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
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.
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.
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.