The Mathematics of Animal Behavior: An Interdisciplinary Dialogue

M athematical ecology has attracted a vibrant community of applied mathematicians. Collaborations with biologists are encouraged, and a variety of nonlinear phenomena have been modeled successfully in several laboratory systems [7]. Examples of “hard science” conducted with mathematical models of field populations and ecosystems are still rather uncommon, however, in part because appropriate data sets are hard to obtain. (By “hard science”, we mean a full integration of mathematical models into the scientific method. Models serve as testable hypotheses, providing quantitative descriptions and predictions.) Lacking examples of a rigorous connection between models and data, many biologists remain skeptical that mathematics is a powerful scientific tool in ecology. Certainly the exercise of modeling is useful in its own right—models help clarify definitions and assumptions, illuminate key concepts, and suggest hypotheses—but, in general, ecologists and their students do not become immersed in the problem of doing science with mathematics. Ecologists of the near future will require mathematical tools. The weight of scientific opinion is that human activity is changing our world at a scale and pace that may lead to irreversible bifurcations in ecological and social systems within this century. Accelerating crises associated with climate change may stimulate increased funding in science, technology, engineering, and mathematics,