Mathematical Sciences: Nonlinear Demographic Dynamics: Mathematical Models, Biological Experiments, and Data Analysis

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The investigators undertake an interdisciplinary project to test nonlinear population theory, incorporating the construction and analysis of mathematical models, the design and implementation of biological experiments, and the development and application of statistical techniques for the analysis of data. They use flour beetles of the genus Tribolium as the experimental organism. In the first part of the project they identify appropriate models and estimate the parameters that control the detailed behavior of the models. In the second part they document transitions in the qualitative behavior of the demographic dynamics. They use combinations of reproductive rates and adult mortality rates that span boundaries in parameter space from stable equilibria, to invariant cycles, to chaos. In the third part they test hypotheses concerning the existence of these unusual demographic phenomena and develop methods for identifying the phenomena in experimental data. Understanding the observed fluctuations in animal numbers is a central question in population biology; indeed, it has far-reaching impacts ranging from food production to the conservation of species diversity. In the past ten years or so, the recognition that simple equations can generate complex dynamics has led to an outpouring of fascinating theoretical possibilities for the explanation of population time series data. This project aims to explore the possibility that populations can exhibit chaotic behavior similar to that seen in other physical phenomena. As indicated above, such behavior would have significant consequences.