Revisiting Levy flight search patterns of wandering albatrosses, bumblebees and deer

The study of animal foraging behaviour is of practical ecological importance(1), and exemplifies the wider scientific problem of optimizing search strategies(2). Levy flights are random walks, the step lengths of which come from probability distributions with heavy power-law tails(3,4), such that clusters of short steps are connected by rare long steps. Levy flights display fractal properties, have no typical scale, and occur in physical(3-5) and chemical(6) systems. An attempt to demonstrate their existence in a natural biological system presented evidence that wandering albatrosses perform Levy flights when searching for prey on the ocean surface(7). This well known finding(2,4,8,9) was followed by similar inferences about the search strategies of deer(10) and bumblebees(10). These pioneering studies have triggered much theoretical work in physics (for example, refs 11, 12), as well as empirical ecological analyses regarding reindeer(13), microzooplankton(14), grey seals(15), spider monkeys(16) and fishing boats(17). Here we analyse a new, high-resolution data set of wandering albatross flights, and find no evidence for Levy flight behaviour. Instead we find that flight times are gamma distributed, with an exponential decay for the longest flights. We re-analyse the original albatross data(7) using additional information, and conclude that the extremely long flights, essential for demonstrating Levy flight behaviour, were spurious. Furthermore, we propose a widely applicable method to test for power-law distributions using likelihood(18) and Akaike weights(19,20). We apply this to the four original deer and bumblebee data sets(10), finding that none exhibits evidence of Levy flights, and that the original graphical approach(10) is insufficient. Such a graphical approach has been adopted to conclude Levy flight movement for other organisms(13-17), and to propose Levy flight analysis as a potential real-time ecosystem monitoring tool(17). Our results question the strength of the empirical evidence for biological Levy flights.