A nonlinear regression approach to test for size-dependence of competitive ability

An individual's competitive ability is often dependent on its size, but the methods commonly used to analyze plant competition experiments generally assume that the outcome of interactions are size independent. A method for the analysis of experiments with paired competition treatments based on nonlinear regression with a power function is presented. This method allows straightforward tests of whether a competitive interaction is size dependent, and for the significance of experimental treatments. The method is applied to three example data sets: (1) an experiment where pairs of plants were grown with and without competition at five fertilization levels, (2) an experiment where the fecundity of two snail species were compared between environments at two densities, and (3) an addition series experiment where two plant species were grown in proportional mixtures at several densities. Competitive ability was size-dependent in two of these examples, which demonstrates that a wide range of ecologically important information can be lost when the assumption of size-dependence is ignored. Regression with a power curve should always be used to test whether competitive interactions are size independent, and for the further analysis of size-dependent interactions.