Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article


Doctor of Philosophy


Applied Mathematics


Zou, Xingfu


This thesis studies the impact of anti-predation strategy on the population dynamics of predator-prey interactions. This work includes three research projects.

In the first project, we study a system of delay differential equations by considering both benefit and cost of anti-predation response, as well as a time delay in the transfer of biomass from the prey to the predator after predation. We reveal some insights on how the anti-predation response level and the biomass transfer delay jointly affect the population dynamics; we also show how the nonlinearity in the predation term mediated by the fear effect affects the long term dynamics of the model system. These results seem to suggest a need to revisit existing predator-prey models in the literature by incorporating the indirect effect and biomass transfer delay.

In the second project, we propose two model systems in the form of ordinary differential equations to mechanistically explore trophic cascade of fear effect. The three species model only considers the cost of the anti-predation response reflected in the decrease of the production, while the four species model also considers the benefit of the response in reducing the predation rate. We perform a thorough analysis on the dynamics of the two models. The results reveal that the 3-D model and 4-D model demonstrate opposite patterns for trophic and such a difference is attributed to whether there is a benefit for the anti-predation response by the meso-carnivore species.

In the last project, to study the evolution of anti-predation strategy, we consider three species predator-prey models in which the two competing prey species have the same population dynamics but different anti-predation strategies. We identify the existence conditions of a singular anti-predation strategy, as well as conditions for it to be a local evolutionarily stable strategy. We use some examples to illustrate our results and compare the results between two different types of predators. Numerical simulations are also carried out to verify our theoretical findings and to demonstrate that three types of outcomes are possible: the mutant fails to invade, or the mutant invades and replaces the resident, or the mutant invades co-persist with the resident. These results help us understand more about the role anti-predation response can play in conveying competitive advantages.

Summary for Lay Audience

Predator-prey interaction is an important topic in ecology and evolutionary biology. Anti-predation response is a common behavior of prey in predator-prey interaction but it is widely ignored in existing predator-prey models and management of ecosystems because the impact of anti-predation response can not be observed as easily as direct predation. Recent researches showed empirical evidence in both theory and practice that anti-predation strategy can strongly affect the population size of the prey species and therefore, should not be ignored. Preys have many different anti-predation strategies to fight against predators. Some strategies allow individuals to improve their fitness while other strategies could lead to extinction. Therefore, studying the impact of these strategies is of theoretical and practical importance for determining the long-term dynamics of the populations. In this thesis, we use mathematical tools to investigate this problem. We develop models which consider the costs and benefits of anti-predation strategies simultaneously. Secondly, we use mathematical methods and theories to analyze our models. The main objective of this thesis is to reveal some new insights from considering anti-predation strategies and explore the existence of the ``best" anti-predation strategy, a strategy which will maximize the long-term survival of the species. Our goal for this thesis is to understand the influence of anti-predation strategies and accordingly suggest ways by which, possible manipulations to the anti-predation response of animals in some area may help preserve the biodiversity of the ecosystem. Some results obtained in this thesis can also be applied to control of some un-wanted biological species in agriculture and forest.