Friday, January 3, 2014

Hunter-gatherers forage using Lévy walks!

Finally! Some anthropologists strapped GPS units to hunter-gatherers and then downloaded the data to analyze the geometry of their hunting and foraging movements (Raichlen et al. 2013).

The test subjects were from the Hadza of Tanzania.

I've been wondering when someone would do this ever since my colleagues and I proposed that human foragers used Lévy flights to forage (Brown et al. 2007)

There are many interesting tidbits in the article, but the main result was that a large plurality--nearly half--of their hunting or foraging trips were, mathematically, Lévy walks (related to Lévy flights). Lévy walks are patterns of movements in which the step lengths are power-law distributed. For each data set (that is, the GPS trace of a trip), the authors fit the data to six models: a power law, a truncated power law, a single exponential, and three composite exponential functions. The large plurality of Lévy walks were those that best fit power laws or truncated power laws. The fitting was done using the ever popular maximum likelihood estimation procedures proposed by Clauset, Shalizi, and Newman (2009). The explanation of how they collected and processed the GPS data was eminently clear, which I appreciate because I have quite a bit of GPS data that I would like to analyze in a similar fashion.

The results are interesting because Lévy walks (or flights) are the most efficient random search patterns for scare targets. Whether this behavior evolved over thousands or millions of years, or whether it has developed as a heuristic, or whether it is a fully conscious methodical strategy is an open question, but it shows that human foragers forage as many other animals do.The Lévy walk movement certainly has implications for optimal foraging models. It may also offer an explanation for fractal patterns of archaeological sites because the turning points of a Lévy walk form a fractal.

Finally, I found it interesting that women, who mostly collect, walked much more Lévy-ly than their men, who hunted much more.

References cited

Brown, Clifford T., Larry S. Liebovitch, and Rachel Glendon (2007). Lévy Flights in Dobe Ju/’hoansi Foraging Patterns. Human Ecology Vol. 35, No. 1, pp. 129-138.

Clauset, A., R. C. Shalizi, and M. E. J. Newman. 2009. Power-law distributions in empirical data. SIAM Review 51(4):661-703.

Raichlen, David A., Brian M. Wood, Adam D. Gordon, Audax Z. P. Mabulla, Frank W. Marlowe,
and Herman Pontzer (2013). Evidence of Lévy walk foraging patterns in human hunter–gatherers. Proceedings of the National Academy of Sciences, Early Edition. 

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