Why do big cities generate disproportionately large amounts of crime? A new mathematical model helped scientists show that it is easier for criminals to partner-up in major metropolitan areas.

Big cities not only house larger concentrations of potential victims, they also breed larger numbers of criminals. That means would-be perpetrators have an easier time finding accomplices.

"In a big city, you have the potential to meet more distinct people each day," Daniel Abrams, researcher at Northwestern University, said in a news release. "You're more likely to find an appropriate partner to start a business or invent something. But perhaps you're also more likely to find the partner you need to commit a burglary."

Previous studies have shown that as cities grow, crime increases exponentially -- particularly, burglary, auto theft and homicide.

"If you double the size of a city, you don't just double the amount of crime," Abrams said. "You actually more than double it."

To explain the phenomenon, researchers designed a mathematical model to analyze the frequency of crime as a function of social interactions.

Abrams, an associate professor of engineering sciences and applied mathematics, partnered with Vicky Chuqiao Yang, a postdoctoral fellow at the Santa Fe Institute and former doctoral student in Abrams' lab, as well as Andrew Papachristos, a sociology professor at Northwestern who studies social networks in urban neighborhoods.

The trio of researchers populated their model with data from the FBI, Chicago Police Department and the National Incident-Based Reporting System. The scientists used their model to analyze co-arrest records -- when multiple people are arrested for the same crime -- for robbery, motor vehicle theft, murder, aggravated assault, burglary, larceny-theft and rape.

Except for rape, which increased linearly, all of the different types of crime grew exponentially -- or "superlinearly" -- as a city's population increased.

Abrams, Yang and Papachristos published the results of the study this week in the journal Physics Review E.

The authors of the new study suggest the social aspect of big cities also yields positive outcomes, like more patents, small businesses and per capita income.

"The world is becoming very quickly urbanized," Abrams said. "There is a huge mass migration to cities from rural areas. It's important to understand what good and bad effects come with that. In order to promote the good side and reduce crime, we have to understand why it occurs."

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