What drives groups of individual animals to act in a coherent manner? Everyone has seen the oddly coordinated behavior exhibited by flocks of birds or schools of fish as they turn, sweep, and rotate seemingly as one. But how does a group of individuals make decisions about how to move and where to go at once? Do they follow some prescribed and describable mathematical behavior? A symposium at this year's AAAS conference attempted to answer this question.

Professor Ian Couzin from Princeton University opened the symposium by describing his work on modeling the underlying behavior of large groups of individuals. In his work, he describes the equation of motion for any individual entity as governed by three factors: a short-range repulsive behavior, an intermediate range desire to align with neighbors, and a long-range attraction to the group as a whole.

Simulated swarms of creatures that follow these simple rules are able to reproduce the complex motions seen in fish in his laboratory's aquarium. If any one of his three rules is neglected, then the medium-range coherent motion disappears. The addition of an "avoid the predator" rule turned out to be very successful in mimicking the behavior of his fish when they were attacked by a robotic fish predator that was designed for his research.

Taking the work further, to understand what it takes to lead and to follow, he looked at a slight modification of these rules in which each individual's motion was defined by two terms: the conventional rules above, plus a linearly weighted "leader" factor that would cause the individual to move towards a goal, or in some specified direction. It turns out that only a few individuals in a group need to know where they are going in order to lead the group, even if they don't do anything to communicate their leadership role other than move.

Also, the larger a group gets, the smaller the percentage of "knowledgeable" or "leader" individuals that are needed. The limit seems to be about five percent; the remaining 95 percent simply followed the herd. This has interesting implications for evolutionary roles and needs as it sheds light on what a group needs to survive.

Swarming high school students

Bridging the gap between swarming creatures and humans, he reported on an experiment of asking undergrads to evacuate a gym with many exits without talking or communicating with one another. Turns out, much like in his simple models, the group would follow a handful of individuals who were told a specific exit to use ahead of time. Interesting implications/explanations for high school abound here.

The following talk also looked at the spontaneous organization of humans in crowds; Pierre Degond of Paul Sabatier University was motivated by an understanding of crowd safety, and how to design comfortable and efficient areas for crowds to gather in or move through. At high densities—greater than seven people per square meter (gah!)—crowds of humans behave much like incompressible fluids, their motion described by the Navier-Stokes equation. However, at lower, more common densities, there is no single way to model a crowd's behavior.

Degond listed a handful of different approaches that have been used to attempt to model crowd behavior, ranging from individual-based modeling (like in the prior talk) to models based on the chemotaxis. All shared a similar shortcoming: they all lack experimental verification and validation. While it would be unethical to pack a large number of people into a space and deliberately cause a panic just to see if one model works better than others, some form of experimental verification would be nice. Turns out techniques used in special effects and video games held the answer.

The lab space created for the experiment was a large circular track where people were simply asked to walk the (approximately 10-15 m) loop in either a clockwise or counterclockwise direction, again without verbally communicating with others on the track. Each person participating in the experiment was fitted with a set of motion capture reflector balls and their entire trajectory was captured on a computer for later analysis. Various trials were run with between 10 and 35 people in the ring at a time, with varying numbers moving in each direction.

Lanes of people traveling in each direction would spontaneously form without any input from experimenters. These lanes were dynamic and could switch locations—inside or outside—over the course of the experiment. The AAAS conference only allows speakers to present published data, and the research team had not yet carried out more detailed analysis of the results. One thing they are looking to understand is if a person's instantaneous velocity is a function of the density of moving individuals, and if so, what that function looks like. Degond's group also presented the early stages of a new model that was based on what an individual was capable of seeing.

Even though large groups of individuals may have their own thoughts and desires, when brought together, collective behavior spontaneously emerges. Also, what looks chaotic and complex at first glance can be explained, at least partially, by a simple set of mathematical rules.