  In a recent paper List, Elsholtz and Seeley [Phil. Trans. Roy. Soc. B. 364
(2009) 755] have devised an agent-based model of the the nest-choice dynamics
in swarms of honeybees, and have concluded that both interdependence and
independence are needed for the bees to reach a consensus on the best nest
site. We here present a simplified version of the model which can be treated
analytically with the tools of statistical physics and which largely has the
same features as the original dynamics. Based on our analytical approaches it
is possible to characterize the co-ordination outcome exactly on the
deterministic level, and to a good approximation if stochastic effects are
taken into account, reducing the need for computer simulations on the
agent-based level. In the second part of the paper we present a spatial
extension, and show that transient non-trivial patterns emerge, before
consensus is reached. Approaches in terms of Langevin equations for continuous
field variables are discussed.
