Speed selection and sampling strategies for terrestrial trail tracking

Terrestrial animals such as ants, mice and dogs use surface-borne odor trails to establish navigation routes or to find food and mates by following adsorbed chemical traces. Trail-tracking behavior is commonly observed, yet the strategies animals use to track trails are largely unknown. We examine generic features of trail-tracking by posing the problem as a search task of finding the trail after each loss of contact. We show that trail geometry imposes strong constraints on tracking speed; the maximal speed scales as the square-root of the typical radius of trail curvature with a strategy-dependent prefactor. By posing the problem in the reinforcement learning framework, we obtain optimal sampling strategies under various movement constraints and sensor configurations. An exactly solvable model in the Hamilton-Jacobi-Bellman framework recapitulates features of sampling strategies obtained via learning and quantifies the trade-off between movement cost, speed and sampling efficiency. Our work provides a general framework for trail tracking and testable hypotheses on the algorithms that animals use to follow trails.