Swarm relations

Every beehive is a family. The queen is the mother of almost all the honey bees in the hive, and the workers her daughters. We're all familiar with the role of bees in gathering pollen and making honey, and how workers explore to find flowers and return to the hive to tell their sisters about the location of flower beds to visit. We also know that bees communicate this information via a so-called "waggle dance".

The waggle dance, though not error-free, is an ingenious way for bees to communicate a relative location. On a vertical hive comb, the vertical direction represents the position of the sun, and the bee can communicate the direction that other bees would have to travel relative to the sun by waggling rapidly off the vertical an appropriate direction.

The number of waggles, and the distance that the bee moves while waggling, indicates the distance from the hive to the jackpot. The number of times the dance is repeated indicates how enthusiastic she is about it. The more enthusiasm she shows, the more likely other bees are to become enthused and visit the site.

But collecting honey is not the only use bees have for the waggle dance.

If the hive has been doing well and its population has grown sufficiently, an old queen can leave the hive with about half the workers and some drones (the male bees) in search of a place to form a new hive. Typically, they then find a tree branch or a fence post (or a biologist's apparatus) to form a swarm, where most of the bees wait and a few of the workers become scouts, looking for a site to settle into and build a home. When scouts who have found a likely location return to the swarm, they perform a waggle dance to indicate the location and perceived quality of the site to the other bees.

If enough other bees get excited about a particular site before too much time has elapsed, quorum is reached, and the swarm takes off and settles there.

The mathematical dynamics of this decision-making process has been studied by University of Sydney Professors Mary Myerscough and Madeleine Beekman and former University of Sydney student Dr Timothy Schaerf of the University of New England, among others. In particular Dr Schaerf has constructed a computer simulation of swarming bees and their decision-making process called an "agent-based model".

An agent-based model (ABM) is a type of simulation in which "creatures", or "agents", are given rules that determine what they can do and when they can do it, and (in some sense) an environment in which to act. By their nature, ABMs are random - or probabilistic - and allow us to test hypotheses very quickly as a form of computer-based experiment (which is much faster than working with real bees!).

An experiment you could try with an ABM is whether or not small swarms (with relatively few scouts) or large swarms (with many) have an advantage over the other when it comes to making a good decision quickly. An ABM that correctly captures the essential dynamics can give us answers that are relevant to the biology.

As part of some school outreach programmes that Associate Professor Peter Kim and I have been involved in, we developed a card game based on the ideas of Dr Schaerf's ABM, that could teach high school pupils some of the ideas of this method of computational mathematics and modelling, as well as being (we hoped!) plain fun.

We’ve trialed the game on two separate occasions: once for a bespoke high school visit by two year ten classes from Gorokan High in October 2016; and once for pupils ranging from year seven to year ten at Spectacular Science a few weeks later. Both times, the game was a hit, and we hope to use it again for future events!

The object of the game is to find the best location for a new hive, but without being able to directly communicate its quality with words, and convince enough other players (bees) to go there, much the same goal as real bees have. One of the biggest differences between players of the game and real (or simulated) bees, though, is that bees usually make close to the best decision collectively before the time runs out. Perhaps it's a good thing we humans are not limited to waggle dancing.

About the author

Danya is an applied mathematician in the School of Mathematics and Statistics. His current work is with Associate Professor Peter Kim, studying the effects of social behaviour on the evolution of human longevity. He worked previously with Professor Holger Dullin on an aspect of the gravitational 3-body problem related – if you can believe it – to how cats can land on their feet. Danya has always had a broad interest in science, mathematics and simulation, and the opportunities he’s received allow him to bring these interests together.