Most methods of multivariate analysis rely on a measure of proximity between individual
cases or samples to quantify inter-sample differences. The choice of this measure is fundamental to
the method and its subsequent results. For example, when data are abundance counts of a set of
species at several sampling locations, some approaches rely on the Bray-Curtis dissimilarity
measure between samples, while other approaches rely on the chi-square distance. A set of
observed species abundances at a location ...
Most methods of multivariate analysis rely on a measure of proximity between individual
cases or samples to quantify inter-sample differences. The choice of this measure is fundamental to
the method and its subsequent results. For example, when data are abundance counts of a set of
species at several sampling locations, some approaches rely on the Bray-Curtis dissimilarity
measure between samples, while other approaches rely on the chi-square distance. A set of
observed species abundances at a location has both size, in the form of the overall levels of the
species counts, and shape, in the form of the relative values of the counts. The aim of this report is
to clarify how much the chosen proximity measure is capturing differences in size between samples
as opposed to differences in shape. After motivating the idea using physical morphometric data, the
study is extended to nonnegative data in general, with special focus on abundance counts and
biomass estimates, which are ubiquitous in ecological research.
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