In addition to the early studies we discussed in Chapter 5, here we review other experimental studies. We focus on animal movement because of the relative abundance of data and larger velocities relative to plant seeds, pollen, etc. We note, however, that seed shadows are often fat tailed [408] (i.e., leptokurtic), so many plants may also disperse superdiffusively.

Arthropods and mollusks

Honey bees, fruit flies, and desert ants

Reynolds et al. [306, 307] studied bees using a variety of techniques. In one study, they [306] used harmonic radar to record the flight paths of honey bees that were searching for their hives. Harmonic radar can differentiate between the harmonic signal returned from a specific target and signals returned from all other passive reflectors. Analysis of the trajectories indicated scale-invariant walks with a power law exponent µ ≈ 2 (see also [300]), corresponding to a Lévy index α = 1. They argued that these results, combined with the no preferred direction characteristic of the segments, demonstrate that the bees were flying an optimal search pattern. An inverse square power law distribution (µ = 2) is exactly what the theory of Lévy flight foraging predicts (see Chapter 10).

In another study, Reynolds et al. [307] trained foraging honey bees to seek out an artificial feeder, which was subsequently removed. The resulting bee flight patterns were recorded using harmonic radar and showed that the flight patterns have the scale-free characteristic of Lévy walks.