Title page for ETD etd-08142006-154319


Type of Document Dissertation
Author Vance, James Aaron
URN etd-08142006-154319
Title Permanent Coexistence for Omnivory Models
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Russell, David L. Committee Chair
Klaus, Martin Committee Co-Chair
Berkson, James M. Committee Member
Kelly, Marcella J. Committee Member
Laubenbacher, Reinhard C. Committee Member
Sun, Shu-Ming Committee Member
Keywords
  • permanent coexistence
  • permanence
  • omnivory
  • intraguild predation
  • sensitivity analysis
Date of Defense 2006-08-10
Availability unrestricted
Abstract
One of the basic questions of concern in mathematical biology is the long-term survival of each species in a set of populations. This question is particularly puzzling for a natural system with omnivory due to the fact that simple mathematical models of omnivory are prone to species extinction. Omnivory is defined as the consumption of resources from more than one trophic level. In this work, we investigate three omnivory models of increasing complexity. We use the notion of permanent coexistence, or permanence, to study the long-term survival of three interacting species governed by a mixture of competition and predation. We show the permanence of our models under certain parameter restrictions and include the biological interpretations of these parameter restrictions. Sensitivity analysis is used to obtain important information about meaningful parameter data collection. Examples are also given that demonstrate the ubiquity of omnivory in natural systems.
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