The Minimum Environmental Perturbation Principle: A New Perspective on Niche Theory.

AbstractFifty 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 evolution and community assembly, where the minimum perturbation increases monotonically under invasion by new species. We also describe a simple experimental setting where the conditions of validity for this optimization principle have been empirically tested.