  Honey bees make decisions regarding foraging and nest-site selection in
groups ranging from hundreds to thousands of individuals. To effectively make
these decisions bees need to communicate within a spatially distributed group.
However, the spatiotemporal dynamics of honey bee communication have been
mostly overlooked in models of collective decisions, focusing primarily on mean
field models of opinion dynamics. We analyze how the spatial properties of the
nest or hive, and the movement of individuals with different belief states
(uncommitted or committed) therein affect the rate of information transmission
using spatially-extended models of collective decision-making within a hive.
Honeybees waggle-dance to recruit conspecifics with an intensity that is a
threshold nonlinear function of the waggler concentration. Our models range
from treating the hive as a chain of discrete patches to a continuous line
(long narrow hive). The combination of population-thresholded recruitment and
compartmentalized populations generates tradeoffs between rapid information
propagation with strong population dispersal and recruitment failures resulting
from excessive population diffusion and also creates an effective colony-level
signal-detection mechanism whereby recruitment to low quality objectives is
blocked.
