Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article

Degree

Master of Science

Program

Mathematics

Supervisor

Zou, Xingfu

2nd Supervisor

Wang, Xiaoying

Affiliation

Trent University/University of Western Ontario

Co-Supervisor

Abstract

In the biological world, many interactions exist between various species. These interactions generally consist of predator-prey relationships, competition between species and beneficial relationships. One observed phenomenon, termed the fear effect, occurs when one species reacts to an increased risk of predation by another species. The fear response causes the affected species to reproduce and forage for food less. In some cases, the fear response can be beneficial, while in other times it can be harmful. In this thesis, we consider a four compartment food-chain model in which there exists a top-level predator, a mesopredator and two types of prey who directly compete with one another. The model accounts for each lesser species’ fear response to the next highest one. We aim to examine how competition and the fear effect can work together to adjust the structure of the food chain. We used some standard techniques of dynamical systems to glean some results about the long-term dynamics of the system. We found that the fear response and competition effects can play an important part in the long-term dynamics of the system and cause a restructuring in the food chain itself.

Summary for Lay Audience

When we consider species in the natural world, one topic that may be of interest is how species and animals interact with each other and their environment. There are three basic interaction types termed predation, competition and mutualism. Predation occurs when a member of one species eats a member of another species. Competition occurs when individual entities fight among the same species, or other species for some sort basic needs which are required for sustenance. Competition can have a negative effect. Mutualism occurs when one species interacting with another has a beneficial or helpful effect. This usually culminates when both species are coexisting peacefully, and their interactions are mutually beneficial. An interesting biological result shows that the threat of predation can have an indirect effect on prey. This phenomenon is known as the fear effect. Put simply, when a species is being eaten more by a predator, or when a species perceives an increased likelihood of being eaten, it will trigger a self-preservation response driven by fear. The fear response manifests itself as the species at risk reproducing less and foraging for food less, thus reducing its interaction with predators. This response can have a beneficial effect, although if too strong a response occurs, it can significantly reduce the population of the affected species. We can use a food chain to represent the various interactions between species. It is possible to devise mathematical models that encode the details of a food chain. We can use these models to study the long-term effects of the various sorts of interactions. In our model, we study the long-term behaviours of a specific food chain model. The food chain consists of a top predator which predates on a mid-level predator who in turn predates on two distinct types of prey. Both preys are in direct competition with each other, and our model accounts for the fear response driven by the next highest member on the food chain. We were able to study the long-term behaviours of this system and study how competition and the fear effect could impact the structure of the food chain.

Download

Share

COinS