Adaptive Lévy walks can outperform composite Brownian walks in non-destructive random searching scenarios

Recently it has been found that composite Brownian walk searches are more efficient than any Lévy walk when searching is non-destructive and when the Lévy walks are not responsive to conditions found in the search. Here a new class of adaptive Lévy walk searches is presented that encompasses composite Brownian walks as a special case. In these new models, bouts of Lévy walk searching alternate with bouts of more intensive Brownian walk searching. Switching from extensive to intensive searching is prompted by the detection of a target. And here, switching back to extensive searching arises if a target is not located after travelling a distance equal to the ‘giving-up distance’. It is found that adaptive Lévy walks outperform composite Brownian walks when searching for sparsely distributed resources. Consequently there is stronger selection pressures for Lévy processes when resources are sparsely distributed within unpredictable environments. The findings reconcile Lévy walk search theory with the ubiquity of two modes of searching by predators and with their switching search mode immediately after finding a prey.