Optimal cooperative searching using purely repulsive interactions

• We explore how repulsive interactions could enhance cooperativity in groups of diffusing foragers.
• We find an optimal repulsive range, where the time to find a resource/target is minimal.
• Optimal repulsion strikes a balance between minimizing redundancy and maximizing total area searched.
• Our results are insensitive to the exact form of the repulsive interaction and scale in a simple manner with forager density.

Foraging, either solitarily or collectively, is a necessary behavior for survival that is demonstrated by many organisms. Foraging can be collectively optimized by utilizing communication between the organisms. Examples of such communication range from high level strategic foraging by animal groups to rudimentary signaling among unicellular organisms. Here we systematically study the simplest form of communication via long range repulsive interactions between multiple diffusing Brownian searchers on a one-dimensional lattice. We show that the mean first passage time for any one of them to reach a fixed target depends non-monotonically on the range of the interaction and can be optimized for a repulsive range that is comparable to the average spacing between searchers. Our results suggest that even the most rudimentary form of collective searching does in fact lower the search time for the foragers suggesting robust mechanisms for search optimization in cellular communities.