Interest in Lévy walks within the context of movement of organisms has recently soared, with some now referring to this approach as the Lévy walk/flight paradigm. The principal assumptions, taken from the world of physics, have been that organisms searching for food or some other resource adopt random walks, whereby the direction of each successive step in the walk is chosen at random from the complete circle and the length of each step, unless terminated through resource encounter, is chosen from a Lévy probability distribution with a particular exponent μ. The additional assumption that organisms forage optimally, such that μ maximizes the rate of resource encounter, has led to the so-called Lévy foraging hypothesis, with many attempts to test it.
However, the Lévy walk model is unrealistic, especially as it omits directionality between successive steps, a typical feature of movements of individual organisms at spatial scales relevant to their movement decisions. It also results in lower foraging efficiency than other more realistic models and the evidence that organisms actually 'do the Lévy walk' is weak to non-existent, despite claims to the contrary. Early optimal foraging studies of movements of organisms and a new generation of movement models avoid these problems.
It is therefore time to divorce the Lévy walk model from optimal foraging theory, revisit some of the early optimal foraging studies of movements and pursue the new generation of movement models. However, the Lévy approach may still prove useful at relatively large spatial scales, in terms of both theory and observations, especially in relation to distribution, dispersal and other population-level phenomena, and in this way biology, physics and mathematics may yet work well together.
- optimal foraging theory
- power law