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The Statistical Analysis of Size Ratios

Size ratios are convenient indexes of the morphological differences between species. They have been variously used to predict multidimensional niche separation, explain coexistence, and even indicate "missing species," depending on whether they are small, moderate, or large. From a statistical viewpoint, ratios of ranked species' sizes are ratios of successive order statistics, which are largely independent of the underlying size distribution. We derive probability density functions for these ratios, assuming that species' sizes are independently drawn from uniform or unimodal distributions. In the absence of frequent character displacement, distributions of ratios should be negative exponential in form, with average values decreasing with increasing guild size. These predictions, which differ from those under a purely competitive model, are tested with several large data sets. In contrast, the statistical analysis of ratios in small data sets, such as individual guilds, depends on arbitrary assumptions about the shape and endpoints of the underlying size distribution. We conclude that size ratios alone are of limited explanatory power and should be supplemented with other data in studies of character displacement and community structure.