An Evolutionary Beverton-Holt Model

J. M. Cushing

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


The classic Beverton-Holt (discrete logistic) difference equation, which arises in population dynamics, has a globally asymptotically stable equilibrium (for positive initial conditions) if its coefficients are constants. If the coefficients change in time, then the equation becomes nonautonomous and the asymptotic dynamics might not be as simple. One reason the coefficients can change in time is their evolution by natural selection. If the model coefficients are functions of a heritable phenotypic trait subject to natural selection then, by standard methods for modeling evolution, the model becomes a planar system of coupled difference equations, consisting of a Beverton-Holt type equation for the population dynamics and a difference equation for the dynamics of the mean phenotypic trait. We consider a case when the trait equation uncouples from the population dynamic equation and obtain criteria under which the evolutionary system has globally asymptotically stable equilibria or periodic solutions.

Original languageEnglish (US)
Title of host publicationTheory and Applications of Difference Equations and Discrete Dynamical Systems, ICDEA 2013
PublisherSpringer New York LLC
Number of pages15
ISBN (Print)9783662441398
StatePublished - 2014
Event19th International Conference on Difference Equations and Applications, ICDEA 2013 - Muscat, Oman
Duration: May 26 2013May 30 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


Other19th International Conference on Difference Equations and Applications, ICDEA 2013

ASJC Scopus subject areas

  • Mathematics(all)


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