Mathematics, Department of


First Advisor

Richard Rebarber

Second Advisor

Brigitte Tenhumberg

Date of this Version

Fall 12-4-2019


A DISSERTATION Presented to the Faculty of The Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor Richard Rebarber and Professor Brigitte Tenhumberg. Lincoln, Nebraska: December, 2019

Copyright 2019 William B. Jamieson


Insecticides play a critical role in agricultural productivity. However, insecticides impose selective pressures on insect populations, so the Darwinian principles of natural selection predict that resistance to the insecticide is likely to form in the insect populations. Insecticide resistance, in turn, severely reduces the utility of the insecticides being used. Thus there is a strong economic incentive to reduce the rate of resistance evolution. Moreover, resistance evolution represents an example of evolution under novel selective pressures, so its study contributes to the fundamental understanding of evolutionary theory.

Insecticide resistance often represents a complex interplay of multiple fitness trade-offs for individual insects. Resistant individuals tend to suffer significant decreases in fitness when no insecticide is present, resulting in non-resistant individuals having the tendency to outcompete resistant ones in areas with no insecticide. In the use of standard modeling practices, difficulties arise when trying to incorporate these complexities in a fashion which facilitates the simulation of the model and analyzing the results. Individual based models (IBMs) are one approach to overcoming these difficulties by leveraging modern computational techniques and modern computer power. In an IBM each member of the population is simulated to follow a set of stochastic rules, which includes rules about the behaviors and interactions of individuals. We propose to apply an IBM approach to modeling the evolution of insecticide resistance in an insect species population.

The fall armyworm is an economically damaging pest which has recently become invasive in Africa, India, and China. A common type of insecticide used control fall armyworms is Bacillus thuringiensis (Bt). We hypothesize that individuals that are resistant to Bt grow at slower rates than their counterparts. This creates a strong fitness disadvantage when Bt is not present because the fall armyworms are cannibalistic, where smaller individuals have a large disadvantage. Thus we use our IBM to explore the nature of the fitness trade-offs between resistance and growth rate in order to understand how it could be exploited to lessen the rate of resistance evolution in the species.

Adviser: Richard Rebarber and Brigitte Tenhumberg