## SPEAKING OF SCIENCE A stinging commentary on efficient use of space

Because I recently had to ship a large number of music CDs for Flaming Moth Studio, I was led to ponder the age-old question of how to most efficiently package three-
dimensional objects into a given three-dimensional space.

I have been told that the most efficient use of three-dimensional space is the hexagon.

Bees, of course, know this and build their honeycomb with hexagonally shaped cells. I am not sure how they figured this out because for many thousands of years they did not live in rectangular containers at all, but in roundish hollow trees and stone crevasses. But modern honey bees mostly live in rectangular boxes supplied by beekeepers.

Maybe bees don’t know what they are doing at all. Maybe they are just doing what they are told.

Inside those rectangular boxes, the beekeeper puts sheets of beeswax (or plastic) with a hexagon imprinted on the wax. This is called foundation. The bees then draw out the pattern with additional beeswax until they have a little hexagon-shaped cup. This is where the queen lays her egg or the workers put honey. This increased efficiency achieved by providing the bees’ foundation is magnified even after the first season as the beekeeper only has to cut the cap off of each cell to drain the honey. The foundation can be reused.

But the second year, all the bees have to do is fill the cell with honey and cap it. The bottom and sides are still in place from the previous year. This makes the hive quite a little factory.

But wait. When wild honeycomb is collected from natural sites, the cells average about 4.8 millimeters (but the range is 4.6 to 5.1) in diameter. Standard foundation that is usually sold is 5.4 millimeters in diameter. Some are even as large as 6.6 millimeters.

Why the discrepancy?

Several things affect the size of the cell besides efficient use of the space.

For example, cells that are used for raising offspring are different in size than cells for storing honey. The size of the bee also affects the cell size, with larger bees making larger cells.

The spacing of the frames influences what kind of cell is manufactured. Presumably early, beekeepers developed larger foundation imprints with the idea that larger cells could hold a larger volume of honey. They also thought that larger cells would create larger bees, which in turn would make more honey.

However, these assumptions aren’t necessarily true. Honey production has little correlation with bee size or cell size. But the cell size has become somewhat standardized from usage, and so most suppliers sell foundation with larger cell imprints than bees normally use.

Unfortunately, these trivial details may have non-trivial effects. There is some evidence that the larger cells encouraged by the commercial foundation may provide more room for certain parasitic mites to live within the hive and make the housecleaning chores of the nurse bees more difficult. This, in turn, leads to greater susceptibility to disease, less healthy bees, loss of colonies, less pollination, poor honey production and more expensive honey.

In addition, the reuse of foundation for several years may lead to the buildup of either parasites or environmental contaminants of various kinds.

As is sometimes the case, it appears that attempting to treat crops and insects as if they were biological factories may backfire, and the result is loss of efficiency. Nature seems to have an efficiency of its own that humans sometimes don’t see.

Sadly, none of this was the least bit helpful as I was attempting to package solid, squarish music CD jewel cases into rectangular shipping boxes.

Gary McCallister is professor of biology at Mesa State College and also owner/operator of Flaming Moth Productions and the “Bee bar Bee Ranch,” supplier of native bees, native bee nests and native bee information.

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