Scaling up population dynamics: integrating theory and data.

How to scale up from local-scale interactions to regional-scale dynamics is a critical issue in field ecology. We show how to implement a systematic approach to the problem of scaling up, using scale transition theory. Scale transition theory shows that dynamics on larger spatial scales differ from predictions based on the local dynamics alone because of an interaction between local-scale nonlinear dynamics and spatial variation in density or the environment. Based on this theory, a systematic approach to scaling up has four steps: (1) derive a model to translate the effects of local dynamics to the regional scale, and to identify key interactions between nonlinearity and spatial variation, (2) measure local-scale model parameters to determine nonlinearities at local scales, (3) measure spatial variation, and (4) combine nonlinearity and variation measures to obtain the scale transition. We illustrate the approach, with an example from benthic stream ecology of caddisflies living in riffles. By sampling from a simulated system, we show how collecting the appropriate data at local (riffle) scales to measure nonlinearities, combined with measures of spatial variation, leads to the correct inference for dynamics at the larger scale of the stream. The approach provides a way to investigate the mechanisms and consequences of changes in population dynamics with spatial scale using a relatively small amount of field data.