QEIB: Stochastic Nonlinear Population Dynamics: Mathematical Models, Biological Experiments, and Data Analyses

University Of Arizona, Tucson AZ

Investigators

Abstract

Cushing 0210474 The project entails a theoretical and experimental study that examines nonlinear population dynamics phenomena in the context of stochasticity and that addresses fundamental concepts of how stochastic and nonlinear forces combine to produce observed population phenomena. The methodology involves an interdisciplinary effort that features a thorough integration of biologically based modeling (deterministic and stochastic), mathematical and numerical analyses of model dynamics, and the derivation and application of statistical techniques for connecting models with data (including parameter estimation and model evaluation). The investigators study the fundamental question about how (demographic) stochasticity at the individual level propagates to the population level. A promising class of models that incorporates both demographic and environmental stochasticity is pursued. A variety of statistical and mathematical questions that arise from these studies are investigated. The validity of this modeling methodology and accuracy of a priori model predictions is directly testable by experiments. The project study includes an experimental test of this modeling approach to demographic and environmental stochasticity, using a laboratory model that the investigators have successfully used in a wide variety of population dynamics and modeling studies during the last decade. The modeling methodology is also applicable to field populations and the investigators pursue the development of field studies with several researchers who have expressed interest in such a collaboration. These collaborators include colleagues at (1) the Center for Environmental Analysis at California State University, Los Angeles in a project modeling the spatially structured dynamics of seashore species, (2) the University of California, Davis in a project to model a lupine-caterpillar-nematode system, (3) Andrews University on mathematical/statistical models of the distribution of marine birds and mammals on Protection Island National Wildlife Refuge in the Strait of Juan de Fuca, and (4) the Virginia Institute of Marine Science on nonlinear models of the blue crab in the Exuma Cays. An understanding of the dynamics of biological populations is fundamental to the understanding of ecological and environmental problems. Mathematical models can be a valuable tool that provides this understanding. They can also provide the means to predict the future of ecosystems and the species that they include. An accurate descriptive and predictive capability gained through mathematical models provides not only a basic understanding of ecological problems, but also the ability to design programs for the assessment, management, and control of ecosystems and for the solution of environmental problems. A fundamental difficulty in the application of mathematical models to ecological problems has been the lack of a close connection of models with biological data. A key problem is the ability of models to incorporate random effects and disturbances. The investigators extend, analyze, and apply a modeling methodology they have developed during a decade of experimental studies, in a controlled laboratory setting, that addresses these difficulties. The methods are not restricted to laboratory populations, however, and the project also includes collaborations with new colleagues for the purpose of applying the methods to field studies of natural populations.