Neil Johnson, a professor of physics in UM's College of Arts and Sciences, has developed a formula for predicting terrorist and insurgent attacks.

University of Miami physicist Neil Johnson and his collaborators have developed a simple mathematical model that can estimate the progression of fatal terrorist and insurgency attacks around the world. The research findings are published in the current issue of the journal Science.

The report unveils a new mathematical model that utilizes the time interval between the first couple of attacks in order to forecast the evolution of the conflict. The study, titled “Pattern in Escalations in Insurgent and Terrorist Activity,” establishes how the frequency of fatal attacks escalates following initial incidents arising in particular parts of the world. This simple tool can be useful in creating a plan of action.

The researchers describe a sequence in the timing and frequency of the attacks by using a simple power-law progress curve. The relationship between actions of the insurgency and the counterforce is the result of the two sides continually adapting to each other’s strategies.

“This work is getting to the heart of how the two sides fight, and more than just how they fight, it shows us how they learn over time to adapt to what the other side is doing,” said Johnson, head of an interdisciplinary research group in complexity in UM’s College of Arts and Sciences and principal investigator of the study. “It opens up the possibility of understanding the best way to train people in the military to fight these kinds of conflicts and how one should assess progress.”

The study looks at the timeline of successive fatal attacks from the wars in Afghanistan and Iraq as well as for terrorist assaults from various groups and suicide bombings, including Hezbollah and Pakistan militants. The data show that there is a surprising mathematical relationship between insurgent groups in different provinces and the way in which their activities evolve throughout the conflict. Although the model is not perfectly accurate, there is enough correlation to demonstrate a real pattern, according to Johnson. “The data show a kind of systematic path with this learned adaptation and subsequent counter adaptation,” Johnson said.

The differences and similarities between the insurgency’s actions in different provinces can be broadly predicted in this way but not yet explained. The results point to a deeper connection in the progression of these conflicts, but precisely what drives this connection remains elusive.

“We interpret the events quantitatively in terms of this dynamic adaptation, but there is a highly unexpected way in which these provinces and groups are actually adapting,” Johnson said. “It’s not explained by sociological, economical, religious, or environmental conditions.”

The researchers generalized an evolutionary concept called the Red Queen hypothesis to describe the way the insurgency and the military are constantly adapting to each other’s tactics. The premise of the hypothesis is that organisms continuously evolve to compete against each other for resources in order to survive.

The hypothesis name is inspired by the Red Queen’s race in Lewis Carroll’s novel Through the Looking-Glass. The Red Queen says to Alice, after they race and find themselves still in the same place: “It takes all the running you can do, to keep in the same place.”

Johnson offers his perspective on the Red Queen hypothesis to explain how the two groups affect each other’s evolution. “I think in real life the Red Queen is not stuck in one spot,” he said. “In a real race you get one side pulling ahead, and then the other side tries to catch up. There is a kind of dynamic process going on.”

The findings can be applied to a wide range of human activities. “This work could be used in any process where agents are learning about a system and the system is countering their learning, like the immune system fighting disease, or a computer system facing increasingly sophisticated cyberattacks,” Johnson added.

The study’s co-authors are Spencer Carran, Joel Botner, Kyle Fontaine, Nathan Laxague, and Philip Nuetzel, undergraduate students in UM’s College of Arts and Sciences; Jessica Turnley, president of Galisteo Consulting Group in Albuquerque, New Mexico; and Brian Tivnan, principal engineer at the MITRE Corporation, McLean, and the Complex Systems Center, University of Vermont.