Studies of Lévy flight search patterns have come under strong scrutiny, especially after the events discussed in Chapter 4. However, the number of reports of Lévy flights and walks in animal movement continues to grow, as discussed in Chapter 6. Here we briefly review the case for and against Lévy flights (and, more generally, superdiffusion).

Measurement and data analysis

Experimental science is always susceptible to measurement problems. Bradshaw et al. [50] systematically studied the effect of ignoring errors when measuring animal trajectories and found that such errors may lead to substantial biases when interpreting movement patterns. As Kölzsch and Blasius [188] point out, the effects of seasonal drift on the migratory patterns of birds render random walk methods useful only if they are modified and interpreted carefully to take seasonal drift into consideration. Nevertheless, the following facts support the case for anomalous diffusion: (1) a large number of studies (listed earlier) have all reached the same conclusion and (2) the authors have used a number of measurement techniques and a variety of experimental setups. These facts, taken together, convey a degree of confidence in the quality of the data and the reliability of the reported conclusions.

A more difficult question concerns not data quality but how the data should be analyzed. Power laws in physical systems (e.g., earthquakes) typically scale over at least 3 orders of magnitude. For biological systems in general, and foraging dynamics in particular, even 2 orders of magnitude of scaling can be a luxury.