Optimal random Lévy-loop searching: New insights into the searching behaviours of central-place foragers

A random Levy-looping model of searching is devised and optimal random Levy-looping searching strategies are identified for the location of a single target whose position is uncertain. An inverse-square power law distribution of loop lengths is shown to be optimal when the distance between the centre of the search and the target is much shorter than the size of the longest possible loop in the searching pattern. Optimal random Levy-looping searching patterns have recently been observed in the flight patterns of honeybees (Apis mellifera) when attempting to locate their hive and when searching after a known food source becomes depleted. It is suggested that the searching patterns of desert ants (Cataglyphis) are consistent with the adoption of an optimal Levy-looping searching strategy.