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Aaron King

       Aaron A. King, Ph.D.

      Assistant Professor of Ecology & Evolutionary Biology and Mathematics
      University of Michigan
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UM Library 		Lattice Effects Observed in Chaotic Dynamics of Experimental Populations

Lattice Effects Observed in Chaotic Dynamics of Experimental Populations

S. M. Henson, R. F. Costantino, J. M. Cushing, Robert A. Desharnais, Brian Dennis, and A. A. King

Science 294:602-605, 2001.

Abstract

Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often displayed by such continuous-state models have stimulated much ecological research; yet discrete-state models with bounded population size can display only cyclic behavior. Motivated by data from a population experiment, we compared the predictions of discrete-state and continuous-state population models. Neither the discrete- nor continuous-state models completely account for the data. Rather, the observed dynamics are explained by a stochastic blending of the chaotic dynamics predicted by the continuous-state model and the cyclic dynamics predicted by the discrete- state models. We suggest that such lattice effects could be an important component of natural population fluctuations.

For reprints of this paper, send a request to me at aaron.king@umich.edu, or to the lead author, Shandelle Henson. An electronic reprint (PDF) is also available.