Nonlocal Mechanistic Models in Ecology: Numerical Methods and Parameter Inferences

Animals utilize their surroundings to make decisions on how to navigate and establish their territories. Some species gather information about competing groups by observing them from a distance, detecting scent markings, or relying on memories of encounters with rival populations. Gathering such information involves a nonlocal process, prompting the development of mechanistic models that incorporate nonlocal terms to explore species movement. These models, however, pose analytical and computational challenges. In this study, we focus on a multi-species advection–diffusion model that incorporates nonlocal advection. To efficiently compute solutions for this system involving a large number of interacting species, we introduce a numerical scheme using spectral methods. Additionally, we examine the influence of various parameters and interaction potentials on population densities. Our investigation aims to provide a method to identify the primary factors driving species movements, and we validate our approach using synthetic data.