Diffusion-limited predator-prey dynamics in Euclidean environments: an allometric individual-based model

We claim that diffusion-limited rates of reaction can be an explanation for the altered population dynamics predicted by models incorporating local interactions and limited individual mobility. We show that the predictions of a spatially explicit, individual-based model result from reduced rates of predation and reproduction caused by limited individual mobility and patchiness. When these reduced rates are used in a mean-field model, there is better agreement with the predictions of the simulation model incorporating local interactions. We also explain previous findings regarding the effects of dimensionality on population dynamics in light of diffusion-limited reactions and Pólya random walks. In particular, we demonstrate that 3D systems are better "stirred" than 2D systems and consequently have a reduced tendency for diffusion-limited interaction rates.