How do foragers use nonlocal information? A novel modeling framework.

Area of Science:

• Mathematical Biology
• Ecology
• Animal Behavior

Background:

• Animal movement in heterogeneous environments is crucial for survival and reproduction.
• Previous models often simplify how animals perceive and react to resource distributions.
• Understanding perception-mediated movement is key to predicting foraging success.

Purpose of the Study:

• To develop and compare a novel integro-partial differential equation model for perception-mediated animal movement.
• To investigate how incorporating nonlocal resource gradients directly into advection terms affects movement strategies.
• To identify conditions where this new model diverges from classical, abundance-based models.

Main Methods:

• Developed an integro-partial differential equation model incorporating nonlocal resource gradients.
• Compared the new model with a classical model using local gradients of synthesized nonlocal quantities.
• Simulated movement under various light patterns (linear, Gaussian, periodic) and resource landscapes (pulsed Gaussian, pulsed uniform).

Main Results:

• The gradient-based model achieved similar maximal foraging success but with smaller optimal detection scales compared to the abundance-based model.
• Strong advection and smooth resource gradients favored smaller detection scales in the gradient-based model.
• Periodic light patterns induced complex crossover behaviors, with gradient-based perception favoring localized sampling.
• Boundary conditions significantly impacted foraging efficiency, especially with absorbing (Dirichlet) conditions near resource peaks.

Conclusions:

• The mathematical representation of nonlocal perception critically influences predicted optimal animal movement strategies.
• Findings provide testable hypotheses for empirical studies on animal foraging and movement.
• Offers guidance for selecting appropriate modeling frameworks in diverse ecological contexts, especially in fragmented habitats.