Adaptive Lévy Walks and Area-restricted Search in Human Foraging.

Abstract

A considerable amount of research has claimed that animals’ foraging behaviors display movement lengths with power-law distributed tails, characteristic of Le ́ vy flights and Le ́ vy walks. Though these claims have recently come into question, the proposal that many animals forage using Le ́ vy processes nonetheless remains. A Le ́ vy process does not consider when or where resources are encountered, and samples movement lengths independently of past experience. However, Le ́ vy processes too have come into question based on the observation that in patchy resource environments resource-sensitive foraging strategies, like area-restricted search, perform better than Le ́ vy flights yet can still generate heavy-tailed distributions of movement lengths. To investigate these questions further, we tracked humans as they searched for hidden resources in an open-field virtual environment, with either patchy or dispersed resource distributions. Supporting previous research, for both conditions logarithmic binning methods were consistent with Le ́ vy flights and rank-frequency methods– comparing alternative distributions using maximum likelihood methods–showed the strongest support for bounded power-law distributions (truncated Le ́ vy flights). However, goodness-of-fit tests found that even bounded power-law distributions only accurately characterized movement behavior for 4 (out of 32) participants. Moreover, paths in the patchy environment (but not the dispersed environment) showed a transition to intensive search following resource encounters, characteristic of area-restricted search. Transferring paths between environments revealed that paths generated in the patchy environment were adapted to that environment. Our results suggest that though power-law distributions do not accurately reflect human search, Le ́ vy processes may still describe movement in dispersed environments, but not in patchy environments–where search was area-restricted. Furthermore, our results indicate that search strategies cannot be inferred without knowing how organisms respond to resources–as both patched and dispersed conditions led to similar Le ́ vy-like movement distributions