Turf wars: math model shows crimes cluster on borders between rival gangs

on Los Angeles’ east side that is bounded by three freeways. Gang activity tends to be confined within the freeway-bounded area.

To determine the home bases for each gang, the researchers relied on a prior study by Tita and his UC Irvine colleagues. The locations of the home bases ranged from a specific street corner to someone’s house, a neighborhood business or any other specific location where a gang gathers most frequently.

Using the Lotka-Volterra formula, Brantingham’s team drew boundaries between the known gangs. Unlike law enforcement’s maps, the resulting effort did not produce gang boundaries that neatly followed streets. Instead, the boundaries ran through the yards of homes and businesses and through alleyways. When the boundaries did land on streets, they were as likely to crisscross them as follow them.

Using police records, the researchers then mapped 563 known gang crimes that occurred between 1999 and 2002 and have been attributed by police to at least one of the thirteen gangs. To their surprise, most of the crimes fell on the borders that the model laid between gang territories. When crime locations did deviate from the borders, they did so in a configuration that was consistent with the model. For instance, the theory predicted that 58.8 percent of the crimes would occur within one-fifth of a mile of the border between two gangs, or just under two blocks, and 87.5 percent within two-fifths of a mile of the border, or just over three blocks. Overall, 99.8 percent of crimes could be expected to occur within one mile of the border, according to the theory.

In fact, the team found that 58.2 percent occurred within two blocks of the border and 83.1 percent within just over three blocks of the border; in total, 97.7 percent of the crimes took place within one mile of the border between gangs.

“You would think that we’re more complicated than other animals, so a model this simplistic shouldn’t work, but I was surprised that it fit as well as it did,” said co-author Martin B. Short, an assistant adjunct professor of mathematics at UCLA.

It is no coincidence that Lotka-Volterra equations would have bearing on the configurations of gang territories: The same forces that define territories in the animal kingdom also are at work in all kinds of rivalries between groups of people, the researchers stress.

“The findings match up with what we know about any conflict,” Tita said. “Skirmishes tend to occur on disputed boundaries on which individuals, organizations or nation-states seek control.”

The researchers plan to compare their gang maps with those derived by law enforcement.

The research, conducted in partnership with the Los Angeles Police Department, was funded by the National Science Foundation and the Air Force Office of Scientific Research.

— Read more in P. Jeffrey Brantingham et al., “The Ecology of Gang Territorial Boundaries,” Criminology (25 June 2012) (DOI: 10.1111/j.1745-9125.2012.00281.x)