Abstract

For nearly a decade the authors have been collaborating on interdisciplinary projects in which modeling principles are applied to the investigation of nonlinear phenomena in population biology. A fundamental goal of the research is to demonstrate that a mathematical model can be a valuable tool in explaining and predicting the dynamics of a biological population and to do so under carefully controlled (and replicated) experimental conditions. Another goal is to document the occurrence of specific, model predicted nonlinear phenomena such as chaos, bifurcation sequences, stable and unstable manifolds, resonances and so on. We are interested in showing how a mathematical model can provide previously unavailable explanations for patterns, even for unexpectedly subtle patterns, in a population's dynamics. To carry out these projects we utilize laboratory cultures of flour beetles (sp. Tribolium). This paper provides an overview of our research program.