Struggle. Plotting the frequency of deadly attacks in an insurgency against their magnitude creates the same pattern as for earthquakes.

J. C. Bohorquez et al./Nature

Power Law Explains Insurgent Violence

War is messy, but it may be predictable. According to a study of nine recent insurgencies around the world, some patterns, such as the risk of violence over time, can be predicted from just a few simple aspects of the conflict.

The insight comes from a study led by Juan Camilo Bohorquez, a physicist at the University of the Andes in Bogotá. In 2005, his team started assembling a database of casualties from the insurgent wars of nine countries: Afghanistan, Peru, Colombia, Indonesia, Iraq, Israel, Northern Ireland, Senegal, and Sierra Leone. The data consisted of 54,679 acts of violence--which they tallied from government and media reports--including the time, date, and the number of casualties for each event. The death toll ranged from a single assassination on the streets of Bogotá to nearly 1000 deaths in August 2005 in Baghdad during a terror-induced stampede.

Although the conflicts have taken place in vastly different contexts--in environments as diverse as jungles, deserts, and urban areas, and with motivations such as religion and land disputes--two striking similarities emerged from the data.

First, the timing of attacks in each conflict proved to be remarkably similar. Rather than occurring randomly, they came in a characteristic "bursty" distribution over time; days of extreme violence were clustered as well. This would be easy to explain if the attacks were coordinated--as they are in traditional command-and-control warfare--but in these conflicts, insurgent groups were acting largely independent of one another, without direct communication.

Even stranger, the distribution of violence within each conflict closely followed a power law, a relationship between two quantities often seen in physical phenomena such as metabolic rates and earthquakes. For example, the power law distribution of earthquakes allows scientists to predict the likelihood of an earthquake of a given magnitude over a given time period. Similarly, a power law seems to determine the chance of a terrorist attack of any given magnitude: such as 10, 100, or 1000 deaths.

To try to explain the mechanism behind these patterns, the team borrowed a simple computer model from economics. The model treated all insurgencies like a marketplace--groups of people constantly deciding whether to act. Rather than coordinating, the groups simply watch the news. The size of the carnage reported at any given time determines the probability that a group of a given size will strike next. Like clockwork, the attacks over the course of the conflict--from the smallest to the most deadly--have the same distribution.

After creating 10,000 virtual wars with the model, the researchers found the same patterns as in the nine real insurgencies. "There is a generic way in which humans 'do' insurgency and terrorism," the researchers conclude in the 17 December issue of Nature. "We are not saying that geography, ethnicity, and cause are irrelevant in conflicts--just that we did not need to consider them to explain the day-to-day data."

It is "an impressively robust finding," says David Lazer, a political scientist at Harvard University, although "it begs a series of follow-up questions." For example, he says, he would like to know more about how the model defines "groups" of insurgents. Even if true, notes Scott Atran, an anthropologist at the University of Michigan, Ann Arbor, the model does not offer much hope of reducing war. "Do they think that just controlling the pulses of the media will choke off the oxygen of insurgencies or terrorism?"