In response to recent elaborations of the community matrix concept, I argue that nonlinear (higher-order) interactions between species are probably very important in many competitive relationships. Several competition coefficients calculated from populations of microcrustaceans in equilibrium microcosm communities change significantly with changes induced in the species composition of the remainder of the community. Because of interdependence among first-order competition coefficients, interpretation of community perturbation experiments becomes exceptionally difficult and subsequent calculations based on an α matrix to predict the number of species expected in the community are inappropriate to the assumptions of the model.