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Scales That Matter: Untangling Complexity in Ecological Systems

Complexity in ecological systems results not only from a large number of components, but also from nonlinear interactions among the multiple parts. The combined effects of high-dimensionality and nonlinearity lead to fundamental challenges in our ability to model, understand, and predict the spatio-temporal dynamics of ecological systems. This essay argues that these challenges are essentially problems of scale- arising from the interplay of variability across scales. It addresses two main consequences of such interplay and sketches avenues for tackling related problems of scale with approaches at the interface of dynamical system theory and time series analysis.

The first consequence involves a 'scale mismatch' between fluctuations of the physical environment and those of ecological variables: in a nonlinear system, forcing at one scale can produce an ecological response with variability at one or more different scales. This scale mismatch challenges our ability to identify key environmental forcings responsible for ecological patterns with conventional statistical approaches based on assumptions of linearity.

In the first half of this essay, theoretical models are used to illustrate the rich array of possible responses to forcing. The models focus on systems for antagonistic interactions, such as those for consumers and their prey or pathogens and their hosts. These examples motivate an important empirical question: how do we identify environmental forcings from ecological patterns without assuming a priori that systems are linear? An alternative approach is proposed, based on novel time series methods for nonlinear systems. Its general framework should also prove useful to predict ecological responses as a function of environmental forcings. General areas for future application of this approach are outlined in two fields of primary importance to humans-fisheries and epidemiology. In these fields, the role of physical forcings has become the subject of renewed attention, as concern develops for the consequences of human-induced changes in the environment.

The nonlinear models used in the proposed approach are largely phenomenological, allowing for unknown variables and unspecified functional forms. As such, they are best- suited for systems whose ecological interactions are well-captured by a low number of variables. This brings us to the second part of this essay, on the relationship between scale of description and dynamical properties, including dimensionality.

Here, a second consequence of the interplay of variability across scales is considered, which involves the level of aggregation at which to sample or model ecological systems. This interplay complicates in fundamental ways the problem of aggregation by rendering simple averaging impossible. Aggregation is, however, at the heart of modelling ecological systems- of defining relevant variables to represent their dynamics, and of simplifying elaborate models whose high-dimensionality precludes understanding and robust prediction.

The second part of this essay addresses the specific problem of selecting a spatial scale for averaging complex systems. A spatial predator-prey model following the fate of each individual is used to illustrate that fundamental dynamical properties, such as dimensionality and determinism, vary with the spatial scale of averaging. Methods at the interface of dynamical system theory and time series analysis prove useful to describe this variation and to select, based on it, a spatial scale for averaging. But scale selection is only the first step in model simplification. The problem then shifts to deriving an approximation for the dynamics at the selected scale. The dynamics of the predator-prey system serve to underscore the difficulties that arise when fine-scale spatial structure influences patterns at coarser scales. Open areas for future research are outlined.

Ecologists axe well-aware of the complicated dynamics that simple low-dimensional systems can exhibit even in the absence of external forcings. The present challenge is to better understand the dynamics of high-dimensional nonlinear systems and their rich interplay with environmental fluctuations. Here, the perplexing order that non-linearity creates opens doors to reduce complexity by exploiting relationships between dynamical properties and scale of description. This simplification is important for understanding and predicting dynamics, and 'ultimately, for better managing human interactions with the environment.