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Police typically identify gang territories by tracking crime, graffiti and other clues. But a simple ecological equation might do the job even better.

There is a mathematical model in the field of theoretical ecology that describes how honeybees and chimpanzees and lions divide up space. In the grand competition for limited resources – i.e., dinner – bee colonies and prides of lions will generally create non-overlapping territories. Boundaries form between one group and the next, as the least bit of competition arises between them, and invariably that boundary sits smack in the middle between the beehives (or lion dens) on either side of it.

All of this sounds a little too simplistic to describe human behavior. As humans, we’d like to think that we rationalize our actions, that we fit them into more complex worldviews than a honeybee could ever contemplate (example: I believe in the importance of small businesses, therefore I shop at the local mom-and-pop corner store). But P. Jeffrey Brantingham, a professor of anthropology at UCLA, believes that human behavior is often far more predictable than we think. And as it turns out, those same spatial Lotka–Volterra competition equations that explain honeybee behavior appear to explain some territorial human behavior, too: specifically, that of rival urban gangs.

Oftentimes, the way we use space is driven by the physical constraints of that space. When you need a gallon of milk, you don’t drive to the grocery store five miles across town. You head for the nearest one, regardless of whether if it’s a Food Lion or a Whole Foods. Social scientists, Brantingham says, tend to look at human behavior from the top-down, examining how people feel and think about such a situation. But in reaching instead for mathematical models, he and his colleagues look at human behavior (and particularly crime) from the bottom-up, examining the basic ways in which our behavior is constrained by physical space.

"If that’s something that constrains humans, that’s also something that constrains many other organisms," he says. "We’re no different than hyenas or lions, or honeybees for that matter."

Honeybees and hyenas stake out territory over a pretty obvious scarce resource: food. But why might gangs do the same? Brantingham and colleagues Martin B. Short, George E. Tita and Shannon E. Reid suggest in a paper published online this week in the journal Criminology that they’re motivated by a similar limited resource: reputation.

"Ultimately, what’s being competed for is your good name, or street credibility, your street rep," says Brantingham, who was the lead author of the paper. "If people recognize you as the toughest person around, then that has all sorts of benefits." (And, of course, more tangible benefits accrue from reputation, too.)

The authors used this mathematical model to identify the territories of 13 street gangs that operate in the Hollenbeck Policing Division of Los Angeles. (Random trivia: not all gangs are territorial by nature. Los Angeles and Chicago have predominantly territorial gangs; the gangs of Vancouver, British Columbia, on the other hand aren’t particularly spatial.)

The researchers identified anchor points of activity for each gang, relying on prior research: the home of a senior gang member, say, a street corner, or a neighborhood park.

"All people are like this," Brantingham says. "You have focal points around your house, or your community center. Honeybees have their hive. Hyenas have their den. And lion prides have their den. Organisms all tend to have an anchor point for their activities, and gangs are no different."

Using these anchor points, the mathematical model drew territorial boundaries between each gang. This is what the development of such territories looks like over time, starting from small densities of initial gang activity:

A mathematical equation obviously can’t take into account the level of detail sociologists can collect on the ground, interviewing gang and community members, documenting graffiti and crime locations. But this theoretical model turned out to predict with pretty remarkable accuracy actual gang violence in Los Angeles. This model suggests most violence would occur not deep into gang territory, but on the contentious borders between gangs. The researchers overlaid actual crime data on top of their model – covering 563 violent crimes, between 1999 and 2002, involving these 13 gangs – and that’s exactly what they saw.

Violent crime in this part of Los Angeles clustered along the theoretical boundaries between gangs produced by the same math equation that tells us how rival honeybees divvy up space. As a practical matter, this suggests police officers might want to focus their resources on these seams between gang territories.

This research also gives us a few other compelling clues about how gangs interact and what causes violence among them. The Lotka–Volterra equation suggests that all things being equal, gangs will divide up space equally (and that may not mean along neat street boundaries). This process occurs when gangs experience more competitive animosity toward outsiders (other gangs) than among themselves. But, importantly, it takes very little competition to create these territories in the first place, or even to maintain them.

"Every time there’s a gang-on-gang shooting, everybody talks about how there’s an 'all-out gang war,'" Brantingham. "But no, the numbers don’t seem to suggest that."

Top image: Skynavin/Shutterstock.com

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