Different modes of resource variation provide a critical test of ideal free distribution models

Abstract

Ideal free distribution (IFD) models are perhaps the group of mathematical models of behavior that have been the most widely and successfully applied by empiricists. These models can be applied to nearly any situation in which consumers compete—by any mechanism—for resources that are patchily distributed in their environment. Although IFD models have come to be broadly accepted, experiments that simultaneously test more than a single prediction are rare. Instead, investigators normally either test (1) for a relationship between the distribution of consumers and the distribution of resources or (2) whether average fitnesses are equal across resource patches. We conducted experiments with pea aphids (Acyrthosiphon pisum Harris) feeding on two patches of fava beans (Vicia faba L.) to fully independently parameterize an IFD model with interference competition and then test quantitative predictions about aphid spatial distributions and the payoffs of patch choice. We found a precise fit between aphids’ predicted and observed reproductive successes. Furthermore, by varying patch “quality” in two ways, we were able to show that aphid distributions vary with the mode of resource variation in the predicted manner: aphids (1) matched resources when patches varied in size but not quality and (2) overmatched the good patch when patches varied in quality but not size (predicted as a consequence of weak interference). The close correspondence between quantitative predictions of the model with observed behaviors suggests that IFD theory is a framework with more explanatory power than is generally appreciated.