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

Jan Oettler,Olivier Rey,Jürgen Heinze,Volker S Schmid,Andreas Dress,Niko Zankl

doi:10.1371/journal.pone.0059739

Jan Oettler, Olivier Rey + Show 4 more

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https://doi.org/10.1371/journal.pone.0059739

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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.

Highlights

The processes underlying biological decentralized organization have become models for modern-age human applications
Workers traveling between the nest and food will deposit a trail of pheromones on the ground
Additional workers are recruited by these pheromones and the trail is reinforced through positive feedback [6], [7]

Summary

Introduction

The processes underlying biological decentralized organization have become models for modern-age human applications. Workers traveling between the nest and food will deposit a trail of pheromones on the ground. Trails will converge towards the most direct path between nest and food source [8], [9]. One way for ants to optimize their path across two surfaces would be to follow Fermat’s principle of least time, which posits that a ray of light traveling between two points follows the fastest (and not necessarily the most direct) route. Ants are under evolutionary selection and path formation results from the interaction of behavior, pheromone properties and the environment. We tested whether ants foraging across two surfaces deviate from the most direct path but not from a time-optimized solution

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