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A three-species model with predator-prey, competition, and mutualistic interactions

by Liu, Minqi

Abstract

This research is inspired by Brown, Bruder and Kummel’s research project on the predator-prey interaction of aphids and ladybugs on yucca plants. An important feature of this study system is that it contains ants as a third species. Therefore, this ecological system is composed of a predator-prey relationship between the ladybugs and aphids, a competitive relationship between the ladybugs and ants, and a mutualistic relationship between the aphids and ants. Most existing mathematical models study one type of interaction or they focus on three species and study a tri-trophic food chain. We develop and analyze a new mathematical model that includes the predator-prey interaction as well as the competitive and mutualistic aspects of the system. The predator-prey interaction is described by a Rosenzweig-MacArthur model, which assumes logistic growth of the predator. To build a mathematical model for the competitive and mutualistic relationships, we use a modified Lotka-Volterra model and include terms representing competition and mutualism. Since the three-species model is substantially harder to analyze, we first study the three submodels, i.e. the predator-prey, competition, and mutualism model. Then we use the submodel results to explore the three-species model and the significance of its parameter values. With the help of Mathematica and MATLAB, we construct phase planes and time series plots, find the equilibria of the systems, and determine the stability of each equilibrium.

Note

The author has given permission for this work to be deposited in the Digital Archive of Colorado College.

Colorado College Honor Code upheld.

Includes bibliographical references.

Administrative Notes

The author has given permission for this work to be deposited in the Digital Archive of Colorado College.

Colorado College Honor Code upheld.

Copyright
Copyright restrictions apply.
Publisher
Colorado College
PID
coccc:11128
Digital Origin
born digital
Extent
30 pages : illustrations
Thesis
Senior Thesis -- Colorado College
Thesis Advisor
Bruder, Andrea
Department/Program
Math and Computer Science
Degree Name
Bachelor of Arts
Degree Type
bachelor
Degree Grantor
Colorado College
Date Issued
2015-05