House Hunting
and the Dynamics of Dancing: Mathematics among the Social Insects
Recently mathematicians and engineers
have become interested in modelling the behaviour of social insects
such as ants, bees and termites. These insects are simple individuals
who interact with their nest mates in simple ways. Many hundreds
or thousands of these insects together form a colony that exhibits
finely tuned, subtle and sophisticated behaviour. There are clear
analogies between social insects and neurons in the brain, components
in a computer or individuals in a human society. As an example
of how individual behaviour can generate a colony-wide outcome,
I will discuss some mathematical modelling that has helped find
how honeybees use dances to choose between potential new nest
sites.
In the spring a swarm of bees
may leave the hive and settle in a hanging cluster while scout
bees search for a new nest. A scout that has found a suitable
new home returns to the swarm and communicates the location and
quality of the new site to other bees by waggle dances. Each of
the scout bees need only visit one potential nest site. Nevertheless,
the swarm is able to reliably choose the best available site.
Mathematics gives a clear insight into how the bees perform this
decentralised decision making.
