An Evolutionary Beverton-Holt Model

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

1 Citation (Scopus)

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.

Original languageEnglish (US)
Title of host publicationSpringer Proceedings in Mathematics and Statistics
PublisherSpringer New York LLC
Pages127-141
Number of pages15
Volume102
ISBN (Print)9783662441398
DOIs
StatePublished - 2014
Event19th International Conference on Difference Equations and Applications, ICDEA 2013 - Muscat, Oman
Duration: May 26 2013May 30 2013

Other

Other19th International Conference on Difference Equations and Applications, ICDEA 2013
CountryOman
CityMuscat
Period5/26/135/30/13

Fingerprint

Population Dynamics
Difference equation
Natural Selection
Globally Asymptotically Stable
Coefficient
Nonautonomous Equation
Logistic Equation
Equilibrium Solution
Dynamic Equation
Model
Periodic Solution
Initial conditions
Modeling

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Cushing, J. M. (2014). An Evolutionary Beverton-Holt Model. In Springer Proceedings in Mathematics and Statistics (Vol. 102, pp. 127-141). Springer New York LLC. https://doi.org/10.1007/978-3-662-44140-4_7

An Evolutionary Beverton-Holt Model. / Cushing, Jim M.

Springer Proceedings in Mathematics and Statistics. Vol. 102 Springer New York LLC, 2014. p. 127-141.

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

Cushing, JM 2014, An Evolutionary Beverton-Holt Model. in Springer Proceedings in Mathematics and Statistics. vol. 102, Springer New York LLC, pp. 127-141, 19th International Conference on Difference Equations and Applications, ICDEA 2013, Muscat, Oman, 5/26/13. https://doi.org/10.1007/978-3-662-44140-4_7
Cushing JM. An Evolutionary Beverton-Holt Model. In Springer Proceedings in Mathematics and Statistics. Vol. 102. Springer New York LLC. 2014. p. 127-141 https://doi.org/10.1007/978-3-662-44140-4_7
Cushing, Jim M. / An Evolutionary Beverton-Holt Model. Springer Proceedings in Mathematics and Statistics. Vol. 102 Springer New York LLC, 2014. pp. 127-141
@inproceedings{0b599e64c24a4de29e68c32a3414de67,
title = "An Evolutionary Beverton-Holt Model",
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.",
author = "Cushing, {Jim M}",
year = "2014",
doi = "10.1007/978-3-662-44140-4_7",
language = "English (US)",
isbn = "9783662441398",
volume = "102",
pages = "127--141",
booktitle = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York LLC",

}

TY - GEN

T1 - An Evolutionary Beverton-Holt Model

AU - Cushing, Jim M

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.

UR - http://www.scopus.com/inward/record.url?scp=84906841959&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906841959&partnerID=8YFLogxK

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

VL - 102

SP - 127

EP - 141

BT - Springer Proceedings in Mathematics and Statistics

PB - Springer New York LLC

ER -