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An Evolutionary Beverton-Holt Model

  • J. M.  CushingEmail author
Conference paper
  • 956 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 102)

Abstract

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.

Keywords

Traitement Par Population Dynamics Equations Global Asymptotic Stability (GAS) Equilibrium Selection Critical Traits 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

J.M. Cushing was supported by NSF grant DMS 0917435.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematics and The Interdisciplinary Program in Applied MathematicsUniversity of ArizonaTucsonUSA

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