The optimal movement patterns for mating encounters with sexually asymmetric detection ranges

Animals have evolved various sex-specific characteristics to improve the efficiency of mating encounters. One is the sex-specific attracting signal. Signal receivers perform a combination of random search and navigation before and after signal detections. On the other hand, signal senders can also modify their movement patterns to optimize their encounter rates, which invokes a reverse side of random search problems that asks for the most efficient movement patterns of signal senders to be found by signal receivers. In this study, we focused on visual and auditory signals in particular, and quantified the efficiency of mating encounters of individual animals performing a Lévy walk, a special class of random walk, with a variety of speeds before signal detection. We found that signal senders should move more slowly and/or less diffusively than receivers to improve mating encounters. The optimal movement patterns of senders ranged from relatively slow to stationary ones depending on the density of individuals, the effective range of signals, and the ability of receivers to locate senders. By focusing on the optimal movement patterns of individuals that are often assumed to be given targets, the present study provides insights into strategies of effective attraction beyond the case of mate search.