  Scale invariant patterns have been found in different biological systems, in
many cases resembling what physicists have found in other nonbiological
systems. Here we describe the foraging patterns of free-ranging spider monkeys
(Ateles geoffroyi) in the forest of the Yucatan Peninsula, Mexico and find that
these patterns resemble what physicists know as Levy walks. First, the length
of a trajectory s constituent steps, or continuous moves in the same direction,
is best described by a power-law distribution in which the frequency of ever
larger steps decreases as a negative power function of their length. The rate
of this decrease is very close to that predicted by a previous analytical Levy
walk model to be an optimal strategy to search for scarce resources distributed
at random Viswanathan et al 1999). Second, the frequency distribution of the
duration of stops or waiting times also approximates a power-law function.
Finally, the mean square displacement during the monkeys first foraging trip
increases more rapidly than would be expected from a random walk with constant
step length, but within the range predicted for Levy walks. In view of these
results, we analyze the different exponents characterizing the trajectories
described by females and males, and by monkeys on their own or when part of a
subgroup. We discuss the origin of these patterns and their implications for
the foraging ecology of spider monkeys.
