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Understanding the factors that drive species to move and develop territorial patterns is at the heart of spatial ecology. In many cases, mechanistic models, where the movement of species is based on local information, have been proposed to study such territorial patterns. In this work, we introduce a nonlocal system of reaction-advection-diffusion equations that incorporate the use of nonlocal information to influence the movement of species. One benefit of this model is that groups are able to maintain coherence without having a home-center. As incorporating nonlocal mechanisms comes with analytical and computational costs, we explore the potential of using long-wave approximations of the nonlocal model to determine if they are suitable alternatives that are more computationally efficient. We use the gradient flow-structure of the both local and nonlocal models to compute the equilibrium solutions of the mechanistic models via energy minimizers. Generally, the minimizers of the local models match the minimizers of the nonlocal model reasonably well, but in some cases, the differences in segregation strength between groups is highlighted. In some cases, as we scale the number of groups, we observe an increased savings in computational time when using the local model versus the nonlocal counterpart.