Submission Date

4-27-2015

Document Type

Paper

Department

Mathematics

Adviser

Mohammed Yahdi

Committee Member

Nicholas Scoville

Committee Member

Cory Straub

Committee Member

Mohammed Yahdi

Department Chair

April Kontostathis

External Reviewer

Luis Melara

Distinguished Honors

This paper has met the requirements for Distinguished Honors

Project Description

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided by Dr. Cory Straub of Ursinus College. Alfalfa is Pennsylvania's second-most important crop and the most cultivated forage legume in the world. Predator and plant diversity can control potato leafhopper (PLH) damage to the host-plant alfalfa. The pest damage is costly and chemical pesticides are unsafe. Ultimately, the framework provides polyculture planting strategies for farmers that are cost-effective and environmentally-safe to minimize the alfalfa damage while maximizing farmer profits.

After the validation and sensitivity analysis of the model, the project focused on designing control strategies. Steady state solutions were determined and a sensitivity analysis established the relative importance of each parameter to reduce the plant damage. Optimal control theory led to designing practical strategies regarding diversity levels to minimize the plant damage while preserving plant nutritional efficacy and minimizing production costs. More specifically, Bang-Bang controls were investigated using switching functions to produce practical discontinuous functionals for the control parameters. Tools used include non-linear systems of differential equations, Hamiltonians, adjoints, Pontryagin's Maximum Principle, and computer simulations.

Comments

Funding from Ursinus College Summer Fellows and the Howard Hughes Medical Institute (HHMI) funded Center for Science and the Common Good (CSCG) and FUTURE programs.