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

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9625576 Cushing A central question in population biology is that of understanding and explaining observed fluctuations in animal numbers. The study of nonlinear dynamics has opened the way to a new phase of population research in which experiments are focused directly on phenomena such as equilibria, periodic and aperiodic cycles, and chaos. The investigators undertake a spectrum of activities essential to the testing of nonlinear population theory: from the translation of biology into the formal language of mathematics, to the analysis of mathematical models, to the development and application of statistical techniques for the analysis of data, to the design and implementation of biological experiments. Laboratory populations of flour beetles of the genus Tribolium are used in the experiments. By means of their studies the investigators provide rigorous experimental tests of nonlinear population phenomena and behavior. These include: (1) dynamical transitions from stable equilibria, to invariant loops (aperiodicities), to period locking, to strange attractors and chaos; (2) transient and intermittent dynamics with aims towards defining practical concepts of intermittency for use with stochastic population models and the testing of some of the unusual transient behaviors forecast by stochastic nonlinear models; (3) the dynamics of meta-populations using beetle populations linked by migration; and (4) the dynamical behaviors that can be produced by the interaction of environmental periodicities with nonlinear demographic effects. The investigators study how biological populations (in particular, populations of insects) fluctuate in time and how different circumstances can lead to drastically different, and sometimes unexpected, changes in these fluctuations. This study is carried out by means of an interdisciplinary program that integrates the use of sophisticated mathematical models and statistical analysis with the design and implementation of l aboratory experiments using species of beetles that are economically important insect pests. The investigators seek to describe and explain a variety of patterns in population fluctuations, ranging from those that are regular and predictable to those that are irregular and "chaotic." They seek to understand the environmental conditions that give rise to these various kinds of population behavior. This understanding is essential if the impact on biological populations of environmental perturbations and manipulations (by Man or by Nature) is to be predicted. These impacts have far-reaching consequences, ranging from food production and pest control to wildlife management and the conservation of species diversity.