The Minimum Environmental Perturbation Principle: A New Perspective on Niche Theory (1901.09673v4)

Abstract: 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.