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Nonlinear Demographic Dynamics: Mathematical Models, Statistical Methods, and Biological Experiments
Author(s) -
Dennis Brian,
Desharnais Robert A.,
Cushing J. M.,
Costantino R. F.
Publication year - 1995
Publication title -
ecological monographs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.254
H-Index - 156
eISSN - 1557-7015
pISSN - 0012-9615
DOI - 10.2307/2937060
Subject(s) - aperiodic graph , nonlinear system , population , mathematics , mathematical model , statistical physics , computer science , statistics , econometrics , ecology , biology , physics , quantum mechanics , demography , combinatorics , sociology
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.