Collective thermoregulation in bee clusters

Swarming is an essential part of honeybee behaviour, wherein thousands of bees cling onto each other to form a dense cluster that may be exposed to the environment for several days. This cluster has the ability to maintain its core temperature actively without a central controller, and raises the question of how this is achieved. We suggest that the swarm cluster is akin to an active porous structure whose functional requirement is to adjust to outside conditions by varying its porosity to control its core temperature. Using a continuum model that takes the form of a set of advection-diffusion equations for heat transfer in a mobile porous medium, we show that the equalization of an effective "behavioural pressure", which propagates information about the ambient temperature through variations in density, leads to effective thermoregulation. Our model extends and generalizes previous models by focusing the question of mechanism on the form and role of the behavioural pressure, and allows us to explain the vertical asymmetry of the cluster (as a consequence of buoyancy driven flows), the ability of the cluster to overpack at low ambient temperatures without breaking up at high ambient temperatures, and the relative insensitivity to large variations in the ambient temperature. Finally, our theory makes testable hypotheses for how the cluster bee density should respond to externally imposed temperature inhomogeneities, and suggests strategies for biomimetic thermoregulation.