The robustness of quantitative measures of compositional dissimilarity between sites was evaluated using extensive computer simulations of species' abundance patterns over one and two dimensional configurations of sample sites in ecological space. Robustness was equated with the strength, over a range of models, of the linear and monotonic (rank-order) relationship between the compositional dissimilarities and the corresponding Euclidean distances between sites measured in the ecological space. The range of models reflected different assumptions about species' response curve shape, sampling pattern of sites, noise level of the data, species' interactions, trends in total site abundance, and beta diversity of gradients.
The Kulczynski, Bray-Curtis and Relativized Manhattan measures were found to have not only a robust monotonic relationship with ecological distance, but also a robust linear (proportional) relationship until ecological distances became large. Less robust measures included Chord distance, Kendall's coefficient, Chisquared distance, Manhattan distance, and Euclidean distance.
A new ordination method, hybrid multidimensional scaling (HMDS), is introduced that combines metric and nonmetric criteria, and so takes advantage of the particular properties of robust dissimilarity measures such as the Kulczynski measure.