Collaborative Research: Non-Linear Population Dynamics: Mathematical Models, Biological Experiments and Data Analysis
Dennis 9981458 Understanding the fluctuations in animal numbers is a central issue in population biology that has far-reaching impact on and implications for problems ranging from food production to the conservation of species. Nonlinear dynamics opens the way to a new phase of population research in which theory and experimentation focus on phenomena such as cycles and quasi-periodicity, chaos and strange attractors, multiple attractors and complicated basins of attraction, saddle sets and their stable manifolds, and so on. This interdisciplinary project, in which Robert Costantino, Jim Cushing, Brian Dennis, Robert Desharnais, and Shandelle Henson collaborate, covers a spectrum of activities essential to testing nonlinear population theory: the translation of the biology into the language of mathematics and back again, the analysis of deterministic and stochastic models, the development and application of statistical techniques for the analysis of data, and the design and implementation of biological experiments. A series of experiments with flour beetles of the genus Tribolium provide rigorous experimental tests of nonlinear phenomena. Topics include nonlinearity in the context of stochasticity, chaos and population control, the impact of periodic environments on animal abundance, demographic dynamics and natural selection, nonequilibrium species interactions, and statistical questions concerning parameterization and validation of models. With a sound understanding of the underlying dynamics of animal populations, ecologists can anticipate the consequences of environmental degradation and learn better ways to manage natural populations and control populations of pests. For example, one of the experiments suggests that, by taking advantage of the "sensitivity to initial conditions" that is the hallmark of a chaotic system, managers can dramatically decrease pest population numbers without the use of chemical pesticides by making small perturbations at critical times. The marriage of ecological theory and experiments by the interdisciplinary research team leads to new techniques for the application of mathematics to ecological problems. The project is supported by the Applied Mathematics, Computational Mathematics, and Statistics programs in MPS and the Population Biology and Ecology programs in BIO.