Are Levy flight patterns derived from the Weber-Fechner law in distance estimation?

Honeybees (Apis mellifera) are regularly faced with the task of navigating back to their hives from remote food sources. They have evolved several methods to do this, including compass-directed “vector” flights and the use of landmarks. If these hive-centered mechanisms are disrupted, bees revert to searching for the hive, using an optimal Levy flight searching strategy. The same strategy is adopted when a food source at a known location ceases to be available. Here, we show that the programming for this Levy strategy does not need to be very sophisticated or clever on the bee’s part, as Levy flight patterns can be derived from the Weber–Fechner law in a bee’s odometer. Odometry errors of a different kind occur in desert ants (Cataglyphis spp., Melophorus bagoti). The searching behaviors of these ants are very similar in overall structure to that of honeybees but do not display any Levy flight characteristics. We suggest that errors in the estimation of distance can be implicitly involved in shaping the structure of systematic search behavior and should not be regarded as merely deficiencies in the odometer.