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Tactile Conditioning And Movement Analysis Of Antennal Sampling Strategies In Honey Bees (Apis mellifera L.)

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Order parameters from image analysis: a honeycomb example.

Forrest H Kaatz¹, Adhemar Bultheel, Takeshi Egami

¹Department of Mathematics and Life/Natural Sciences, Owens Community College, Toledo, OH 43699, USA. fhkaatz@yahoo.com

Die Naturwissenschaften

|July 18, 2008

Summary

Honeybees create ordered hexagonal combs, with natural combs being more liquid-like than those built on foundation wax. This study quantifies honeycomb order using novel real and reciprocal space parameters.

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Area of Science:

Biophysics
Materials Science
Entomology

Background:

Honeybee combs exhibit remarkable hexagonal geometric order, a subject of fascination since antiquity.
Quantifying the structural order in naturally formed honeycombs is crucial for understanding bee construction.
Previous analyses lacked comprehensive methods to measure honeycomb structural perfection.

Purpose of the Study:

To quantitatively assess the degree of order in honeybee combs using advanced analytical techniques.
To compare the structural order of naturally built combs versus those constructed with artificial foundation wax.
To introduce and apply the Debye-Waller Factor (DWF) for analyzing honeycomb structure.

Main Methods:

Employed real-space methods: pair distribution function (PDF) and radial distribution function (RDF).

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Utilized reciprocal-space analysis incorporating the Debye-Waller Factor (DWF).

Derived real-space (OP(3)) and reciprocal-space (u) order parameters, ranging from 0 (disordered) to 1 (perfectly ordered).

Main Results:

Analyzed honeycombs (Apis mellifera ligustica) showed OP(3) values from 0.33 to 0.60 and u values from 0.59 to 0.69.
Naturally constructed combs exhibited a 'liquid-like' order compared to the more crystalline structures built on foundation wax.
Man-made foundation wax significantly enhances the orderliness of honeybee-constructed hexagonal cells.

Conclusions:

Honeybee combs, while ordered, display a degree of 'liquid-like' characteristics in their natural state.
The use of foundation wax by humans leads to highly ordered hexagonal cell arrays.
The employed PDF, RDF, and DWF methods provide a robust framework for quantifying order in 2D arrays, applicable beyond honeycombs.