In the model we've been working with so far, an ants switches tasks if it encounters fifteen other ants doing the same task within a fixed time. In higher density areas, any given ant will encounter fifteen other ants more quickly than it would in lower density areas. Therefore, overall more ants will be leaving task areas with higher densities than areas with lower densities. When the number of ants entering and leaving each of the three regions is the same, the task distribution stabilizes at 50/25/25% because the densities of ants have now become the same in all three regions. This pattern is an example of a "dynamic equilibrium", a pattern whose stability does not depend on no movement of its parts but rather on a balanced movement of those parts.
What would happen if we reduced the number of encounters that causes an ant to switch tasks? Try it, by moving the Threshold slider to a larger value (say 30), clicking on Setup ants, and then Go. Notice that the 50/25/25% task allocation pattern still results; it is independent of the encounter threshholds so long as they are equal across tasks.
Now start with a fixed number of one kind of ant, say foragers, and see how long it takes for the 50/25/25% pattern to emerge. A timer begins when you click Go and measures how long it takes for the colony to stabilize. You'll find that while the stable pattern is the same for different thresholds (but equal across all three tasks), it takes longer for that pattern to emerge with larger thresholds and less time to emerge with smaller thresholds. This is a general characteristics of dynamic equilibria, as seen in a variety of situations including diffusion.
The question we started with though was whether the 50/25/25% pattern is inevitable, i.e. is it the only stable pattern that a system like this can produce? Try altering the encounter threshold for just one of the tasks. Does a stable distribution emerge in this case? Is the pattern the 50/25/25% pattern or some different one? How many different stable patterns do you think this system can yield? This too is a general property of dynamic equilibria, and quite significant in, for example, the generation of resting potentials in neurons.
Dynamic equilibria have some other interesting properties too. Suppose that the size of the task regions was for some reason changed. Would there then be the wrong number of ants for particular tasks or would the ants automatically alter their task assignments to adjust to changes in the space alloted for particular tasks? Try increasing the forager task area by clicking on Add foraging and drawing on the arena (you can do the same for any other area). When you increase the area devoted to a particular task the percentage of ants doing that task increases even though each ant is continuing to interact with other ants in exactly the same way. Can you figure out why?
But let's get back to social organization and ant colonies. Supposing there WERE a director who wanted to change the numbers or proportions of ants doing different tasks. What would happen if they just added ants to try and change the proportions? How could they alter the proportions?
Social organizations seem to have "a life of their own", i.e. they may resist change by a director, and even to have properties that seem to be independent of the particular individuals that make them up. Could the latter occur in a system as simple as the one we are working with? Let's explore that question next...
Organization and Interactions: Part 1 Part 2 Part 3 Part 4
Changing Group Behavior: Part 1 Part 2
Conclusions and Extensions
Complete Model and Model Details
Exhibit by Laura Cyckowski and Paul Grobstein, in association with the Serendip/SciSoc Group, Summer 2006.
Applets created by Laura Cyckowski, using NetLogo, the availability of which is gratefully acknowledged.
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