Mathematics, Department of


First Advisor

Richard Rebarber

Second Advisor

Brigitte Tenhumberg

Date of this Version



A dissertation presented to the faculty of the Graduate College at the University of Nebraska in partial fulfilment of requirements for the degree of Doctor of Philosophy

Major: Mathematics

Under the supervision of Professors Richard Rebarber and Brigitte Tenhumberg

Lincoln, Nebraska, December 2023


Copyright 2023, Molly R. Creagar


Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along with ideas from game theory, to examine how defense strategies and maintenance costs influence population outcomes in herbaceous plants. When herbivory is modeled as isotropic across space with defense modeled directly as a public good, our model predicts an evolutionarily stable proportion of cooperators and defectors (mixed stable strategy), but the proportion of cooperators is higher in a population of perennial plants than in a population of annual plants. We also show that including a metabolic cost of maintaining stored resources does not change the proportion of cooperators but does decrease plant fitness and allocation to overwinter storage. Then, we compare the outcomes when we incorporate an individual-based model for the herbivore population and allow the herbivores to move between plants. In this case, defense is only a neighborhood benefit, and this approach yields the possibility of a population evolving to consist of only cooperators or only defectors (pure stable strategy), as well as the possibility of a mixed stable strategy. We show that our model offers a theoretical explanation for the neighborhood effect seen in empirical evidence.

Advisors: Richard Rebarber and Brigitte Tenhumberg