Simple temporal models for ecological systems with complex spatial patterns

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Abstract
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.