Date Published: June 18, 2018
Publisher: Public Library of Science
Author(s): Andy Reynolds, Eliane Ceccon, Cristina Baldauf, Tassia Karina Medeiros, Octavio Miramontes, Alastair Smith.
Movement patterns resembling Lévy walks, often attributed to the execution of an advantageous probabilistic searching strategy, are found in a wide variety of organisms, from cells to human hunter-gatherers. It has been suggested that such movement patterns may be fundamental to how humans interact and experience the world and that they may have arisen early in our genus with the evolution of a hunting and gathering lifestyle. Here we show that Lévy walks are evident in the Me’Phaa of Mexico, in Brazilian Cariri farmers and in Amazonian farmers when gathering firewood, wild fruit and nuts. Around 50% of the search patterns resemble Lévy walks and these are characterized by Lévy exponents close to 1.7. The other search patterns more closely resemble bi-phasic walks. We suggest potential generative mechanisms for the occurrence of these ubiquitous Lévy walks which can be used to guide future studies on human mobility. We show that frequent excursions and meanderings from pre-existing trails can account for our observations.
In recent years there has been an accumulation of evidence that a wide variety of organisms have movement patterns resembling Lévy walks (sometimes called Lévy flights in the biological and ecological literature) [1–15]. Lévy walks alternate clusters of many short steps with longer steps between them, creating fractal movement patterns that have no characteristic scale. The self-similar, fractal properties of Lévy walks can be advantageous when randomly searching, and as a result it has been hypothesised that there could be natural selection for Lévy walks [16,17]. Lévy walk movement patterns in human hunter-gatherers were first reported to exist in the Dobe Ju/’hoansi in the Kalahari Desert in Botswana and Namibia  and later, in a more detailed study, in the Hadza of northern Tanzania , prompting the suggestion that Lévy search patterns may be fundamental to how individuals experience and interact with the world across a wide range of ecological contexts . Indeed, it is tempting to speculate that Lévy walking arose early in our genus with the advent of hunting and gathering, playing an important role in the evolution of human mobility .
All participants in Mexico and Brazil volunteered freely and informed consent was obtained from all subjects. Observations performed did not involve retrieval of any human biological material such as tissue or fluids and no experimental procedure of a psychological nature was performed.
We found that around 50% of the search patterns resemble Lévy walks typically characterised by power-law (Lévy exponents) close to 1.7 and around 50% of the search patterns more closely resemble bi-phasic walks (Figs 1–3). The Lévy walks and bi-phasic walks can, however, provide very similar fits to the data and visually the fits are sometimes indistinguishable. There is no support for tri-phasic walks. Lévy walks typically characterised by power-law (Lévy) exponents, μ, around 1.7 were found to occur in similar abundance in the search patterns of the Hadza . (But note that in  steps were determined by two kinds of events, turns and pauses rather than just by turns which break directional persistence). The remaining search patterns more closely resemble multi-phasic walks. We also find that the farmers are frequently walking on or close to pre-existing trails (Figs 4–6 and S1 File). This juxtaposition of Lévy walk characteristics and trail/feature following is evident, at least on one day (the exemplar in ), in the Hadza (Fig 7). However, it remains to be seen whether trail-following is common in the Hadza.
At first glance there might seem to be a clear contradiction between Lévy walk foraging patterns and trail/feature following as the trails/features are not likely to be shaped in ways that will result in Lévy walk patterns for trail/feature followers. These movements can, nonetheless, arise in a variety of ways. Gravity, for instance, influences water and it influences people, often leading to similarities in the courses of rivers and the paths that energetically optimal paths follow. Least cost paths often correlate with, or follow, natural features of the landscape, avoiding elevation gains. If the trails were to follow contour lines, which connect point of equal elevation (least effort); ridge tops (drainage divides); or streams in the valley then they may be fractal, and so result in Lévy-like movement patterns. This is because contour lines are analogous to coastlines which are known to have fractal properties. Indeed, the coastlines of Great Britain and Norway as well as a variety of contour lines across the United States are reported to be characterized by fractal dimensions ranging between about 1.2 and 1.5 [24–26]. But such fractal scaling seems not to account for our observations because Lévy walks have fractals dimension μ-1 (i.e., fractal dimensions around 0.7)  and, more pertinently, because the Me’Phaa are foraging over (rather than around) hilly terrain  whilst the Cariri and Amazon people mostly forage over flat terrain.
It has become clear that movement patterns resembling Lévy flight patterns occur widely across taxa [1–15] and frequently in scenarios seeming to fall outside of the “Lévy flight foraging hypothesis” [16,17] and the incumbent notion of optimal probabilistic searching. The identification of Lévy walk movement patterns in the Hadza is perhaps the most striking and important example of Lévy walking that cannot be attributed to optimized probabilistic searching, as humans have sophisticated cognitive abilities and so can return to locations where resources were found previously. Here we showed that the Hadza are not alone in this regard, as the Me’Phaa, the Brazilian Cariri and Amazonian farmers perform the same kind of Lévy walks. This apparent universality seems remarkable given that human behaviours are strongly shaped by an individual’s psyche and by complex social and environmental interactions, and given that “humans are the most cognitively complex foragers on Earth” . These findings could have important implications for understanding human movement in both the present and the past . It is also suggestive of an important link between the foraging patterns of humans and non-human animals .
All field activities were carried were approved by the relevant civil organizations acting on behalf of the volunteers. In Mexico this was the Xuajin Me’Phaa A.C. In Brazil it was: Associação de Moradores de Cacimbas (município de Jardim–CE); Associação dos Pequenos Produtores do Sitio Macaúba (município de Barbalha–CE); Associação dos Seringueiros da Reserva Extrativista do Rio Ouro Preto (município de Guajará-Mirim- RO); Associação dos Seringueiros Agroextrativistas do Baixo Rio Ouro Preto (município de Guajará-Mirim- RO); and the Comitê de Ética de Pesquisa em Humanos da UERN (Universidade Estadual do Rio Grande do Norte). In the case of research carried on public lands in Brazil, the project was reviewed and approved by ICMBio, the Chico Méndez Institute for Biological Diversity.