Using Transfer Function Analysis in Modelling Biological Invasions

Abstract

This thesis is made up of seven chapters and two appendices. Chapter 1 provides an introduction whilst Chapter 7 o ers a conclusion. In Chapter 2 we provide preliminaries on population projection models and robustness analysis. In Chapter 3 we introduce a stage-structured model in a context of biological invasions. Using a Transfer Function Approach, we provide a detailed analysis of the invasion model where the existence and local stability of all possible equilibria are characterised in terms of the underlying parameters of the model. In Chapter 4, a Lyapunov function approach is used to estimate the basin of attraction for each equilibrium. In Chapter 5, harvesting is incorporated into the model and we speci cally examine the e ect of harvesting on whether one or both of the species are eliminated. In Chapter 6 we introduce a novel technique to measure the possibility of invasion in non-normal systems where the traditional invasion exponent technique is unreliable.