Note to users. If you're seeing this message, it means that your browser cannot find this page's style/presentation instructions -- or possibly that you are using a browser that does not support current Web standards. Find out more about why this message is appearing, and what you can do to make your experience of our site the best it can be.
Lattice Effects Observed in Chaotic Dynamics of Experimental Populations
Shandelle M. Henson,1*R. F. Costantino,2J. M. Cushing,3Robert A. Desharnais,4Brian Dennis,5Aaron A. King6
Animals and many plants are counted in discrete units. The
collection of possible values (state space) of population numbersis
thus a nonnegative integer lattice. Despite this fact, manymathematical population models assume a continuum of system states.The
complex dynamics, such as chaos, often displayed by such
continuous-statemodels have stimulated much ecological research; yet
discrete-statemodels with bounded population size can display only
cyclic behavior.Motivated by data from a population experiment, we
compared thepredictions of discrete-state and continuous-state
populationmodels. Neither the discrete- nor continuous-state models
completelyaccount for the data. Rather, the observed dynamics are
explainedby a stochastic blending of the chaotic dynamics predicted bythe continuous-state model and the cyclic dynamics predicted bythe
discrete-state models. We suggest that such lattice effectscould be an
important component of natural population fluctuations.
1 Department of Mathematics, Andrews
University, Berrien Springs, MI 49104, USA.
2 Department of Biological Sciences, University of
Rhode Island, Kingston, RI 02881, USA.
3 Department
of Mathematics, Interdisciplinary Program in Applied Mathematics,
University of Arizona, Tucson, AZ 85721, USA.
4 Department of Biology and Microbiology, California
State University, Los Angeles, CA 90032, USA.
5 Department of Fish and Wildlife Resources and
Division of Statistics, University of Idaho, Moscow, ID 83844, USA.
6 Department of Environmental Science and Policy,
University of California, Davis, CA 95616, USA.
*
To whom correspondence should be addressed. E-mail:
henson{at}andrews.edu
The editors suggest the following Related Resources on Science sites:
In Science Magazine
TECHNICAL COMMENTS
Gábor Domokos, István Scheuring, Aaron A. King, Robert A. Desharnais, Shandelle M. Henson, R. F. Costantino, J. M. Cushing, and Brian Dennis (27 September 2002) Science297 (5590), 2163a.
[DOI: 10.1126/science.297.5590.2163a] |Full Text »|PDF »
THIS ARTICLE HAS BEEN CITED BY OTHER ARTICLES:
Anatomy of a chaotic attractor: Subtle model-predicted patterns revealed in population data.
A. A. King, R. F. Costantino, J. M. Cushing, S. M. Henson, R. A. Desharnais, and B. Dennis (2004)
PNAS
101, 408-413
|Abstract »|Full Text »|PDF »
Random Perturbations and Lattice Effects in Chaotic Population Dynamics.
G. Domokos, I. Scheuring, A. A. King, R. A. Desharnais, S. M. Henson, R. F. Costantino, J. M. Cushing, and B. Dennis (2002)
Science
297, 2163a-2163
|Full Text »|PDF »
