Competitive dynamics in size-structured populations with reproductive delays

Persistent Link:
http://hdl.handle.net/10150/282668
Title:
Competitive dynamics in size-structured populations with reproductive delays
Author:
Garcia-Alvarado, Martin Gildardo, 1962-
Issue Date:
1998
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:
In this work we study the dynamics of populations whose individuals are divided into two size categories (juveniles and adults) and are competing through the exploitation of a single nutrient resource. First we study the case of a single species population. The modeling approach we use results in a partial integro-differential system for the population density and the nutrient level. In view of the lack of techniques to obtain an explicit solution, we derive a system of time varying delay differential equations for the resource level and certain population density related functionals. We study the existence and stability of steady state solutions in terms of the inherent net reproductive number and conclude that if individuals are capable of, at least, replacing themselves (by reproduction) the population equilibrates at a positive level; otherwise, the population suffers extinction. Numerical simulations seem to indicate that it is not possible to destabilize positive equilibrium solutions. The case of several species interaction is treated from the resident/invader point of view. The first observation is that it is not possible for two or more species to coexist in equilibrium. A species that can successfully exist alone at a certain resource level is called the resident species. If another species, the invader, with inherent net reproductive number less than one enters the competition, then the invader goes extinct. Otherwise the resident extincts and the invader survives at equilibrium.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Cushing, James M.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleCompetitive dynamics in size-structured populations with reproductive delaysen_US
dc.creatorGarcia-Alvarado, Martin Gildardo, 1962-en_US
dc.contributor.authorGarcia-Alvarado, Martin Gildardo, 1962-en_US
dc.date.issued1998en_US
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.abstractIn this work we study the dynamics of populations whose individuals are divided into two size categories (juveniles and adults) and are competing through the exploitation of a single nutrient resource. First we study the case of a single species population. The modeling approach we use results in a partial integro-differential system for the population density and the nutrient level. In view of the lack of techniques to obtain an explicit solution, we derive a system of time varying delay differential equations for the resource level and certain population density related functionals. We study the existence and stability of steady state solutions in terms of the inherent net reproductive number and conclude that if individuals are capable of, at least, replacing themselves (by reproduction) the population equilibrates at a positive level; otherwise, the population suffers extinction. Numerical simulations seem to indicate that it is not possible to destabilize positive equilibrium solutions. The case of several species interaction is treated from the resident/invader point of view. The first observation is that it is not possible for two or more species to coexist in equilibrium. A species that can successfully exist alone at a certain resource level is called the resident species. If another species, the invader, with inherent net reproductive number less than one enters the competition, then the invader goes extinct. Otherwise the resident extincts and the invader survives at equilibrium.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorCushing, James M.en_US
dc.identifier.proquest9831842en_US
dc.identifier.bibrecord.b3864678xen_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.