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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.