Local interactions predict large-scale pattern in empirically derived cellular automata

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Abstract
An important unanswered question in ecology is whether processes such as species interactions that occur at a local scale can generate large-scale patterns seen in nature. Because of the complexity of natural ecosystems, developing an adequate theoretical framework to scale up local processes has been challenging. Models of complex systems can produce a wide array of outcomes; therefore, model parameter values must be constrained by empirical information to usefully narrow the range of predicted behaviour. Under some conditions, spatially explicit models of locally interacting objects (for example, cells, sand grains, car drivers, or organisms), variously termed cellular automata or interacting particle models, can self-organize to develop complex spatial and temporal patterning at larger scales in the absence of any externally imposed pattern. When these models are based on transition probabilities of moving between ecological states at a local level, relatively complex versions of these models can be linked readily to empirical information on ecosystem dynamics. Here, I show that an empirically derived cellular automaton model of a rocky intertidal mussel bed based on local interactions correctly predicts large-scale spatial patterns observed in nature.