Collaborative Research: Non-Linear Population Dynamics: Mathematical Models, Biological Experiments and Data Analysis

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Dennis9981458 Understanding the fluctuations in animal numbers is acentral issue in population biology that has far-reaching impacton and implications for problems ranging from food production tothe conservation of species. Nonlinear dynamics opens the way toa new phase of population research in which theory andexperimentation focus on phenomena such as cycles andquasi-periodicity, chaos and strange attractors, multipleattractors and complicated basins of attraction, saddle sets andtheir stable manifolds, and so on. This interdisciplinaryproject, in which Robert Costantino, Jim Cushing, Brian Dennis,Robert Desharnais, and Shandelle Henson collaborate, covers aspectrum of activities essential to testing nonlinear populationtheory: the translation of the biology into the language ofmathematics and back again, the analysis of deterministic andstochastic models, the development and application of statisticaltechniques for the analysis of data, and the design andimplementation of biological experiments. A series of experimentswith flour beetles of the genus Tribolium provide rigorousexperimental tests of nonlinear phenomena. Topics includenonlinearity in the context of stochasticity, chaos andpopulation control, the impact of periodic environments on animalabundance, demographic dynamics and natural selection,nonequilibrium species interactions, and statistical questionsconcerning parameterization and validation of models. With a sound understanding of the underlying dynamics ofanimal populations, ecologists can anticipate the consequences ofenvironmental degradation and learn better ways to manage naturalpopulations and control populations of pests. For example, one ofthe experiments suggests that, by taking advantage of the"sensitivity to initial conditions" that is the hallmark of achaotic system, managers can dramatically decrease pestpopulation numbers without the use of chemical pesticides bymaking small perturbations at critical times. The marriage ofecological theory and experiments by the interdisciplinaryresearch team leads to new techniques for the application ofmathematics to ecological problems. The project is supported bythe Applied Mathematics, Computational Mathematics, andStatistics programs in MPS and the Population Biology and Ecologyprograms in BIO.