Aaron A. King, Ph.D.

Nelson G. Hairston Collegiate Professor of Ecology, Evolutionary Biology,
Complex Systems, and Mathematics, University of Michigan
External Professor, Santa Fe Institute
Fellow of the American Association for the Advancement of Science

Lattice effects observed in chaotic dynamics of experimental populations

S. M. Henson, R. F. Costantino, J. M. Cushing, R. A. Desharnais, B. Dennis, and A. A. King
Science 294:  602–605, 2001.

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.

The official version of the paper is here.   Please contact Prof. King if you'd like a reprint.

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