Graduate Studies

 

Date of Award

Spring 2024

Document Type

Dissertation

Department

Mathematics

First Advisor

Richard Rebarber

Second Advisor

Brigitte Tenhumberg

Abstract

Herbivory is often believed to always negatively affect the growth of plants, but there are plant species that can actually benefit from being consumed by herbivores. These plants have a phenotypic trait known as “compensatory growth.” A plant that exhibits compensatory growth is able to increase its intrinsic growth rate as a response to taking damage caused by herbivory, and as a result, produce more biomass. Very few mathematical models used to describe plant-herbivore interactions have accounted for plant compensatory growth. Moreover, these models tend to assume that herbivores follow a Holling type II functional response, which may not necessarily be prevalent in all plant-herbivore interactions. In Chapter 1 of this dissertation, we will present a system of nonlinear ordinary differential equations that can be used to model the interactions between a compensating plant and an herbivore that exhibits a Holling type III functional response. The model is analyzed in Chapters 2-4, and the analysis consists of determining the conditions for the existence and stability of positive steady-states where compensating plants and herbivores coexist. There are three cases that are analyzed. Chapter 2 discusses equilibrium conditions in the absence of compensatory growth in a plant. Chapter 3 discusses the possible interactions where the intrinsic growth rate of a plant is increased by the largest possible scaling term. Chapter 4 discusses the possible interactions where the intrinsic growth rate of a plant is not necessarily increased by the largest possible scaling term. We also address the changes in the stability that can occur at different intensities of plant compensatory growth when all other biological parameters remain fixed.

Comments

Copyright 2024, Lawrence Gustavo Seminario-Romero. Used by permission

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