Models of complex spatial environmental and ecological systems are usually constructed using partial differential equations (PDEs), but cellular automata (CA's) can provide microscopically simple yet macroscopically rich alternatives. We develop a cellular automata model of a hierarchical predator-prey system and show that even a minimal automaton is able to capture the essential boom-bust and dynamical behaviour of real physical systems. A single probability rate of predator death is used to control predator behaviour. We describe the model in detail and explore the CA model for one- and two-predator food chains. We find a well delineated phase transition in the 2-predator system when the predator lifetime parameter is varied and present some system analysis and quantitative metrics. We discuss the CA model in comparison with PDE and more detailed event-driven agent-based models.
Keywords: cellular automata; spatial models; predator-prey; Lotka-Volterra; food chains; phase transition; stochastic rate equation.
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