Date Thesis Awarded

5-2011

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Sarah Day

Committee Member

Leah B. Shaw

Committee Member

Junping Shi

Committee Member

Robert Michael Lewis

Abstract

Ecologists use Ricker patch models to study meta-population dynamics for populations undergoing growth and dispersal in a patchy environment. This project uses a modified model in which patch-wise extinction thresholds are used to model local extinction events. Computational homology is used to measure shifts in spatial patterns as extinction occurs and to quantify the ways in which dispersal rates affect pattern formation and degradation. Numerical simulations for certain parameters exhibit a decoupling of the system into small regions with periodic dynamics prior to extinction. Lastly, the existence of certain stable periodic orbits which affect population robustness are rigorously proven to exist.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

Comments

Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.

Share

COinS