An Analysis of the Evolutionary Dynamic Version of the Dennis Model for Allee Effects

Persistent Link:
http://hdl.handle.net/10150/297551
Title:
An Analysis of the Evolutionary Dynamic Version of the Dennis Model for Allee Effects
Author:
Djordjevic, Luka
Issue Date:
2013
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This paper studies evolutionary dynamics of a species in the presence of the biological phenomenon known as the strong Allee effect. This phenomenon can be modeled in a multitude of ways but we choose to use the dynamic model developed by Dennis [1989]. We consider an evolutionary game theoretic version of Dennis’ model. This model introduces a dynamical system for population density n and a mean phenotypic trait u. The system depends on several parameters, namely the inherent growth rate r = r (u), the inherent carrying capacity k = k (u), the loss from not mating λ = λ (u), and the population density at which there is a 50% chance of mating which is denoted θ = θ (u). In this paper we obtain sufficient conditions for the stability of the equilibrium points of our evolutionary model, drawing biological punchlines as needed. The results of this paper are summarized in a general theorem. In addition, we provide a specific example to illustrate the application these results as we consider specific functions for the Allee parameters of r, k, λ, and θ.
Type:
text; Electronic Thesis
Degree Name:
B.S.
Degree Level:
bachelors
Degree Program:
Honors College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Cushing, Jim

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleAn Analysis of the Evolutionary Dynamic Version of the Dennis Model for Allee Effectsen_US
dc.creatorDjordjevic, Lukaen_US
dc.contributor.authorDjordjevic, Lukaen_US
dc.date.issued2013-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThis paper studies evolutionary dynamics of a species in the presence of the biological phenomenon known as the strong Allee effect. This phenomenon can be modeled in a multitude of ways but we choose to use the dynamic model developed by Dennis [1989]. We consider an evolutionary game theoretic version of Dennis’ model. This model introduces a dynamical system for population density n and a mean phenotypic trait u. The system depends on several parameters, namely the inherent growth rate r = r (u), the inherent carrying capacity k = k (u), the loss from not mating λ = λ (u), and the population density at which there is a 50% chance of mating which is denoted θ = θ (u). In this paper we obtain sufficient conditions for the stability of the equilibrium points of our evolutionary model, drawing biological punchlines as needed. The results of this paper are summarized in a general theorem. In addition, we provide a specific example to illustrate the application these results as we consider specific functions for the Allee parameters of r, k, λ, and θ.en_US
dc.typetexten_US
dc.typeElectronic Thesisen_US
thesis.degree.nameB.S.en_US
thesis.degree.levelbachelorsen_US
thesis.degree.disciplineHonors Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorCushing, Jim-
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