Simple temporal models for ecological systems with complex spatial patterns

Spatial patterns are ubiquitous in nature. Because these patterns modify the temporal dynamics and stability properties of population densities at a range of spatial scales, their effects must be incorporated in temporal ecological models that do not represent space explicitly. We demonstrate a connection between a simple parameterization of spatial effects and the geometry of clusters in an individual-based predator-prey model that is both nonlinear and stochastic. Specifically we show that clusters exhibit a power-law scaling of perimeter to area with an exponent close to unity. In systems with a high degree of patchiness, similar power-law scalings can provide a basis for applying simple temporal models that assume well-mixed conditions.