We develop an integro-partial differential equation model that incorporates nonlocal resource gradients directly into the advection term to represent perception-mediated animal movement in heterogeneous environments. By systematically comparing this formulation with a classical model based on local gradients of synthesized nonlocal resource quantities, we identify key regimes where their predictions diverge. Under varying light patterns (linear, Gaussian, and periodic) and resource landscapes (pulsed Gaussian and pulsed uniform), both models exhibit changes in foraging success and optimal detection scales with movement rates. The gradient-based model consistently achieves similar maximal foraging success as the abundance-based model but with smaller optimal detection scales, particularly under strong advection and smoothly varying resource gradients. Periodic light patterns generate intricate crossover behavior in the relative foraging success of the two models as detection scale increases, with gradient-based perception favoring more localized sampling under such conditions. Boundary conditions critically shape foraging outcomes: when resource peaks occur near domain boundaries, absorbing (Dirichlet) conditions can substantially reduce foraging efficiency, especially at higher diffusion rates and larger detection scales, highlighting the importance of accounting for boundary effects in fragmented or constrained habitats. Our findings demonstrate how the mathematical representation of nonlocal perception affects predicted optimal movement strategies, providing testable hypotheses for empirical studies and guidance for selecting modeling frameworks in diverse ecological contexts.
Wang et al. (Wed,) studied this question.