Lévy Processes in Animal Movement: An Evolutionary Hypothesis

The origin of fractal patterns is a fundamental problem in many areas of science. In ecological systems, fractal patterns show up in many subtle ways and have been interpreted as emergent phenomena related to some universal principles of complex systems. Recently, Lévy-type processes have been pointed out as relevant in large-scale animal movements. The existence of Lévy probability distributions in the behavior of relevant variables of movement, introduces new potential diffusive properties and optimization mechanisms in animal foraging processes. In particular, it has been shown that Lévy processes can optimize the success of random encounters in a wide range of search scenarios, representing robust solutions to the general search problem. These results set the scene for an evolutionary explanation for the widespread observed scale-invariant properties of animal movements. Here, it is suggested that scale-free reorientations of the movement could be the basis for a stochastic organization of the search whenever strongly reduced perceptual capacities come into play. Such a proposal represents two new evolutionary insights. First, adaptive mechanisms are explicitly proposed to work on the basis of stochastic laws. And second, though acting at the individual-level, these adaptive mechanisms could have straightforward effects at higher levels of ecosystem organization and dynamics (e.g. macroscopic diffusive properties of motion, population-level encounter rates). Thus, I suggest that for the case of animal movement, fractality may not be representing an emergent property but instead adaptive random search strategies. So far, in the context of animal movement, scale-invariance, intermittence, and chance have been studied in isolation but not synthesized into a coherent ecological and evolutionary framework. Further research is needed to track the possible evolutionary footprint of Lévy processes in animal movement.