Geometric solutions in beehives and wasps’ nests

Biology, Mathematics, Robotics

Peek into a beehive or a wasp’s nest (not literally, please) and you will see a queen insect being served by thousands of infertile female workers. Besides taking care of the new offspring laid only by the queen, it is the workers’ job to construct the nest using their own specialised building material.  Bees produce beeswax in abdominal glands while wasps chew on tree bark and wooden objects to create a malleable pulp. In both species, the ‘cement’ is used to build hundreds of six-sided compartments joined together. These hexagonal cells are an almost perfect design, offering maximum stability with minimum material – that is, until the nest truly begins to expand. As the colony grows, other members besides the queen are given permission to reproduce. Since these new fertile females and males are larger than the non-reproductive workers that came before them, bigger cells must be added to the nest. This presents an architectural issue: how can different sized hexagonal cells be joined together indefinitely, without wasting any ‘cement’ by filling in the gaps?  

Researchers across different universities and institutions combined their skills to understand the insects’ solution to this problem. Headed by Michael Smith, a biologist at Auburn University, photos of beehives and wasps’ nests were taken from 10 different species found in Thailand, Costa Rica, Belgium, New Zealand and the United States. Roboticists at Cornell University then developed an image analysis tool to scan over 20,000 cells, gathering information on the lengths of their walls and neighboring compartments. At first, the researchers ignored five-side and seven-sided cells, writing them off as misshapen mistakes. However, they eventually noticed that five- and seven-sided chambers were always built as a pair, bridging the gap between small cells for workers and large cells for new males and queens. Since five-seven pairings have the same number of open sides as hexagonal pairings, they don’t disrupt the nest-building that follows later.  

Incredibly, both bees and wasps use this same form of adaptive architecture even though they aren’t closely related and have evolved to build nests out of entirely different materials. The insects’ most recent shared ancestor goes back 179 million years but both still use the five-seven rule to maintain a population of mainly six-sided cells. This known as convergent evolution - where two different species evolve similar traits independently of one another – and is also a great example of nature’s knack for solving geometric problems in the most optimal way.

Journal references:

M.L. Smith et alHoney bees and social wasps reach convergent architectural solutions to nest-building problemsPLOS Biology. Published online July 27, 2023. doi: 10.1371/journal.pbio.3002211.

M.L. Smith, N. Napp and K.H. Petersen. Imperfect comb construction reveals the architectural abilities of honeybeesProceedings of the National Academy of Sciences. Vol. 118, August 3, 2021, e2103605118. doi: 10.1073/pnas.21036051.

Adaptive architecture: Buildings and objects that are designed to adapt to their ever-changing surroundings.

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