Mantel tests are not the only way to examine relationships between dissimilarity matrices: A regression and cross-validation alternative

Background/Question/Methods The comparison of dissimilarity matrices calculated from independent sets of multivariate data has been used for a number of questions in community and geographical ecology. The standard measure of the relationship between two dissimilarity matrices is a correlation coefficient or a statistic with similar properties, and the statistical significance of such correlations is routinely tested with a Mantel randomization test, in which the row to row correspondence between the two matrices is shuffled. However, the interpretation of such statistics is limited to a simple strength of correlation, and complications arise when randomization tests are applied to matrices of dissimilarities between community change vectors. Another more general approach is to select a regression model for the relationship between the two sets of dissimilarities, using a “leave out n” cross-validation procedure to select the appropriate model complexity.

Results/Conclusions Two benefits result. First, the technical problems associated with community change vectors go away. Second, the parameters of an explicit model of the relationship between two dissimilarity matrices have potentially useful interpretations, depending on the context; for example, in the context of change vector analysis, the y-intercept can be taken as a measure of the expected variability of trajectories of plots that have identical initial states. The approach is demonstrated for two matrices of changes in forest community composition, one measured in the field and another generated from a simulation model.