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


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 nature1,2. 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 automata3,4 or interacting particle models5, can self-organize to develop complex spatial and temporal patterning at larger scales in the absence of any externally imposed pattern1,6,7,8. 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.

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Figure 1
Figure 2: Frequency distribution of gap size (length of consecutive non-M. californianus points encountered in random transects) observed in mussel beds of Tatoosh Island, Washington (filled circles; n = 876), and generated by various versions of mussel-bed models that had empirical parameters.
Figure 3: Example of spatial structure generated by the mussel-bed simulation model with external wave-initiated disturbance events.
Figure 4: Composition of the mussel-bed community in each ecological state observed from transects (black bars) and predicted by different mussel-bed models with empirical parameters.


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I thank the Makah Tribal Council and the United States Coast Guard for providing access to Tatoosh Island; A. Miller, R. Raynor, K. Rose, J. Salamunovitch, B. Scott, J. Sheridan, F. Stevens and A. Sun for field assistance; and P. Kareiva, R. Paine, C. Pfister and A. Sun for helpful comments. The work was supported in part by the A. W. Mellon Foundation and personal funds.

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Wootton, J. Local interactions predict large-scale pattern in empirically derived cellular automata. Nature 413, 841–844 (2001).

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