The Minimum Environmental Perturbation Principle

Variational principles have served as powerful conceptual tools throughout all areas of physics, often providing some geometrical intuition for the behavior of an otherwise intractable model. Variational principles have also been found for some of the paradigmatic models of theoretical ecology, but they usually lack a clear physical interpretation, and are therefore of limited use for building intuition. In this talk, I will show that competition among consumers for a common pool of resources leads to steady-state resource concentrations that solve a constrained optimization problem. Specifically, the magnitude of the environmental perturbation induced by resource consumption is minimized, subject to the constraint that the per-capita growth rate of each consumer species in the regional pool is zero or negative. This "Minimum Environmental Perturbation Principle" applies to a wide class of models with arbitrarily large numbers of species and resource types, whether the resources are substitutable or essential. But it is broken by environmental feedbacks, whereby consumers return resources to the environment as metabolic byproducts or decaying biomass.