Using Mathematical Models to Investigate Phenotypic Oscillations in Cichlid Fish: A Case of Frequency-dependent Selection

Persistent Link:
http://hdl.handle.net/10150/195981
Title:
Using Mathematical Models to Investigate Phenotypic Oscillations in Cichlid Fish: A Case of Frequency-dependent Selection
Author:
Arpin, Sheree
Issue Date:
2007
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:
Perissodus microlepis is a species of cichlid fish endemic to Lake Tanganyika (Africa). Adult P. microlepis are lepidophages, feeding on the scales of other living fish. As an adaptation for this feeding behavior P. microlepis exhibit lateral asymmetry with respect to jaw morphology: the mouth either opens to the right or left side of the body. Field data illustrate a temporal phenotypic oscillation in the mouth-handedness, and this oscillation is maintained by frequency-dependent selection. To better understand the oscillation, Takahashi and Hori model frequency-dependent selection in P. microlepis using a population genetic model. Their results are intriguing, and the purpose of this dissertation is to improve and extend their model, which fails to account for important biological aspects.We model P. microlepis with a novel approach that fuses the disparate modeling traditions of population genetics and population dynamics; we account for both processes since, in the case of P. microlepis, they occur on the same time scale (a case of microevolution). We construct our models using systems of difference equations. We prove the existence and uniqueness of a positive equilibrium, which corresponds to a 1 : 1 phenotypic ratio. Using a local stability and bifurcation analysis, we show that the equilibrium becomes unstable when frequency-dependent selection is sufficiently strong. We determine necessary and sufficient conditions for onset of oscillation. Local bifurcation analysis indicates key features of the oscillation that may suggest critical experiments.We determine the role of stage structure and the role of strong and weak intraspecific competition. We show that stage-structure is not necessary for, but enhances, oscillatory behavior. Finally we demonstrate the complicated interplay between population dynamic and population genetic processes. Our findings indicate that classical population genetic models can fail to elucidate complex dynamics.
Type:
text; Electronic Dissertation
Keywords:
Population genetics; population dynamics; phenotypic oscillation; Perissodus microlepis; cichlid fish; frequency-dependent selection
Degree Name:
PhD
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Cushing, Jim M.
Committee Chair:
Cushing, Jim M.

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleUsing Mathematical Models to Investigate Phenotypic Oscillations in Cichlid Fish: A Case of Frequency-dependent Selectionen_US
dc.creatorArpin, Shereeen_US
dc.contributor.authorArpin, Shereeen_US
dc.date.issued2007en_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.abstractPerissodus microlepis is a species of cichlid fish endemic to Lake Tanganyika (Africa). Adult P. microlepis are lepidophages, feeding on the scales of other living fish. As an adaptation for this feeding behavior P. microlepis exhibit lateral asymmetry with respect to jaw morphology: the mouth either opens to the right or left side of the body. Field data illustrate a temporal phenotypic oscillation in the mouth-handedness, and this oscillation is maintained by frequency-dependent selection. To better understand the oscillation, Takahashi and Hori model frequency-dependent selection in P. microlepis using a population genetic model. Their results are intriguing, and the purpose of this dissertation is to improve and extend their model, which fails to account for important biological aspects.We model P. microlepis with a novel approach that fuses the disparate modeling traditions of population genetics and population dynamics; we account for both processes since, in the case of P. microlepis, they occur on the same time scale (a case of microevolution). We construct our models using systems of difference equations. We prove the existence and uniqueness of a positive equilibrium, which corresponds to a 1 : 1 phenotypic ratio. Using a local stability and bifurcation analysis, we show that the equilibrium becomes unstable when frequency-dependent selection is sufficiently strong. We determine necessary and sufficient conditions for onset of oscillation. Local bifurcation analysis indicates key features of the oscillation that may suggest critical experiments.We determine the role of stage structure and the role of strong and weak intraspecific competition. We show that stage-structure is not necessary for, but enhances, oscillatory behavior. Finally we demonstrate the complicated interplay between population dynamic and population genetic processes. Our findings indicate that classical population genetic models can fail to elucidate complex dynamics.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectPopulation geneticsen_US
dc.subjectpopulation dynamicsen_US
dc.subjectphenotypic oscillationen_US
dc.subjectPerissodus microlepisen_US
dc.subjectcichlid fishen_US
dc.subjectfrequency-dependent selectionen_US
thesis.degree.namePhDen_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.chairCushing, Jim M.en_US
dc.contributor.committeememberGoriely, Alain I.en_US
dc.contributor.committeememberWatkins, Joseph C.en_US
dc.identifier.proquest2428en_US
dc.identifier.oclc659748341en_US
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