Nonlinear Demographic Dynamics: Mathematical Models, Statistical Methods, and Biological Experiments

Authors

Brian Dennis
Robert A. Desharnais
J. M. Cushing
R. F. Costantino, University of Rhode Island

Document Type

Article

Date of Original Version

1995

Department

Zoology

Abstract

Our approach to testing nonlinear population theory is to connect rigorously mathematical models with data by means of statistical methods for nonlinear time series. We begin by deriving a biologically based demographic model. The mathematical analysis identifies boundaries in parameter space where stable equilibria bifurcate to periodic 2—cycles and aperiodic motion on invariant loops. The statistical analysis, based on a stochastic version of the demographic model, provides procedures for parameter estimation, hypothesis testing, and model evaluation. Experiments using the flour beetle Tribolium yield the time series data. A three—dimensional map of larval, pupal, and adult numbers forecasts four possible population behaviors: extinction, equilibria, periodicities, and aperiodic motion including chaos. This study documents the nonlinear prediction of periodic 2—cycles in laboratory cultures of Tribolium and represents a new interdisciplinary approach to understanding nonlinear ecological dynamics.

Citation/Publisher Attribution

Dennis, B. , Desharnais, R. A., Cushing, J. M. and Costantino, R. F. (1995), Nonlinear Demographic Dynamics: Mathematical Models, Statistical Methods, and Biological Experiments. Ecological Monographs, 65: 261-282. doi:10.2307/2937060 Available at: https://doi.org/10.2307/2937060