Abstract
Ants, mice, and dogs often use surface-bound scent trails to establish navigation routes or to find food and mates, yet their tracking strategies remain poorly understood. Chemotaxis-based strategies cannot explain casting, a characteristic sequence of wide oscillations with increasing amplitude performed upon sustained loss of contact with the trail. We propose that tracking animals have an intrinsic, geometric notion of continuity, allowing them to exploit past contacts with the trail to form an estimate of where it is headed. This estimate and its uncertainty form an angular sector, and the emergent search patterns resemble a "sector search." Reinforcement learning agents trained to execute a sector search recapitulate the various phases of experimentally observed tracking behavior. We use ideas from polymer physics to formulate a statistical description of trails and show that search geometry imposes basic limits on how quickly animals can track trails. By formulating trail tracking as a Bellman-type sequential optimization problem, we quantify the geometric elements of optimal sector search strategy, effectively explaining why and when casting is necessary. We propose a set of experiments to infer how tracking animals acquire, integrate, and respond to past information on the tracked trail. More generally, we define navigational strategies relevant for animals and biomimetic robots and formulate trail tracking as a behavioral paradigm for learning, memory, and planning.