Mathematical modeling of insurgencies

A few weeks ago Nature had a fascinating article that presented a mathematical model that explains the patterns of insurgencies - their timing of attacks and casualties (Nature 462, 911–914; 2009 - you will need subscription to access it). The data is based on 54,000 events from nine insurgent wars - including Iraq, Afghanistan, Columbia, Sierra Leone, etc. The model suggests that, despite their diverse geographical and political elements, there is a commonality to the way humans wage these wars irrespective of political, cultural, and geographical factors. As expected, there is also some skepticism regarding their claims. Nevertheless, this is a fascinating approach to understanding human warfare. Here is an analysis of the paper:

"We found that the way in which humans do insurgent wars — that is, the number of casualties and the timing of events — is universal," says team leader Neil Johnson, a physicist at the University of Miami in Florida. "This changes the way we think insurgency works."

Johnson and his colleagues argue that the pattern arises because insurgent wars lack a coherent command network and operate more as a "soup of groups", in which cells form and disband when they sense danger, then reform in different sizes and composition. The timing of attacks, the authors say, is driven by competition between insurgent groups for media attention.

Now there are many factors that go into making these assumptions. However, the data can be best explained as a power-law (astronomers also love power-law distributions!):

The researchers collected data on the timing of attacks and number of casualties from more than 54,000 events across nine insurgent wars, including those fought in Iraq between 2003 and 2008 and in Sierra Leone between 1994 and 2003. By plotting the distribution of the frequency and size of events, the team found that insurgent wars follow an approximate power law, in which the frequency of attacks decreases with increasing attack size to the power of 2.5. That means that for any insurgent war, an attack with 10 casualties is 316 times more likely to occur than one with 100 casualties (316 is 10 to the power of 2.5).

"This is surprising because these wars are all fought in different terrains and under different circumstances," says Johnson. "It shows that there is something going on in the way these wars are fought that is common to all."

To explain what was driving this common pattern, the researchers created a mathematical model that assumes that insurgent groups form and fragment when they sense danger, and strike in well-timed bursts to maximize their media exposure. The model gave results that resembled the power-law distribution of actual attacks.

And here are few critiques of the assumptions made in their model:

"They show a nice agreement between the data and their model, which is an important first step," says Aaron Clauset, who researches the mathematics of conflict at the Santa Fe Institute in New Mexico. But he and others question the model's assumptions, such as the number of insurgents in the conflict remaining roughly fixed over time. Clauset says that this idea does not match with other findings.

The model also assumes that insurgent groups can freely break up then re-form. But Roy Lindelauf, who models terrorist networks at the Netherlands Defence Academy in Breda, notes that some insurgents in Iraq are battling each other as well as the coalition forces, and would therefore not merge into a single group.

Lars-Erik Cederman, a researcher in international conflict at the Swiss Federal Institute of Technology in Zurich, adds that the model "has the potential to improve knowledge about warfare". But, he says, the authors "go too far in claiming they have found a universal underlying pattern" because their work includes only nine wars. Cederman, part of a group that regards insurgency as similar to general warfare, also says that although terrorist attacks can be driven by competition for media attention, it remains far from clear whether insurgencies have the same motive.

These are relevant concerns. But this is still a fantastic effort and can potentially be improved as more data comes in. Read this report here and the original paper here (you will need subscription to Nature to read both of these).