Everyday entropy: waggle dance

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“The bee’s dance is analog.

– Orrin W. “Rob” Robinson

This is the thing that information theory can’t describe.  The bee’s dance is literally analog, not figuratively digital.  Bees are not trying to convey 7.4 bits of information in an approximate way, they are just dancing in way that sometimes conveys information.  Only 10% of bees follow the instructions a waggler, and among them, the quantum of onboard information is uncertain.  The dance itself isn’t being recorded, stored or copied, so its digital equivalent is moot.  What information the recruits actually understand and how they understand it are both hidden inside the whole system, nerves, muscles and skeleton.  It is possible to conceptualise the dance in terms of information so that a digital replica of the dance would need 8 bits, but the dance itself is physical and entropic.

The dance is also resonant – the vibrations of the dancer‘s waggle resonate with the physical structures of the listening bees.  The dance imprints vibrations and vectors; it commutes between bees in waves of approximation.

 

The spatial information content of the honey bee waggle dance

Roger Schürch and Francis L. W. Ratnieks

“In 1954, Haldane and Spurway published a paper in which they discussed the information content of the honey bee waggle dance with regard to the ideas of Norbert Wiener, who had recently developed a formal theory of information. We return to this concept by reanalyzing the information content in both vector components (direction, distance) of the waggle dance using recent empirical data from a study that investigated the accuracy of the dance. Our results show that the direction component conveys 2.9 bits and the distance component 4.5 bits of information, which agrees to some extent with Haldane and Spurway’s estimates that were based on data gathered by von Frisch. Of course, these are small amounts of information compared to what can be conveyed, given enough time, by human language, or compared to what is routinely transferred via the internet. Nevertheless, small amounts of information can be very valuable if it is the right information. The receivers of this information, the nestmate bees, know how to react adaptively so that the value of the information is not negated by its low information content.

In 1954, Haldane and Spurway (1954) published a paper in the scientific journal Insectes Sociaux with the title “A statistical analysis of communication in Apis mellifera and a comparison with communication in other animals.” Haldane and Spurway (1954), using the data set of Karl von Frisch, looked at the waggle dance communication using an information theory approach, at least in terms of the direction communicated by a dancing bee (von Frisch, 1946, 1967). Of course, von Frisch’s primary target was to understand the dance language, not to obtain a precise calibration to study where the bees had foraged: he chose to work only with good dancers (Chittka and Dornhaus, 1999), which seems to underestimate systematically the error present in the dances (Schürch and Couvillon, 2013; Schürch et al., 2013) and therefore bias the data.

Despite the limitations outlined above, our calculations are a first step, and important questions arise from the calculations. For example, how much information in a dance is useful to a colony? Is one bit of spatial information helpful, that is, fly north or south? How useful are two bits that could communicate four directions unambiguously (north, east, south, west)? And how much better are the 2.9 bits, that is sectors of the circle of about 50°, that bees communicate? Much will probably depend on the environment (Sherman and Visscher, 2002; Donaldson-Matasci and Dornhaus, 2012; Okada et al., 2012), or the benefits of the spatial information may also depend on colony size (Donaldson-Matasci et al., 2013). For example, if a hive were situated in the middle of a large-scale farming landscape with mass flowering crops, a dance with relatively little information might be informative, whereas in a more fragmented landscape with small flower patches, more information will be necessary to allow a dance follower to find an advertised resource. Future honey bee foraging models should incorporate variability in the dance’s information to investigate the relationship between spatial information content and adaptiveness of the dance.”

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