Nonlinear Population Dynamics

I am currently working on a interdisciplinary research project that integrates mathematical, statistical, and experimental methods for the investigation of nonlinear population dynamics. This research is being conducted in collaboration with four other scientists:

• Dr. Robert F. Costantino, a population biologist at the University of Arizona, Tucson
• Dr. Jim Cushing, a mathematician at the University or Arizona, Tucson
• Dr. Brian Dennis, a statistician at the University of Idaho, Moscow
• Dr. Shandelle Henson, a mathematician at Andrews University, Berrien Springs, MI

and my graduate student, Mr. Warren Cheung. Our goal is to provide experimental tests of dynamic behaviors such as periodic cycles, aperiodic orbits, multiple attractors, unstable equilibria with stable and unstable manifolds, chaos, and strange attractors. Laboratory populations of flour beetles of the genus Tribolium are serving as an animal model. For example, we reported an experiment that provides the first convincing example of chaos in ecology (Costantino et al. 1997, Science 275: 389-391 [reprint-pdf-346KB]). Check out our Nonlinear Population Dynamics web pages for more information about this research program.

Spatially-Mediated Dynamics in Benthic Communities

I am working with Dr. Carlos Robles, a marine ecologist at Cal State LA, my postdoctoral fellow, Dr. Doug Donalson, and my two graduate students, Ms. Patricia Arriola and Ms. Jennifer Geluso, on a project that investigates the dynamics of size-specific predation of mussels by sea stars and spiny lobsters in rocky intertidal communities. Our working hypothesis is that spatial neighborhood effects in both recruitment and predation play an important role in these dynamics and that the relative strengths of these neighborhood effects vary over environmental gradients of wave energy and tidal exposure.

The research strategy is to integrate empirical data into a variety of models of the intertidal zone including stochastic cellular automata, mean field ordinary differential equations, and agent-based models. Rates of prey recruitment, growth, and mortality are varied along environmental gradients of tidal height and wave exposure. These rates are also affected by local interactions among prey. The functional forms used to determine the transition rates come from the empirical data. Simulations of the model generate size frequency distributions over space that can be compared to real patterns from field observations. An description of our research approach can be found in a contribution to a Special Feature on "Paradigms in Ecology" (Robles and Desharnais 2002, Ecology 83: 1521-1536 [reprint-pdf-442KB]). Check out our web site on Modelling Spatially-Structured Dynamics for Benthic Predation for more details.