Fermat’s Principle of Least Time Predicts Refraction of Ant Trails at Substrate Borders

Abstract

Fermat’s principle of least time states that light rays passing through different media follow the fastest (and not the most direct) path between two points, leading to refraction at medium borders. Humans intuitively employ this rule, e.g., when a lifeguard has to infer the fastest way to traverse both beach and water to reach a swimmer in need. Here, we tested whether foraging ants also follow Fermat’s principle when forced to travel on two surfaces that differentially affected the ants’ walking speed. Workers of the little fire ant, Wasmannia auropunctata, established “refracted” pheromone trails to a food source. These trails deviated from the most direct path, but were not different to paths predicted by Fermat’s principle. Our results demonstrate a new aspect of decentralized optimization and underline the versatility of the simple yet robust rules governing the self-organization of group-living animals.