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 can 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 and thermoregulation. 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 4000-10000 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 {approx} 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.