Drivers of population cycles in ecological systems

Abstract

In this thesis, mathematical models are used to investigate potential drivers of population cycles. Population cycles are a common ecological phenomenon, yet the mechanisms underpinning these oscillations are not always known. We focus on two distinct systems, and evaluate potential causes of cyclic dynamics. In the first part of the thesis, we develop and analyse a host–pathogen model, incorporating density-dependent prophylaxis (DDP). DDP describes when individuals invest more in immunity at high population densities, due to the increased risk of becoming infected by a pathogen. The implications of this for the population dynamics of both host and pathogen are examined. We find that the delay in the onset of DDP is critical in determining whether DDP increases or decreases the likelihood of population cycles. Secondly, we focus on a particular cyclic vole population, that of Kielder Forest, Northern UK. We construct a model to test the hypothesis that the population oscillations observed in this location are caused by the interaction between the voles and the silica in the grass they consume. We extend our model by including seasonal forcing, and study the effects of this on the population dynamics.