What the bees know

I’ve written a news story for Nature on a new paper claiming that the bees’ honeycomb is made hexagonal by surface tension, rather than the engineering skills of the bees. They just make cylindrical cells, the researchers say, and physics does the rest. This isn’t a new idea, as I point out in the story: D’Arcy Thompson suggested as much, and Darwin suspected it. However, it seems to be to be potentially underestimating the role of the bees. The weird thing about the work is that it essentially freezes the honeycomb in an unfinished state, by smoking out the worker bees, and they find that the incomplete cells are circular in cross-section – but there’s apparently no reason to believe that the bees had done all they were going to do, leaving the rest to surface tension. Who’s to say they wouldn’t have kept shaping the cells if left undisturbed? It may be that the authors are right, but this current work seems to me to be some way from a proof of that. Well, here first is the story…

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Physical forces rather than bees’ ingenuity might create the hexagonal cells.

The perfect hexagonal array of the bees’ honeycomb, admired for millennia as an example of natural pattern formation, owes more to simple physical forces than to the skill of the bees, according to a paper published in the Journal of the Royal Society Interface [1].

Engineer Bhushan Karihaloo of the University of Cardiff in Wales and his coworkers say that the bees simply make cells of circular cross-section, packed together like a layer of bubbles, and that the wax, softened by the heat of the bees’ bodies, then gets pulled into hexagonal cells by surface tension.

The finding feeds into a long-standing debate about whether the honeycomb is an example of exquisite biological engineering or blind physics.

To make a regular geometric array of identical cells with simple polygonal cross-sections, they can only have one of three forms: triangular, square or hexagonal. Of these, hexagons divide up the space using the least amount of wall area, and thus the least amount of wax.

This economy was noted in the fourth century by the mathematician Pappus of Alexandria, who claimed that the bees had “a certain geometrical forethought”. But in the seventeenth century the Danish mathematician Erasmus Bartholin suggested that they don’t need any such foresight, since the hexagons would result automatically from the pressure of each bee trying to make its cell as large as possible, much as the pressure of bubbles packed in a single layer creates a hexagonal foam.

In 1917 the Scottish zoologist D’Arcy Thompson argued that, again by analogy with bubbles, surface tension in the soft wax will pull the cell walls into hexagonal, threefold junctions [2]. A team led by Christian Pirk of the University of Würzburg in Germany showed in 2004 that molten wax poured into the space between a regular hexagonal array of cylindrical rubber bungs will indeed retract into hexagons as it cools and hardens [3].

Karihaloo and colleagues now seem to clinch this argument by showing that bees do initially make cells with a circular cross-section – as Charles Darwin suspected – and that these develop into hexagons by the flow of wax at the junctions where three walls meet.

They interrupted honeybees in the act of making a comb by smoking them out of the hive, and found that the most recently built cells have a circular shape while those just a little older have developed into hexagons. They say the worker bees that make the comb knead and heat the wax with their bodies until it reaches about 45 oC – warm enough to flow like a viscous liquid.

Karihaloo thinks that no one thought previously to look at cells before they are completed “because no one imagined that the internal profile of the cell begins as a circle” – it was just assumed that the final cell shape is the one the bees make. He says they got the idea from experiments on a bunch of circular plastic straws which changed to the hexagonal form when heated [4].

The question is whether there is anything much left for the bees to do, given that they do seem to be expert builders. They can, for example, use their head as a plumb-line to measure the vertical, tilt the cells very slightly up from horizontal to prevent the honey from flowing out, and measure cell wall thicknesses extremely precisely. Might they not continue to play an active role in shaping the circular cells into hexagons, rather than letting surface tension do the job?

Physicist and bubble expert Denis Weaire of Trinity College Dublin in Ireland suspects they might, even though he acknowledges that “surface tension must play a role”.

“I have seen descriptions of bees steadily refining their work by stripping away wax”, he says. “So surely those junctions of cell walls must be crudely assembled then progressively refined, just as a sculptor would do?”

While Karihaloo says “I don't think the bees know how to measure angles”, he admits that further experiments are needed to rule out that possibility.

Weaire adds that “if the bee’s internal temperature is enough to melt wax, the temperature of the hive will always be close to the melting point, so the wax will be close to being fluid. This may be more of a nuisance than an advantage.”

But Karihaloo explains that not all the bees act as 'heaters'. "The ambient temperature inside the comb is just 25o C", he says. Besides, he adds, the insects strengthen the walls over time by adding recycled cocoon silk to it, creating a kind of composite.

References
1. Karihaloo, B. L., Zhang, K. & Wang, J. J. R. Soc. Interface advance online publication doi:10.1098/rsif.2013.0299 (2013).
2. Thompson, D. W. On Growth and Form (Cambridge University Press, 1917).
3. Pirk, C. W. W., Hepburn, H. R., Radloff, S. E. & Tautz, J. Naturwissenschaften 91, 350–353 (2004).
4. Zhang, K., Zhao, X. W., Duan, H. L., Karihaloo, B. L. & Wang, J. J. Appl. Phys. 109, 084907 (2011).

Now I want to add a few further comments. It seems the authors didn’t know that Darwin had looked extensively at this issue. He felt some pressure to show how the hexagonal hive could have arisen by natural selection. He conducted experiments himself at Down House, and corresponded with bee experts, noting that bees first excavate hemispherical pits in the wax which they gradually work into the cell shapes. There is some fascinating correspondence on this in the link given above, though Darwin never found the evidence he was looking for.

One of the problems with leaving it all to surface tension, however, is what happens when you get an irregular cell, either because the bees make a mistake (as they do) or because edge effects create defects. As Denis Weaire pointed out,

“Bees do make topological mistakes, or are led into them by boundary conditions. Surface tension would entirely destroy their work, because of this, if unchecked! (five-sided cells shrink etc...):there is no equilibrium configuration!”

Another worry that Denis voiced is what happens to the excess wax if the cell walls are thinned and straightened by flow. This does seem to have an explanation: Karihaloo says that wax is not actually removed, it just begins in a somewhat loose, porous state, which gets consolidated.

I also wondered about the cell end caps. The cells in the honeycomb are made in two back-to-back layers, married by a puckered surface made from end caps that consist of three rhombi in a fragment of a rhombic dodecahedron. This turns out – as Denis showed in 1994 (Nature 367, 123) – to be the minimal surface for this configuration. So one might imagine it too could result from surface tension, if the authors’ argument is right. But when I asked about it, Karihaloo said “Pirk et al. have shown that the end caps are not rhombic at all; it is just an optical illusion.” I was surprised by this, and asked Weaire about it – he said this was the first time he’d heard that suggestion, and that he has pictures of natural combs which show that these polygonal end faces are certainly not illusory. Indeed, Darwin and his correspondents mention the rhombi, and those old gents were mighty careful natural historians. So this suggestion seems to be wrong.