Travel times figure prominently in patch models, which, as we observed earlier,
are directly relevant to understanding Ju/’hoansi camp movements. The model
examines how patches are chosen and at what point a forager should leave an
exploited patch for a fresh one. This model is clearly relevant to understanding
Ju/’hoansi foraging behavior in the Kalahari given (1) the scarce and patchy distri-
bution of food in the Ju/’hoansi environment, (2) the tendency for the Ju/’hoansi to
camp in or at resource patches, and (3) the propensity for the Ju/’hoansi to “eat out”
(substantially exploit) an area before moving on to a fresh patch. The generic patch
model predicts that a forager will leave a patch when the marginal rate of gain
declines to the point at which it equals the long-term average rate of energy intake
in the habitat. In the basic and common formulation of the model, the average travel
time between patches is taken to be the inverse of the patch encounter rate. Thus,
when the encounter rate is maximized, time is minimized, and in fact some models
have explicitly examined time minimization as a model goal (e.g., Abrams 1984).
So, average search time is a key variable in the calculation of most models. In the
case of a Lévy flight, however, there is no average travel time between patches. The
mean simply does not exist because power laws do not have stable means
(Liebovitch 1998, pp. 74–105; Liebovitch and Scheurle 2000; Liebovitch and
Todorov 1996; Liebovitch et al. 1999). This tells us that the standard formulation
of the patch model cannot be accurately calculated for a forager who forages using
a Lévy flight pattern. We do not assert that this “disproves” optimal foraging theory,
but we do believe that optimal foraging models that analyze human behavior should
employ more realistic assumptions about forager behavior.