Networks

Original Article:

http://www.sciencemag.org/content/333/6038/81.full.pdf

Secondary Article (and Image source):

http://www.economist.com/node/18483411

What if there is a way to predict the severity of wars? Or to predict future attacks? In 2011, Neil Johnson and several of his colleagues at the University of Miami may have found a pattern that could aid military officials in predicting future insurgent attacks on American troops in Iraq and Afghanistan.

In 1948, Lewis Fry Richardson’s discovered  a significant mathematical pattern regarding a correlation between then frequency of wars  and the death tolls associated with each conflict.  His study indicates that very few conflicts have high fatality rates while the vast majority of wars have very low death tolls, and the relationship between the severity and the frequency of war can be illustrated in the Power Law curve function: f(x) = a/(k^c).  In other words, because there is a clear pattern for predicting the severity  of certain wars, the most devastating wars are not pure exceptions and are to be expected given the number of wars in the given history.

Richardson’s study provided the framework for Johnson’s research. Johnson investigated insurgent attacks in 23 different provinces in Iraq and Afghanistan, but instead of focusing on the death tolls associated with each attack, he focused on the frequency of the attacks, or the interval of days between one attack and the next attack. At the end of the study, he noticed that the relationship between the intervals between attacks and the number of attacks follows a progress curve that can be represented by the power law equation: Tn = T1/(n^b), similar to Richardson’s 1948 study. In this equation,  Tn represents the number of days between the attack n and the attack n+1; for example,T1 would be the disparity between the 1st and 2nd attack, T2 would be the interval between the 2nd and 3rd attack, etc. By isolating this equation, it could be possible to predict future attacks based on the time difference between the first attack and the second attack.

In his article, Johnson believes that this trend is largely due to the insurgent groups becoming more accustomed to carrying out attacks and adapting to their situation.  Hence, the insurgents can attack more frequently and efficiently.  He compares the increase in attacks to the scenario in the Red Queen Hypothesis, a theory that is stemmed in evolutionary biology. The Red Queen, which symbolizes the insurgent groups, is engaged in a perpetual struggle with the its opponent, the Blue King, which is represented by the American military forces. Both forces are constantly adapting to its opponent’s movements. Eventually, the intervals between attacks decrease until they reach a predictable interval. As a result, a curve that would follow the logarithmic power law trend is seen.

Intervals between Insurgent Attacks in Farah Province, Afghanistan (The Economist Mar 2011)

However, the equation is not a perfect predictor.  There are several factors that are not included into his calculations that could impact the frequency of attacks, such as changes in leadership structure in the insurgent groups and changes in technology.  There are concerns about the equation itself; the power law curve, while the alignment is close, does not necessarily fit the data perfectly. Moreover, assuming that this study’s conclusion is accurate, there are concerns that if this information is publicized,  insurgents may readjust their movements and make it more difficult for the military to predict their actions . Thus,the study’s application would be rendered useless. However, Johnson dispels this criticism; he asserts that there are external constraints such as the locals’ opinion of the insurgency and the availability of explosive material that would prevent insurgents from acting spontaneously

Nonetheless, even with these issues, Johnson’s study is significant. It could provide the foundation for aiding the military in  predicting future terrorist attacks, which could reduce casualties in these kinds of conflicts.  Furthermore, it is interesting that that these seemingly erratic and random attacks may follow an unintentional pattern.  More research is needed before one can fully conclude that this pattern definitely exists, but Johnson’s study could provide more opportunities for researchers to explore this pattern, and perhaps, be able to apply to other aspects of warfare in hopes of reducing casualties.