Aaron A. King, Ph.D.
Assistant Professor of Ecology & Evolutionary Biology and MathematicsUniversity of Michigan
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A Chaotic Attractor in Ecology: Theory and Experimental Data
Brian Dennis, R. F. Costantino, and Aaron King.
Chaos, Solitons, & Fractals, 12: 219-34, 2001.
Abstract
Chaos has now been documented in a laboratory population. In controlled laboratory experiments, cultures of flour beetles (Tribolium castaneum) undergo bifurcations in their dynamics as demographic parameters are manipulated. These bifurcations,
including a specific route
to chaos, are predicted by a well-validated deterministic model
called the "LPA model". The LPA model is based on the nonlinear
interactions among the life cycle stages of the beetle (larva,
pupa, and adult). A stochastic version of the model accounts for
the deviations of data from the deterministic model and provides
the means for parameterization and rigorous statistical validation.
The chaotic attractor of the deterministic LPA model and the
stationary distribution of the stochastic LPA model describe the
experimental data in phase space with striking accuracy. In
addition, model-predicted temporal patterns on the attractor are
observed in the data. This paper gives a brief account of the
interdisciplinary effort that obtained these results. For reprints of this paper, contact me at aaron.king@umich.edu. An electronic reprint (PDF) is also available.