Scientists trying to understand the workings of the complex natural world often build simplified models of nature. Unfortunately, leaving out the complexities of the world may lead to incorrect conclusions about its behavior. Complex models that try to capture the full breadth of reality may be too unwieldy to analyze. Where is the channel between the Scylla of unwieldy, complicated models and the Charybdis of unrealistic, simple models? The scientist's challenge is to know when and how to simplify a complex system to help understand a complex problem.

As part of a larger project funded by The Andrew W. Mellon Foundation, IES scientists Drs. David Strayer, Seth Bigelow and Holly Ewing are focusing on one particular kind of complexity - spatial heterogeneity - that is especially characteristic of ecosystems. This spatial heterogeneity (see photo) suggests the need for extremely complex models to account for processes occurring within different patches and interactions among patches. To avoid this complexity, ecologists often have ignored the spatial structure of ecosystems, working within relatively uniform habitats or building simplified models that assume uniform conditions. But uniform systems may not behave like variable ones.

To chart a course between these twin hazards of model-building, IES scientists have identified three conditions when it might be necessary to include information about spatial patterning in analyses of ecosystems. First, many important ecological processes have nonlinear dynamics (exponential growth and predator satiation are examples of nonlinear functions). The average of a nonlinear function is not the same as the value of that function at the average value of the independent variable, so simple models of systems with nonlinear dynamics may be inaccurate. Second, an ecological process may depend on the size of a patch as well as its identity. One hundred one-hectare woodlots may not have the same value as habitat as a single 100-ha woodlot. Third, patches may interact with one another. Interactions among patches are very common in ecological systems, and can be asymmetric (e.g., one patch may be downhill, downwind, or downstream of another) or symmetric. Each of these conditions requires a different model, some relatively simple and others very complicated. Interestingly, the same issues that complicate analyses of spatially variable ecosystems also complicate analyses of ecosystems that vary over time.

Because all ecosystems vary over space and time, we might ask why simple ecological models work at all. Three important ameliorating factors probably are responsible for much of the success of simple models of complex ecosystems. First, the scale of spatial variation of some variables may be small relative to the question under study. A study of nutrient export from the Hudson River may not need to consider the very great heterogeneity that occurs within a few millimeters of soil, for example. Second, approximate answers may suffice, as long as simplification causes only a modest amount of error. Finally, ecologists often use empirical approaches, in which the structure and parameters of the model are derived from real data, rather than from first principles (theory). This empirical approach is a practical way to eliminate the bias between realistic but complex models and simple models. Thus, while ecological systems are spatially and temporally complex, it is not always necessary to include such complexity in models of these systems.