Modelling patch dynamics on rocky shores using deterministic cellular automata

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Abstract
A model of biologically driven patchiness in the Fucus-Limpet-barnacle mosaic on rocky shores was developed using deterministic cellular automata. The model is based on interconnected small areas of approximately 1 limpet foraging diameter (1 m). Five states are recognised, which re present stages in the natural cycle of development of patches: (1) dense barnacle cover with no Limpets; (2) patches of young Fucus plants (escapes); (3) aggregations of limpets under ageing fucoids; (4) limpet aggregations from which fucoids have been lost; and (5) areas from which limpets have dispersed. Rules governing the transitions between these states were derived from experimental studies and qualitative models. These rules are based on the abundance of fucoids and limpets in adjoining areas and the current state of the areas themselves. Spatial patterns and spatial dynamics produced are sensitive to the sets of rules considered and the criteria for local dependence of state transitions. Certain conditions result in large stable patches of limpet aggregations or fucoids that are resistant to invasion by the other. Different conditions create large-scale areas of synchrony of patch cycling in which waves of areas in the same state propagate from local foci. These conditions produce limited grid-scale cycling in the abundance of fucoids, barnacles and limpets. Despite the qualitative nature of the model and the patterns and dynamics produced, its heuristic value remains. Local dependence of the fate of small areas requires further experimental study before the dependence of larger-scale fluctuations on these small-scale interactions can be established.