The evolutionary origins of Lévy walk foraging

Abstract

We study through a reaction-diffusion algorithm the influence of landscape diversity on the efficiency of search dynamics. Remarkably, the identical optimal search strategy arises in a wide variety of environments, provided the target density is sparse and the searcher’s information is restricted to its close vicinity. Our results strongly impact the current debate on the emergentist vs. evolutionary origins of animal foraging. The inherent character of the optimal solution (i.e., independent on the landscape for the broad scenarios assumed here) suggests an interpretation favoring the evolutionary view, as originally implied by the Lévy flight foraging hypothesis. The latter states that, under conditions of scarcity of information and sparse resources, some organisms must have evolved to exploit optimal strategies characterized by heavy-tailed truncated power-law distributions of move lengths. These results strongly suggest that Lévy strategies—and hence the selection pressure for the relevant adaptations—are robust with respect to large changes in habitat. In contrast, the usual emergentist explanation seems not able to explain how very similar Lévy walks can emerge from all the distinct non-Lévy foraging strategies that are needed for the observed large variety of specific environments. We also report that deviations from Lévy can take place in plentiful ecosystems, where locomotion truncation is very frequent due to high encounter rates. So, in this case normal diffusion strategies—performing as effectively as the optimal one—can naturally emerge from Lévy. Our results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

Lévy-like movement patterns of metastatic cancer cells revealed in microfabricated systems and implicated in vivo

“…Specifically, non-destructive Lévy walk searches with μ~ 2 were considered optimal provided that targets are randomly distributed and scarce and searcher does not have prior knowledge about the target locations 30 – 32 . However, more recent theoretical work has shown that Lévy walk searches (again, with μ ~ 2 ) are optimal under much broader environmental conditions than previously thought and that Lévy searchers experience fewer long periods of starvation (compared with exponential, composite Brownian and ballistic searchers) 33 , 66 . Furthermore, the so-called adaptive Lévy searching (where searcher has some knowledge of the target distribution and, upon target detection, responds by switching from extensive Lévy searching to intensive Brownian searching) has been shown to outperform adaptive ballistic and composite Brownian searches 67 .…”

Tuning movement for sensing in an uncertain world

“…Foraging theory, such as Charnov’s marginal value theorem ( Charnov, 1976 ), has modeled animals with random displacements—a situation in which the statistics of resources in the habitat dominates, while whether the resource is within sensing range (or engages learning or memory systems) is not considered to play a role. Lévy walk foraging is only predictive in information-scarce and low resource density contexts ( Wosniack et al, 2017 ). This conceptual gap between ecological (animals as stochastic unthinking agents) and neuroscience (animals with sensory systems, memory, and processing) approaches to foraging has a rich historical background ( Hein et al, 2016 ; Mobbs et al, 2018 ).…”

A Langevin dynamics approach to the distribution of animal move lengths

“…Our approach differs markedly from the Ornstein-Uhlenbeck processes [6,[64][65][66][67] In addition, it might be also argued [71] that the number of candidates for move length distributions that lead to plastic and overall efficient movement patterns may be not too large. This contrasts with strictly context-dependent situations, where specific local interactions can give rise to far more diverse families of P ( ).…”