A Nonparametric Method for Comparing Dissimilarity Matrices, a General Measure of Biogeographical Distance, and Their Application

The pairwise relationships among a set or objects can be divided into two subsets, namely, those indicating the objects which are relative neighbors, and those which do not. If it is reasonable to expect that the same subsets should be obtained from a different source for the relationships, then a contingency table can be formed, and a hypothesis of marginal independence can be examined. In an example in which the spoken letters of the alphabet were compared with what is heard, it was found that there was a high degree of association, but none between either of these two sets and their lowercase visual appearance. In a second example, a hypothesis was examined which postulates that species which recently diverged should tend to be geographically close. Before this could be evaluated, it was necessary to define a distance between distinct taxa occupying not necessarily disjoint geographical regions. With the hypothesis that the set of species morphologically similar to each includes some or all of those which diverged recently from it (others may be included), a significant association was found between morphologically alike and geographically near species of Medicago, which is interpreted as evidence confirming the prediction.