Trails of ants converge or diverge through lens-shaped impediments, resembling principles of optics

Abstract

Analogies across disciplines often indicate the existence of universal principles such as optimization, while the underlying proximate mechanisms may differ. It was reported recently that trails of ants refract at the border of substrates, on which walking speeds differ. This phenomenon is analogous to the travel-time-minimizing routes of light refracting at the borders between different media. Here, we further demonstrate that ant tracks converge or diverge across lens-shaped impediments similar to light rays through concave or convex optical lenses. The results suggest that the optical principle of travel time reduction may apply to ants. We propose a simple mathematical model that assumes nonlinear positive feedback in pheromone accumulation. It provides a possible explanation of the observed similarity between ant behavior and optics, and it is the first quantitative theoretical demonstration that pheromone-based proximate mechanisms of trail formation may produce this similarity. However, the future detailed empirical observations of ant behavior on impediment edges during the process of pheromone trail formation are needed in order to evaluate alternative explanations for this similarity.