Optimal random Lévy-loop searching: New insights into the searching behaviours of central-place foragersA. M. Reynolds
Rothamsted Research - Harpenden, Hertfordshire, AL5 2JQ, UK, EU
received 27 September 2007; accepted in final form 18 February 2008; published April 2008
published online 20 March 2008
A random Lévy-looping model of searching is devised and optimal random Lévy-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 Lévy-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 Lévy-looping searching strategy.
02.50.Ey - Stochastic processes.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
05.40.Fb - Random walks and Levy flights.
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