Persistent Link:
http://hdl.handle.net/10150/185477
Title:
A discrete size-structured competition model.
Author:
Crowe, Kathleen Marie.
Issue Date:
1991
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:
Matrix difference equations have been used to model the discrete time dynamics of a variety of populations whose individual members have been categorized into a finite number of classes based on, for example, age, size, or stage. Examples of such models include Leslie's age-structured model and the Usher model, a size-classified model which has been applied to trees, corals, sea turtles, copepods, and fish. These matrix difference equations can incorporate virtually any type of nonlinearity arising from the density dependence of fertility and survival rates and transition probabilities between classes. Under a fairly general set of assumptions, it can be shown that the normalized class distribution vector equilibrates, and thus an asymptotic or limiting equation for total population size can be derived. In this research we assume the existence of a dynamically modeled resource in limited supply for which the members of the species compete, either exploitatively or through interference. The existence and stability of population size equlibria or cycles is then studied by means of bifurcation theory. Several biological considerations are addressed, including the Size-Efficiency Hypothesis of Brooks and Dodson, the effects of changes in individual physiological parameters on the size and competitive success of a species, and the effects of delays on the viability of a species.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic; Animal populations; Ecology -- Mathematical models.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Cushing, Jim M.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleA discrete size-structured competition model.en_US
dc.creatorCrowe, Kathleen Marie.en_US
dc.contributor.authorCrowe, Kathleen Marie.en_US
dc.date.issued1991en_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.abstractMatrix difference equations have been used to model the discrete time dynamics of a variety of populations whose individual members have been categorized into a finite number of classes based on, for example, age, size, or stage. Examples of such models include Leslie's age-structured model and the Usher model, a size-classified model which has been applied to trees, corals, sea turtles, copepods, and fish. These matrix difference equations can incorporate virtually any type of nonlinearity arising from the density dependence of fertility and survival rates and transition probabilities between classes. Under a fairly general set of assumptions, it can be shown that the normalized class distribution vector equilibrates, and thus an asymptotic or limiting equation for total population size can be derived. In this research we assume the existence of a dynamically modeled resource in limited supply for which the members of the species compete, either exploitatively or through interference. The existence and stability of population size equlibria or cycles is then studied by means of bifurcation theory. Several biological considerations are addressed, including the Size-Efficiency Hypothesis of Brooks and Dodson, the effects of changes in individual physiological parameters on the size and competitive success of a species, and the effects of delays on the viability of a species.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academicen_US
dc.subjectAnimal populationsen_US
dc.subjectEcology -- Mathematical models.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorCushing, Jim M.en_US
dc.contributor.committeememberScott, Alwyn C.en_US
dc.contributor.committeememberSecomb, Timothy W.en_US
dc.contributor.committeememberLomen, David O.en_US
dc.identifier.proquest9125455en_US
dc.identifier.oclc710469249en_US
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