Mathematical and Statistical Modelling of Animal Movement

Good understanding of individual animal movement is needed in the context of epidemiology in order to predict the rate of spread of infectious diseases. It is also required for problems arising in nature conservation such as biological invasions or pest monitoring. A question that often appears in the centre of the movement studies is which movement pattern is 'faster' or more efficient. For instance, it is widely believed that the pattern quantified by a power law distribution of movement steps is faster than Brownian motion. Another common query is do animals actually move using power law distributions. Would other distributions be a better fit for the movement? In pest monitoring a key area is the efficiency of the traps used to calculate the population density of insects. Different shaped traps are rarely compared equally, often the traps will vary in size or surface area. This thesis has three distinct parts and aims to provide insight into three different overlapping areas. The first part looks at different ways to compare probability distributions, and describes a way of comparing distributions without a mean or variance. The second part looks at the movement pattern of Tenebrionid beetles and has a detailed analysis of how these beetles move in a laboratory setting, with an emphasis on checking if any of the beetles tested moved with super-diffusive or ballistic motion. The third part is a comparison of the capture rate of different shaped traps using simulations of particles moving like Tenebrionid beetles.