‘Optimal’ behaviour in a
biological system is not simply that which maximizes a mean, or
temporally and spatially averaged, fitness function. Rather, population
dynamics and demographic and environmental stochasticity are
fundamental evolutionary ingredients. Here, we revisit the problem of
optimal foraging, where some recent studies claim that organisms should
forage according to Levy walks. We show that in an ecological scenario
dominated by uncertainty and high mortality, Levy walks can indeed be
evolutionarily favourable. However, this conclusion is dependent on the
definition of efficiency and the details of the simulations. We analyse
measures of efficiency that incorporate population level
characteristics, such as variance, superdiffusivity and heavy tails,
and compare the results with those generated by simple maximizing of
average encounter rate. These results have implications on stochastic
search problems in general, and also on computational models of
evolutionary optima.