Permanent Coexistence for Omnivory Models

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2006

Author dc:creator

• Vance, James Aaron

Chairs dc:contributor.committeechair

• Russell, David L.
• Klaus, Martin

Committee members dc:contributor.committeemember

• Laubenbacher, Reinhard C.
• Sun, Shu-Ming
• Kelly, Marcella J.
• Berkson, James M.

• permanent coexistence
• permanence
• omnivory
• intraguild predation
• sensitivity analysis

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-08142006-154319

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28660