Ecological Cellular Automata: A New Approach to Spatio-Temporal Modelling of Interacting Populations

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This project will provide a wide-ranging and detailed investigation of cellular automata (CA) models as descriptions of ecological interactions in space and time. CA models are essentially discretized versions of reaction-diffusion models; they are closely related to patch-occupancy models for metapopulation dynamics. The research program will construct models for competition, predation, and predator-mediated coexistence. It will extend the usual CA approaches to include substrate heterogeneity and disturbance size distributions. The analysis of these models will include a range of non-spatial or mean-field properties (state and species frequencies, mean alpha and beta diversities, interspecific associations, and turnover rates) as well as explicitly spatial methods (fractal dimensions, other scaling relationships, and wavelet analysis). The models will be applied to a number of specific problems, including the relationship of biotic and substrate heterogeneity, the contrast of CA models with the corresponding spatially averaged patch-occupancy models, and the conditions required for pattern generation in the ecological analogs of excitable media. This research will provide new insights into spatial relationships of many basic processes in population and community ecology.