Summer Workshop:
Discrete Dynamical Systems & Their Applications to Population Dynamics

Adult flour beetle


Nonlinear population theory remains controversial twenty years after its modern revival, primarily, because experimental evidence for dynamic behaviors such as periodic cycles, aperiodic orbits, multiple attractors, unstable equilibria with stable and unstable manifolds, chaos, and strange attractors is meager. There is a need for new experiments. Our interdisciplinary research program is intended to help fill that need.

Our research program covers a spectrum of activities essential to testing nonlinear population theory: from the translation of the 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. The statistical analyses, mathematics, and biology are thoroughly integrated.

Laboratory populations of flour beetles of the genus Tribolium are serving as an animal model. Laboratory populations maintained under constant environmental conditions usually exhibit dramatic fluctuations in density and age-structure. These fluctuations are the result of strong behavioral and physiological interactions among the life stages--the most important being cannibalism. We are using a simple three-life-stage model, which we call the LPA model, to capture the main features of these dynamics. This model allows us to make predictions and guides us in the design of new experiments.

This work was supported in part by grants DMS-9306271, DMS-9319073, DMS-9625576, DMS-9616205, DMS-9981374, DMS-9973126, DMS-9981458, and DMS-9981423 from the U.S. National Science Foundation. All opinions expressed are those of the authors and not necessarily those of the NSF.

Copyright © 1997-2002, Robert A Desharnais
Department of Biological Sciences
California State University, Los Angeles, CA, 90032-8201