Multivariate Techniques — Nonmetric Clustering

Treating a sample on a given day as a vector of values, x = (xj... xn), with one value for each of the measured biotic parameters, allows multivariate distance functions to be computed. 

Euclidean distance between two sample points x and y is computed as 

Subtracting the cosine from one yields a distance measure, rather than a similarity measure, with the measure increasing as the points get farther from each other. 

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The following examples demonstrate the usefulness of multivariate methods in the evaluation of field ecological data and laboratory multispecies toxicity tests. In each of the examples, several multivariate techniques were used — generally Euclidean and cosine distances (Figure 11.29), principal components, and nonmetric clustering and association analysis. 

In both studies, nonmetric clustering outperformed the metric tests, although both principal components analysis and correspondence analysis yielded some additional insight into large-scaled patterns, which was not provided by the nonmetric clustering results. However, nonmetric clustering provided information without the use of inappropriate assumptions, data transformations, or other dataset manipulations that usually accompany the use of multivariate metric statistics. The success of these studies and techniques led to the examination of community dynamics in a series of two multispecies toxicity tests. 

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