According to a new study led by University of Cambridge researchers, the processes that drive atoms or molecules to aggregate as a crystal have the exact same mathematical structure as the processes that drive stingless bees of the genus Tetragonula when generating their combs.
Combs of two species of the stingless bee Tetragonula displaying structures of (major left) target patterns of Tetragonula carbonaria, (major correct) spirals of Tetragonula carbonaria, (bottom left) double spirals Tetragonula carbonaria and (bottom correct) much more disordered terraces of Tetragonula hockingsi. Image credit: Elke Haege / Tim Heard.
Tetragonula is a genus of more than 30 species in the tribe Meliponini (stingless bees) located in Australia, New Guinea, Indonesia, The Philippines, the Solomon Islands, Malaysia, Thailand, Sri Lanka and India.
These bees are black or dark brown but they have dense white fur on their faces and sides. They measure involving three and four mm in length and are stingless and so are harmless to humans.
Tetragonula bees are extremely social, with a ratio of 1 queen to up to 10,000 workers, and have strict hierarchies.
They naturally nest in hollow trunks, tree branches and rock crevices. They pollinate various essential tropical crops and retailer honey and pollen in honeycomb cells.
“Various species of the genus Tetragonula construct brood combs with open 3D structures consisting of terraces built one on top of another,” stated lead author Professor Silvana Cardoso and her colleagues from the University of Cambridge, the Universidad de Granada and the Messerli Research Institute at the University of Veterinary Medicine Vienna.
“Worker bees add new cells to the edges of each terrace, each of which is then filled with an egg and closed before repeating the process.”
“The resulting morphology is similar to what we see in crystal growth, where crystals grow in terraces of atoms or molecules one on top of another.”
“Likewise, although bees are free to move across and between the terraces — the levels are open so that the bees can get between them like a multi-storey car park — bees are found concentrated at the terraces in these 3D structures.”
Combs of Tetragonula carbonaria: (left) the open structure is like a multi-storey car or truck park or, in this case of a spiral ramp, like the Guggenheim museum in New York (correct) worker bees are observed to invest time clustered at the increasing edges of terraces. Image credit: Tim Heard.
Professor Cardoso and co-authors aimed to investigate how Tetragonula bees produce such complicated brood comb structures.
The researchers examined the bee nests and located a selection of structures that can be classified into: target (i.e. bull’s eye-shaped) patterns, spirals, double spirals and much more disordered terraces.
They then utilized mathematical modeling to simulate the building of the Tetragonula combs.
“Our model shows the minimal complexity necessary — the minimal amount of information a bee needs — to be able to construct such a structure,” they explained.
“It has been considered that bees might be using some overall plan set down — for example — by diffusing chemicals. But our model demonstrates that they do not need such an overall plan if they have the small set of behavioral rules to follow.”
“Thus bee behavior is determined by something: pressure measurements, chemical measurements or dimension/flatness measurements. Bees sense something in their environment, make some sort of computations and then do something.”
“But what is fundamentally different between one view and the other is that in one case only local information is available; in the other view global information is available, albeit sampled locally.”
The team’s model shows that Tetragonula bee comb building, like crystal building, can be the outcome of self-organization.
“Crystal growth and bee comb construction are two systems operating within very different spheres of science,” the scientists stated.
“So what leads to the similar structures? This is the beauty of the applicability of mathematics to nature.”
“It turns out, so often, that similar laws and similar principles govern the formation of very different systems in different areas of science, and thus are describable by the same mathematics. And this is one of those cases.”
“Both crystal growth and this bee comb construction are describable within the mathematical framework of excitable media.”
“Crystals, slime molds, the brain, the heart, chemical oscillators, forest fires and many other systems can function as excitable media. And, in this instance, bees making their combs too.”
The study was published in the Journal of the Royal Society Interface.
S.S.S. Cardoso et al. The bee Tetragonula builds its comb like a crystal. J. R. Soc. Interface 17: 20200187 doi: 10.1098/rsif.2020.0187