Mean-field, Stochastic, and Individual-based Models of Insect Movement in the Context of Trapping and Ecological Monitoring

Abstract

In this thesis, we attempt to understand the conditions that affect insects' and animals' movements in the real world. Mathematical modelling is an efficient research tool that can help to bridge this gap in our knowledge. Herein, we revisit the straightforward, yet powerful simulation framework of individual-based modelling using Brownian Motion (BM), Correlated Random Walk (CRW), and Biased Random Walk (BRW). In chapter \ref{chapter1}, we outline previous research in this area. In chapter \ref{chapter2}, we consider trapping problems, where we suppose there to be two particular traps, i.e., baited and non-baited, and we verify whether a large non-baited trap is equivalent to a small baited trap. Thereafter, we determine how the trap position affects the results, i.e., where there is a competition area between two traps. Furthermore, we verify which trap shape is more effective, circular or square. In chapter \ref{chapter3}, we then study different insects' behaviours as a response to an attraction. To this end, we consider several different response types as quantified by different combinations of turning angle and step size distributions. We show that, depending on the response type, trap counts can be counter-intuitive and misleading. Then, in the chapter \ref{chapter4}, we simulate realistic slug movement by using data on slug spatial distributions collected during a three-year project conducted in crop fields across England. In particular, we study how slugs' movements depend on their population density, reception radius, and density threshold. Our simulation results are consistent with the above field data. Finally, chapter \ref{chapter5}, summarises the results for each chapter and discusses potential future work.