Using spatio-temporal chaos and intermediate-scale determinism to quantify spatially extended ecosystems

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Abstract
We discuss the question of how to quantify and analyse dynamics and patterns in spatially extended ecologies and introduce several new tools and ideas which use space-time dynamical structure. To illustrate our ideas, we introduce an artificial ecology model of a resource-predator-prey community which is interesting in its own right both ecologically and mathematically. This is a generalized probabilistic cellular automata. The model is stochastic and spatially non-homogeneous. We show how to identify a spatial scale intermediate between the noise dominated microscale and the infinite size limit at which non-trivial determinism is maximized. This is the scale at which to measure the system's dynamics. At this scale the population dynamics are essentially deterministic, low-dimensional and chaotic. This allows us to characterize the complex spatial patterns by a low-dimensional vector. This mapping from spatial patterns to low dimensional vectors provides effective and faithful data compression and is a powerful technique for synthesizing ecological information. It facilitates new analytical techniques. As an application we consider how to distinguish structural change within an ecosystem from natural dynamics. Such change is detected by using our parameterization to construct recurrence plots. Other applications such as the reconstruction of the dynamics of invisible species are discussed elsewhere.

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