Although the natural world is almost always in flux, ecological theory has been largely developed using mathematical models that assume that ecosystems come to a stable equilibrium. In recent decades, such models have been supplemented and partially replaced by models in which the physical environment varies in time and space. However, those model environments have invariably had the property of stationarity, which means that they can be characterized by a fixed set of statistics, such as averages, about which fluctuations occur, and measures of the magnitude and nature of the fluctuations. Although much has been learned from these models, it is now clear that the assumption of stationarity does not hold in nature, because environments are not stable over time. The challenge of anthropogenic climate change means that more realistic nonstationary assumptions about the physical environment are essential for the future, but they are also needed for more accurate understanding of past and present ecology. This research will develop models of interacting species subject to nonstationary environments to predict the impact of nonstationarity on the maintenance of biological diversity. The project will develop mathematical tools for making ecological predictions about diversity maintenance that allow stationary predictions to be replaced or modified for more realistic, nonstationary conditions. This will help show which aspects of species and of the environment have large effects on the maintenance of diversity in the nonstationary case as compared with the previous stationary assumptions. The project will also study how migration of different species at different rates in response to a changing environment affects the outcomes of the interactions between species and the maintenance of biological diversity.
The results of the research will have application to the conservation and management of natural environments, and help society face the challenges of global environmental change, for which nonstationary theory is essential. In addition, there will be a major education and training component for students and postdoctoral fellows in new tools for ecological models in nonstationary environments. High school teachers also will be given training in ecological models for changing environments to foster the development of materials for classroom instruction.