Nonlinear demographic dynamics: Mathematical models, statistical methods, and biological experiments

Brian Dennis, Robert A. Desharnais, Jim M Cushing, Robert F Costantino

Research output: Contribution to journalArticle

180 Citations (Scopus)

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 identities 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 Hour 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.

Original languageEnglish (US)
Pages (from-to)261-281
Number of pages21
JournalEcological Monographs
Volume65
Issue number3
StatePublished - 1995

Fingerprint

dynamic models
Tribolium (Coleoptera)
mathematical models
statistical analysis
demographic statistics
time series analysis
population theory
experiment
time series
periodicity
mathematical analysis
interdisciplinary approach
hypothesis testing
chaotic dynamics
extinction
testing
Coleoptera
beetle
prediction
method

Keywords

  • Bifurcation analysis
  • Chaos
  • Cycles
  • Equilibrium
  • Hypothesis testing evaluation
  • Nonlinear demographic dynamics
  • Parameter estimation
  • Stability
  • Tribolium

ASJC Scopus subject areas

  • Ecology

Cite this

Nonlinear demographic dynamics : Mathematical models, statistical methods, and biological experiments. / Dennis, Brian; Desharnais, Robert A.; Cushing, Jim M; Costantino, Robert F.

In: Ecological Monographs, Vol. 65, No. 3, 1995, p. 261-281.

Research output: Contribution to journalArticle

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