A method of estimating the slope of upper bounds of plots of body size and abundance in natural animal assemblages

Plots of species body size versus abundance in natural assemblages of animals often reveal polygonal relationships. Theory predicts that the slope of the upper bound of such polygons will approximate to -0.75, but has never been tested because of the lack of a statistical technique to estimate the slope. We present and test a method whereby the upper bound slope can be measured by dividing assemblage data into size classes, and using the highest abundance in each class to estimate the regression slope. The method accurately estimates slopes from simulated data of known upper bound, and estimates from real and simulated data vary in a similar manner when different numbers of size classes are used. We conclude that this method may be used with confidence to estimate upper bound slopes from polygonal relationships, and gives the first chance to test different hypotheses about the magnitude of such slopes.