An Optimal Strategy for Energy Allocation in a Multiple Resource Environment

Abstract

We consider a model for a population in discrete time with nonoverlapping generations that has fecundity proportional to the amounts of two essential resources obtained up to a saturating level. A population’s strategy defines how individuals divide their total available energy between efforts to obtain the two resources. We assume that the total amount of each resource obtained is a positive, increasing, concave down function of the total energy exerted toward the resource. By considering two competing subpopulations that have different energy allocation strategies, we characterize the stability of all possible equilibria and find a unique optimal strategy where a fixed subpopulation resists invasion by a small competing subpopulation using any other strategy. Except when one of the resources is readily obtained above the saturation level, this optimal strategy is to divide effort equally between the resources. We illustrate the behavior of the model, directly showing the effects of an invading subpopulation with pairwise invasibility plots.