Nonlocal Mechanistic Models in Ecology: Numerical Methods and Parameter Inferencing

Abstract: Animals use various processes to inform themselves about their environment and make decisions about how to move and form their territory. In some cases, populations inform themselves of competing groups through observations at distances, scent markings, or memories of locations where an individual has encountered competing populations. As the process of gathering this information is inherently nonlocal, mechanistic models that include nonlocal terms have been proposed to investigate the movement of species. Naturally, these models present analytical and computational challenges. In this work we study a multi-species model with nonlocal advection. We introduce an efficient numerical scheme using spectral methods to compute solutions of a nonlocal reaction-advection-diffusion system for a large number of interacting species. Moreover, we investigate the effects that the parameters and interaction potentials have on the population densities. Finally, we propose a method using maximum likelihood estimation to determine the most important factors driving species' movements and test this method using synthetic data.