Some discrete competition models and the competitive exclusion principle

Jim M Cushing, Sheree Levarge, Nakul Chitnis, Shandelle M. Henson

Research output: Contribution to journalArticle

121 Citations (Scopus)

Abstract

A difference equation model, called that Leslie/Gower model, played a key historical role in laboratory experiments that helped establish the "competitive exclusion principle" in ecology. We show that this model has the same dynamic scenarios as the famous Lotka/Volterra (differential equation) competition model. It is less well known that some anomalous results from the experiments seem to contradict the exclusion principle and Lotka/Volterra dynamics. We give an example of a competition model that has non-Lotka/Volterra dynamics that are consistent with the anomalous case.

Original languageEnglish (US)
Pages (from-to)1139-1151
Number of pages13
JournalJournal of Difference Equations and Applications
Volume10
Issue number13-15
DOIs
StatePublished - Nov 2004

Fingerprint

Competitive Exclusion
Competition Model
Discrete Model
Anomalous
Leslie model
Lotka-Volterra Equations
Lotka-Volterra
Volterra
Ecology
Difference equation
Experiment
Differential equation
Difference equations
Scenarios
Differential equations
Model
Experiments

Keywords

  • Competition models
  • Competitive exclusion principle
  • Difference equations
  • Global stability
  • Leslie/Gower model
  • Lotka/Volterra dynamics

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Applied Mathematics

Cite this

Some discrete competition models and the competitive exclusion principle. / Cushing, Jim M; Levarge, Sheree; Chitnis, Nakul; Henson, Shandelle M.

In: Journal of Difference Equations and Applications, Vol. 10, No. 13-15, 11.2004, p. 1139-1151.

Research output: Contribution to journalArticle

Cushing, Jim M ; Levarge, Sheree ; Chitnis, Nakul ; Henson, Shandelle M. / Some discrete competition models and the competitive exclusion principle. In: Journal of Difference Equations and Applications. 2004 ; Vol. 10, No. 13-15. pp. 1139-1151.
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