TY - GEN

T1 - An Evolutionary Beverton-Holt Model

AU - Cushing, J. M.

N1 - Funding Information:
J.M. Cushing was supported by NSF grant DMS 0917435.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-662-44140-4_7

DO - 10.1007/978-3-662-44140-4_7

M3 - Conference contribution

AN - SCOPUS:84906841959

SN - 9783662441398

T3 - Springer Proceedings in Mathematics and Statistics

SP - 127

EP - 141

BT - Theory and Applications of Difference Equations and Discrete Dynamical Systems, ICDEA 2013

PB - Springer New York LLC

T2 - 19th International Conference on Difference Equations and Applications, ICDEA 2013

Y2 - 26 May 2013 through 30 May 2013

ER -