Exponential distributions arise for the length of a set of walks when, at each step in
a walk, there is a constant probability that the walk will end. Sometimes the walk
ends after only a few steps, sometimes after many steps. Longer walks are less
likely because they must survive many more equally likely terminations. It can be
shown that if the probability per unit length to terminate the walk remains constant,
the distribution of lengths of many walks has an exponential form. (See, for exam-
ple, Liebovitch et al. 1987 where this is derived in terms of durations of time, which
are here analogous to the lengths of the walks.) This model could represent human
behavior. The band continues a walk, at each moment deciding whether it has been
worthwhile and whether, with the same chance, it should be continued or ended.
We also wish to test an exponential function because Ju/’hoansi migration distances
(in the sense of the distance between the birthplaces of spouses, see below) seem to
resemble an exponential distribution. Interestingly, the step lengths of the Ju/’hoansi
data do not appear to match an exponential distribution well, as shown by theKolmogorov–Smirnov test statistic of p = 0.018 (Table 3). We also tried to fit an
exponential curve to the step length data using the multihistogram method (Fig. 3).
The coefficient of determination (R2) for the exponential distribution is 0.910,
markedly lower than the same coefficient for the power law (R2 = 0.965). This, of
course, suggests that the power law is a better fit to the data. We conclude that the
power law distribution of step lengths, which implies a Lévy flight model of move-
ment, is the best fit to the data of the alternatives tested.