Characteristic Length Scales of Spatial Models in Ecology via Fluctuation Analysis

A technique of uctuation analysis is introduced for the identiication of characteristic length scales in spatial models, with similarities to the recently introduced methods by Rand & Wilson (1995). The identiied length scale provides the optimal size to extract nontrivial large-scale behaviour in such models. The method is demonstrated for three biological models: genetic selection, plant competition and a complex marine system; the rst two are coupled map lattices and the last one is a cellular automaton. These cover the three possibilities for asymptotic (long time) dynamics: xation (the system converges to a xed point), statistical xation (the spatial statistics converge to xed values) and complex statistical structure (the statistics do not converge to xed values). The technique is shown to have an additional use in the identiication of aggregation or dispersal at various scales. The method is rigorously justiiable in the cases when the system under analysis satisses the FKG (Fortuin-Kasteleyn-Ginibre) property and has a fast decay of correlations. We also discuss the connection between the error analysis length scale with hydrodynamic limits methods used by Durrett & Levin (1995) to derive large scale equations for ecological models.