Displaced Honey Bees Perform Optimal Scale-Free Search Flights

Abstract

Honey bees (Apis mellifera) are regularly faced with the task of navigating back to their hives from remote food sources. They have evolved several methods to do this, including compass-directed "vector" flights and the use of landmarks. If these hive-centered mechanisms are disrupted, bees revert to searching for the hive, but the nature and efficiency of their searching strategy have hitherto been unknown. We used harmonic radar to record the flight paths of honey bees that were searching for their hives. Our subsequent analysis of these paths revealed that they can be represented by a series of straight line segments that have a scale-free, Lévy distribution with an inverse-square-law tail. We show that these results, combined with the "no preferred direction" characteristic of the segments, demonstrate that the bees were flying an optimal search pattern. Lévy movements have already been identified in a number of other animals. Our results are the best reported example where the movements are mostly attributable to the adoption of an optimal, scale-free searching strategy.

A Lévy-flight diffusion model to predict transgenic pollen dispersal

“…(Online version in colour.) 13 metres when looking for alternative food sources or attempting to locate a displaced hive [17,18,43]. These long displacements may result in long-distance pollination and hence increase the risk of adventitious mixing between GM and non-GM crops.…”

“…The searching patterns of foraging honeybees have been studied extensively by Reynolds et al [17,18,43]. They have conducted field experiments using harmonic radar to track the movements of displaced honeybees searching for their hive, or for alternative food resources after a known source of food has been removed.…”

“…They are, therefore, well suited to represent movement which includes a non-negligible probability for very large displacements. Lévy-type foraging patterns have been observed for a broad range of organisms, including honeybees [17,18], bumblebees [19], fruit flies [20], large marine predators [21,22], human T cells [23], jellyfishes [24], albatrosses [25] and even human hunter-gatherers [26]. All of these Lévy patterns have been identified through sound statistical techniques, but there is still some debate on the underlying driving mechanism: natural selection to optimize search efficiency [27] or spontaneous emergence from innate behaviours [28].…”

Lévy flights with power-law absorption

“…In this context, the kind of motion performed by the "searcher" plays a crucial role and, as evidenced by extensive experiments in the last two decades, anomalous diffusion seems to be widespread among real organisms [2]. In fact, many animals, ranging from birds (e.g., albatross [3]), to arthropods (e.g., bees [4], butterflies [5]), to aquatic animals (e.g., sharks, sea turtles, and penguins [6]), and even to mammals (e.g., deer [3], goats [7]) rarely display Gaussian probability functions for displacement with a variance scaling linearly with time, as prescribed by normal diffusion. Rather, they display Lévy walk movement patterns [8,9].…”

Why Lévy Foraging does not need to be ‘unshackled’ from Optimal Foraging Theory

“…It is this marked advantage in foraging efficiency, coupled with the apparent ubiquity of these move step-length distributions in empirical data [3][4][5][6][7][8][9][10][11], that have led to ideas about how natural selection would have favoured power law distributions over simple exponential distributions of step-lengths when animals need to perform random searches. It should be noted that these 'Lévy' movements do not need to have an exponent of µ = 2.000 to be more efficient; a range of exponent values, from 1.5 to 2.5 have been shown to easily outperform simple Brownian motion [2].…”