From Individual Movement Rules to Population Level Patterns: The Case of Central-Place Foragers

We consider a model for the dynamics of a consumer-resource population where the foraging behavior of the central-place forager is explicitly modeled as a random walk. The model consists of a discrete map between generations and a partial differential equation within a season. We determine analytically the conditions under which the consumer can stay in the system. We then explore numerically how different assumptions on the foraging strategy affect the stability of the coexistence equilibrium. We find a number of ways in which foraging behavior destabilizes the coexistence equilibrium and leads to population cycles. We also find an instability resembling a flip bifurcation even though the model has compensatory dynamics. This modeling framework can serve in the future to explore the evolution of foraging strategies, thereby complementing previous ecological theory of central-place foraging.