  Fifty years ago, Robert MacArthur showed that stable equilibria optimize
quadratic functions of the population sizes in several important ecological
models. Here, we generalize this finding to a broader class of systems within
the framework of contemporary niche theory, and precisely state the conditions
under which an optimization principle (not necessarily quadratic) can be
obtained. We show that conducting the optimization in the space of
environmental states instead of population sizes leads to a universal and
transparent physical interpretation of the objective function. Specifically,
the equilibrium state minimizes the perturbation of the environment induced by
the presence of the competing species, subject to the constraint that no
species has a positive net growth rate. We use this "minimum environmental
perturbation principle" to make new predictions for eco-evolution and community
assembly, and describe a simple experimental setting where its conditions of
validity have been empirically tested.
