  What is the fastest way of finding a randomly hidden target? This question of
general relevance is of vital importance for foraging animals. Experimental
observations reveal that the search behaviour of foragers is generally
intermittent: active search phases randomly alternate with phases of fast
ballistic motion. In this letter, we study the efficiency of this type of two
states search strategies, by calculating analytically the mean first passage
time at the target. We model the perception mecanism involved in the active
search phase by a diffusive process. In this framework, we show that the search
strategy is optimal when the average duration of "motion phases" varies like
the power either 3/5 or 2/3 of the average duration of "search phases",
depending on the regime. This scaling accounts for experimental data over a
wide range of species, which suggests that the kinetics of search trajectories
is a determining factor optimized by foragers and that the perception activity
is adequately described by a diffusion process.
