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

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Cushing0210474 The project entails a theoretical and experimental studythat examines nonlinear population dynamics phenomena in thecontext of stochasticity and that addresses fundamental conceptsof how stochastic and nonlinear forces combine to produceobserved population phenomena. The methodology involves aninterdisciplinary effort that features a thorough integration ofbiologically based modeling (deterministic and stochastic),mathematical and numerical analyses of model dynamics, and thederivation and application of statistical techniques forconnecting models with data (including parameter estimation andmodel evaluation). The investigators study the fundamentalquestion about how (demographic) stochasticity at the individuallevel propagates to the population level. A promising class ofmodels that incorporates both demographic and environmentalstochasticity is pursued. A variety of statistical andmathematical questions that arise from these studies areinvestigated. The validity of this modeling methodology andaccuracy of a priori model predictions is directly testable byexperiments. The project study includes an experimental test ofthis modeling approach to demographic and environmentalstochasticity, using a laboratory model that the investigatorshave successfully used in a wide variety of population dynamicsand modeling studies during the last decade. The modelingmethodology is also applicable to field populations and theinvestigators pursue the development of field studies withseveral researchers who have expressed interest in such acollaboration. These collaborators include colleagues at (1) theCenter for Environmental Analysis at California State University,Los Angeles in a project modeling the spatially structureddynamics 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 thedistribution of marine birds and mammals on Protection IslandNational Wildlife Refuge in the Strait of Juan de Fuca, and (4)the Virginia Institute of Marine Science on nonlinear models ofthe blue crab in the Exuma Cays. An understanding of the dynamics of biological populationsis fundamental to the understanding of ecological andenvironmental problems. Mathematical models can be a valuabletool that provides this understanding. They can also provide themeans to predict the future of ecosystems and the species thatthey include. An accurate descriptive and predictive capabilitygained through mathematical models provides not only a basicunderstanding of ecological problems, but also the ability todesign programs for the assessment, management, and control ofecosystems and for the solution of environmental problems. Afundamental difficulty in the application of mathematical modelsto ecological problems has been the lack of a close connection ofmodels with biological data. A key problem is the ability ofmodels to incorporate random effects and disturbances. Theinvestigators extend, analyze, and apply a modeling methodologythey have developed during a decade of experimental studies, in acontrolled laboratory setting, that addresses these difficulties.The methods are not restricted to laboratory populations,however, and the project also includes collaborations with newcolleagues for the purpose of applying the methods to fieldstudies of natural populations.