Simple temporal models for ecological systems with complex spatial patterns

Mercedes Pascual,* Manojit Roy and Alain Franc Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109-1048, USA. INRA, Forest and Natural Environment Department, Paris and Orsay University, Laboratory ESE, France *Correspondence: E-mail: [email protected] 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.