This undated image released by the U.S. Military in Baghdad, Iraq Thursday, June 8, 2006 purports to show Abu Musab al-Zarqawi, the al-Qaida-linked militant who led a bloody campaign of suicide bombings, kidnappings and hostage beheadings in Iraq, who was killed Wednesday in a U.S. airstrike, Iraq's Prime Minister Nouri al-Maliki announced Thursday, June 8, 2006. (AP Photo/U.S. Military) (HO/ASSOCIATED PRESS)

Gen. John Allen, the retired Marine who is coordinating the campaign against the Islamic State, gave an upbeat briefing to Congress last week. He said that because of airstrikes by the U.S.-led coalition, the group has “lost half of its Iraq-based leadership and thousands of hardened fighters.”

“Decapitation” is the graphic term for this strategy of killing leaders of terrorist groups. The United States adopted this approach against al-Qaeda, most dramatically in the 2011 killing of Osama bin Laden, and many American analysts have assumed that it worked. President Obama made that argument a centerpiece of his 2012 reelection campaign.

But a skeptical caution about the efficacy of targeting top leaders comes from Jenna Jordan, an assistant professor at the Sam Nunn School of International Affairs at the Georgia Institute of Technology. She first distilled her critique in a 2009 article in Security Studies titled, “When Heads Roll: Assessing the Effectiveness of Leadership Decapitation.”

“Decapitation is not an effective counterterrorism strategy,” Jordan wrote bluntly. She said killing top leaders “does not increase the likelihood of organizational collapse,” and that “decapitation is more likely to have counterproductive effects in larger, older, religious and separatist organizations.”

Al-Qaeda’s deadly persistence, in morphed affiliates and offshoots like the Islamic State, is a warning that eradicating a terrorist group is as hard as killing cancer. The Islamic State arose from the embers of al-Qaeda in Iraq, a group that had seemed to be all but destroyed by the U.S. troop surge in 2007 and 2008. Its leader, Abu Musab al-Zarqawi, was killed, but his reincarnation in the Islamic State’s “caliph,” Abu Bakr al-Baghdadi, appears even more toxic.

Analyzing 298 incidents from 1945 to 2004, Jordan found that killing the leader of a group resulted in its collapse only 30 percent of the time. With religious organizations, less than 5 percent collapsed after the leader was killed. Overall, organizations were actually more prone to decline if their leaders survived.

This statistical argument was bolstered with some case studies. Jordan noted, for example, that Israel had been killing top leaders of Hamas since the mid-1990s without blunting that group’s potency. “Not only was Hamas able to continue its activities in the face of repeated attacks to its leadership, it gained strength as the intifada continued.” Similar resiliency was shown by the FARC terrorist group in Colombia.

Jordan updated her contrarian assessment last year in in an article titled “Attacking the Leader, Missing the Mark” in the journal International Security. Here, she focused on the decade-long decapitation campaign against al-Qaeda following its Sept. 11, 2001, attacks on the United States. She found that the United States launched 109 strikes on al-Qaeda leadership between 2001 and 2011. But the number of attacks by the group and its affiliates “rose steadily” over that decade. As the lethality of attacks from al-Qaeda’s core declined, that of its affiliates increased.

“Essentially, al-Qaeda did not suffer a period of degradation,” she warned in the 2014 study. The lesson was that, “even if organizations are weakened after the killing or arrest of their leaders, they tend to survive, regroup and continue carrying out attacks.”

Given the limits of a decapitation strategy, what’s the best policy for the United States and its allies in dealing with the Islamic State? The best analysis I’ve read is an article in the current issue of the Atlantic by Graeme Wood, titled “What ISIS Really Wants.” He makes clear that the group’s viral growth, in social media and on the ground in Iraq and Syria, is the product of a potent appeal to disaffected Muslims by “a religious group with carefully considered beliefs.”

By using the Internet for recruitment and command and control, the Islamic State has become agile and resilient. As its leaders fall in battle, new ones replace them. The images of beheading and torture that alienate mainstream Muslims seem to animate and inspire a hard core of young militants. As Twitter and other social media sites suspend accounts advocating violent jihad, new ones spring up. “Your virtual war on the Internet will pull you into real wars on earth,” boasted a recent post by a pro-Islamic State media group.

What’s ahead is a years-long battle, not just against the Islamic State’s leaders but also its thousands of followers, virtual and real. Wood argues that the group is so red-hot that it is ultimately self-limiting. “Properly contained, the Islamic State is likely to be its own undoing. No country is its ally, and its ideology ensures that this will remain the case.”

The United States may decide that killing the leaders of the Islamic State is necessary, but it won’t be sufficient.

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