Strength-mass scaling law governs mass distribution inside honey bee swarms

To survive during colony reproduction, bees create dense clusters of
thousands of suspended individuals. How does this swarm, which is orders
of magnitude larger than the size of an individual, maintain mechanical
stability? We hypothesize that the internal structure in the bulk of the
swarm, about which there is little prior information, plays a key role in
mechanical stability. Here, we provide the first-ever 3D reconstructions
of the positions of the bees in the bulk of the swarm using x-ray computed
tomography. We find that the mass of bees in a layer decreases with
distance from the attachment surface. By quantifying the distribution of
bees within swarms varying in size (made up of 4000–10,000 bees), we find
that the same power law governs the smallest and largest swarms, with the
weight supported by each layer scaling with the mass of each layer to the
≈1.5 power. This arrangement ensures that each layer exerts the same
fraction of its total strength, and on average a bee supports a lower
weight than its maximum grip strength. This illustrates the extension of
the scaling law relating weight to strength of single organisms to the
weight distribution within a superorganism made up of thousands of
individuals.