  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.
