Bees aren't just communicating, they are also doing Math!

Summary of key points in the new paper by Seeley, et al, on Swarm Decision
Making. (In American Scientist)

Swarms leave their hives and spend some time, commonly on a tree branch,
until they have chosen a suitable nest site. The simplest explanation would
be that bees dance for various sites and "persuade" a majority of scouts
that their site is the best. Then the swarm would go to that site. 

But it was observed that swarms would sometimes take flight while there were
still two distinct groups dancing for two different sites. Seeley theorized
that the swarm may have "decided" upon a site based upon the number of bees
*at that site*, which he calls a "quorum". This idea suggests that bees
"vote" for a site by lingering there, and a truly better site will gain
adherents more rapidly than less suitable locations.

Two particularly interesting observations are reported. First, bees perform
more waggle dance circles for better sites, up to 100 circles, vs. as few as
a dozen  or so for a mediocre site. This longer duration causes more
recruits to go to the better site.  

Second, the dancing bees return to the site, wait, and then return to dance
again -- but upon returning the duration of the dance is reduced by a
definite mathematical amount. The amount appears to be optimal, as confirmed
by Mary Myercough, a mathematical biologist from Sydney, Australia. 

Using mathematical models, it was determined that a faster rate of reduction
in the duration of the dance would actually prolong the decision making
process, and slower rate (longer dances continuing) would fail to produce a
clear winner.

Seeley and his co-authors state therefore that the honey bee scouts'
behavior has been fine tuned to produce a "favorable balance between … speed
and accuracy" in the decision making process. 

One can see that without such a system, some swarms would be unable to
decide between very similar nest sites. This system, like any successful
system of voting, must produce a winner. 

[I hope I have presented this in a clear fashion. It is certainly worth
reading the whole articel, but as I said, it is copyrighted and so can't be
posted it here without permission]

pb

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