Most natural processes, from interactions among subatomic particles to atmospheric processes that dictate weather, are nonlinear, meaning that the relationships among variables cannot be described by simple lines. Nonlinearities lead to such mathematical phenomena as chaos and catastrophes, in which small changes to the inputs to a system lead to large changes in the outputs. Ecological systems are full of nonlinearities, and in addition they experience stochastic noise created by a random, unpredictable environment. The combination of nonlinear dynamics and stochastic noise has the potential for making ecological systems impossible to predict, because the chaos and catastrophes of nonlinearities are exacerbated by the noisiness of natural systems.
The proposed work will address the interactions between nonlinear dynamics and stochastic noise in model ecological systems in an attempt to find general properties that will make natural systems more predictable. Even though there is the potential for extremely complex interactions between nonlinear dynamics and stochastic noise, many data sets from real ecological systems show patterns approximating the behavior of noisy but linear systems. Part of the research project will be directed towards confirming or refuting this observation by developing statistical techniques to detect nonlinearities in ecological data. The other part of the research will ask from a theoretical perspective what types of dynamics are expected to be exhibited by nonlinear stochastic systems, and whether these expectations are in fact similar to truly linear stochastic dynamics. Many key environmental problems require stochastic population models. The proposed work will offer ecologists new tools for interpreting data. There will be excellent training for one post-doc, and many opportunities for undergraduates
