Following research that demonstrated its robustness and superior performance to alternative methods, nonmetric multidimensional scaling (NMDS) has become widely used by ecologists for ordination of community data. Apart from the selection of dissimilarity measure, NMDS involves several option choices, some of which may be crucial to its success in effectively summarizing the major dimensions of community variation. The software commonly used by ecologists to perform NMDS does not allow control over certain options and this may account for dissatisfaction with the method expressed by some authors. NMDS derives an ordination in a specified number of dimensions in which inter-point distances are, as far as possible, in rank-order agreement with dissimilarities among sampling units (SUs). Agreement is quantified by stress, a normalized measure of the badness-of-fit of a monotonic regression of distances on dissimilarities. There are two ways of treating tied dissimilarities in monotonic regression: the primary (weak) approach allows pairs of SUs with equal dissimilarities to have unequal distances with no penalty to stress, while the secondary (strong) approach penalizes stress unless such pairs have equal distances. We hypothesized that in community data with high beta diversity, which results in many tied dissimilarities of 1.0 (corresponding to SU pairs with no shared species), secondary tie-treatment will result in curvilinear representation of community gradients, as NMDS attempts to construct an ordination in which all such pairs are equally distant. Community data were simulated with increasing levels of beta diversity and ordinated by NMDS using Bray-Curtis dissimilarity and both primary and secondary tie-treatment. Performance was measured by fitting ordinations to the known ecological structure of the models using Procrustes analysis.
Results/Conclusions
When beta diversity of the longest gradient exceeded 1 R (the level at which SUs at opposite extremes of a gradient have no species in common), NMDS ordinations with secondary tie-treatment were less successful in recovering the simulated gradient structure, relative to ordinations based on primary tie-treatment. In support of our hypothesis, they exhibited curvilinear distortion of gradients and the degree of distortion increased with beta diversity. We conclude that applications of NMDS to community data should use primary or weak treatment of ties. One of the major strengths of NMDS in comparison to linear ordination methods (e.g., principal components analysis, correspondence analysis) is its ability to ordinate community data of high beta diversity without curvilinear distortion and its success in this regard depends on the appropriate choice of tie-treatment.