Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions

Abstract

Highlights Lévy walk foragers are optimal under a broader set of conditions than previously thought  The importance of prey-targeting has been largely overlooked  Lévy foragers outperform other strategies when prey is sparse and searching is required  Composite Brownian walk foragers outperform at some high levels of prey abundance, when searching is not required  Optimal Lévy foragers experience significantly fewer long periods of starvation Keywords: Simulation; Composite Brownian; Predator; Movement; Power-law Abstract While evidence for optimal random search patterns, known as Lévy walks, in empirical movement data is mounting for a growing list of taxa spanning motile cells to humans, there is still much debate concerning the theoretical generality of Lévy walk optimisation. Here, using a new and robust simulation environment, we investigate in the most detailed study to date (24 x 10 6 simulations) the foraging and search efficiencies of 2-D Lévy walks with a range of exponents, target resource distributions and several competing models. We find strong and comprehensive support for the predictions of the Lévy flight foraging hypothesis and in particular for the optimality of inverse square distributions of move step-lengths across a much broader range of resource densities and distributions than previously realised. Further support for the evolutionary advantage of Lévy walk movement patterns is provided by an investigation into the 'feast and famine' effect, with Lévy foragers in heterogeneous environments experiencing fewer long 'famines' than other types of searchers. Therefore overall, optimal Lévy foraging results in more predictable resources in unpredictable environments.

Sit-and-wait versus active-search hunting: A behavioral ecological model of optimal search mode

“…While there is empirical literature suggesting directionality to prey and/or predator movements (summary in Scharf et al, 2006), evidence suggests that a wide range of searching predators adopt Lévy or Lévy-like walks (Humphries and Sims, 2014;Reynolds, 2013), including humans (Raichlen et al, 2014), while others conform to Brownian movement (examples in Tani et al, 2014). Lévy walks are characterized by a distribution of step lengths with randomized turns equally likely in any compass direction.…”

Why Lévy Foraging does not need to be ‘unshackled’ from Optimal Foraging Theory

“…What has proved surprising about these step-length distributions is the extent to which they improve the efficiency of random searches over simple Brownian motion. It has been shown unequivocally that a power law distribution of move step lengths is more efficient, in terms of prey items located per unit distance travelled, than any other distribution of move step-lengths so far tested (up to 3 times better than Brownian), and over a range of prey field densities spanning more than 4 orders of magnitude [2]. …”

“…It should be noted that these 'Lévy' movements do not need to have an exponent of µ = 2.000 to be more efficient; a range of exponent values, from 1.5 to 2.5 have been shown to easily outperform simple Brownian motion [2]. Therefore, animal movements do not need to be carefully tuned to a specific parameterisation; almost any exponent in the Lévy range (1 < µ ≤ 3) will be significantly better than Brownian, making the selection and evolution of these distributions all the more likely.…”

“…Therefore, animal movements do not need to be carefully tuned to a specific parameterisation; almost any exponent in the Lévy range (1 < µ ≤ 3) will be significantly better than Brownian, making the selection and evolution of these distributions all the more likely. Further, even movement patterns with underlying mechanisms that are not power laws, such as hyper-exponentials (composite Brownian) but which approximate Lévy patterns, can provide significant improvements in foraging efficiency [2].…”

“…A simple statistical distribution of move-step lengths is insufficient to reconstruct a realistic movement path, or to predict how an animal might move throughout a land Source file (Word or (La)TeX) Click here to view linked References (or sea) scape. A Lévy distribution of move step-lengths has been shown to be advantageous when random searching is required -when foraging without the need for searching, the advantage diminishes [2]. Therefore, the presence of a Lévy distribution can be seen as a signature of possible random searching; an activity which might at times be rare or non-existent, or might be present only as very brief bouts in a movement path dominated by other behaviours.…”