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Male moths locate females by navigating along her pheromone plume, often flying hundreds of meters en route. As the first male to find a calling female is most apt to be her mate, this can be termed "a race to find the female" and it is assumed to be under strong selective pressure for efficiency and rapidity. Locating a distant, odor-linked resource involves two strategies. The first is to contact the outer envelope of the odor plume. When wind direction is relatively invariant, the plume stretches and then crosswind flights may be favored, although when wind direction shifts over 60°, upwind and downwind paths may be optimal. Alternatively, the path may be random with respect to the direction of wind flow, with periodic changes in direction, as in either Lévy or Random Walks. After first detecting the pheromone, a second strategy follows: moths navigate along the plume by heading upwind when the pheromone is detected, with crosswind casting to re-establish contact if the plume is lost. This orientation path is not straightforward in nature, however, because atmospheric turbulence fragments the plume, thereby creating large odor gaps. Furthermore, a shifting wind direction can lead the responder out of the plume. One way to explore which strategies are optimal for enabling initial contact with the plume and subsequent navigation is through modeling of plumes' dispersal and of insects' flight strategies. Our simulations using the flight characteristics of the male gypsy moth (Lymantria dispar) suggest that search strategies similar to Lévy Walks are most apt to result in a high probability of contact with plumes. Although a searching trajectory aimed predominately crosswind performed almost as well as those with a random orientation when wind direction was relatively stable, downwind biased trajectories were least successful. A random orientation with respect to immediate wind flow, as used in our simulations of Lévy and Random Walks, seems optimal both for initial discovery of the plume and likelihood of locating an odor source. In the two available direct field observations, moths adopted a random orientation with respect to concurrent wind direction.

Modeling Optimal Strategies for Finding a Resource-Linked, Windborne Odor Plume: Theories, Robotics, and Biomimetic Lessons from Flying Insects