically integrated in a different way.