The New York Times

ANN ARBOR, Mich.
The coordinated train bombings in Madrid have altered Europe's political structure, shaken global financial markets and unsettled the American-led coalition in Iraq. Although we still do not know for sure who committed the atrocity, the only groups to have claimed responsibility so far say they represent Al Qaeda.

In any event, the attacks are clearly consistent with jihadist doctrine and aims. Osama bin Laden, specifically mentioning the loss of southern Spain to Christianity in 1492, has made it clear that any land once in Muslim hands was fair game for global jihad.

For the last year the Israeli historian Reuven Paz has monitored jihadist writings about Spain, which focused on the Spanish government's participation in Iraq. "In order to force the Spanish government to withdraw from Iraq," one online tract read, "it is a must to exploit the coming general elections in Spain." It added that two to three attacks would ensure "the victory of the Socialist Party and the withdrawal of Spanish forces," the first domino in the collapse of the American-led coalition.

No matter who is responsible for the Madrid attacks, they remind us that America faces a task reminiscent of Hercules' fight against the Hydra, the monster who sprouted new heads for each one severed. From the bombings in Morocco, Indonesia and Turkey last year, to the more recent suicide attacks in Iraq and Pakistan on the Shiite holy day of Ashura, it is clear that since 9/11 we have misunderstood the nature of global jihad.

While most Westerners have imagined a tightly coordinated transnational terrorist network headed by Al Qaeda, it seems more likely we face a set of largely autonomous groups and cells pursuing their own regional aims. Yes, some groups ? from Ansar al-Islam in Iraq to Jemaah Islamiyah in Indonesia to Pakistan's Jaish-e-Muhammed ? seem to be coordinating strategy and perhaps tactical operations among themselves. But for the most part the factions are swarming on their own initiative ? homing in from scattered locations on various targets and then dispersing, only to form new swarms.

While these groups share the motivations and methods of Al Qaeda, it is likely they have had only distant relations with Osama bin Laden and the Sunni salafists around him. In fact, Mr. bin Laden and the Qaeda hardcore should perhaps be viewed as they were in the 1990's, as just one hub of a loosely knit global network of mujahedeen leaders left over from the Soviet-Afghan war. It was only after the F.B.I. began investigating the 1998 American Embassy bombings in Africa that American prosecutors ? and the rest of the world ? began referring to Al Qaeda as a global terrorist organization. We may be overestimating Mr. bin Laden's reach.

The suicide bombings last November in Istanbul are a case in point. Turkish officials immediately attributed the bombings to Al Qaeda, although it quickly became clear that the explosives were probably made and detonated by Turkish groups claiming to represent Al Qaeda's aims. In fact, Osama bin Laden's greatest threat may be that simply by claiming to act in his name, regional groups are better able to recruit and coordinate operations.

United States special forces have recently stepped up their pursuit of Mr. bin Laden in the no man's land between Pakistan and Afghanistan. While it would of course be a triumph to capture or kill him, his demise is unlikely to prove decisive. The war in Iraq has energized so many disparate groups that global terrorism is better prepared than ever to carry on without Mr. bin Laden. Even with many top Qaeda leaders now dead or in custody, the International Institute of Strategic Studies in London is reporting that global recruitment for anti-American jihad is rising and that many small, decentralized groups have sprung up that are harder for governments to identify and neutralize than was the case before the invasion.

Last year, there were 98 suicide attacks around the world, more than any year in contemporary history. Suicide terrorism plagues Iraq for the first time since the 13th-century assassins. A distinct pattern in this litany of atrocities has been pointed out by Robert Axelrod, a political scientist at the University of Michigan. Charting terrorist attacks by organization and lethality, he has noted an increasing interest in well-planned attacks intended to produce high numbers of civilian casualties ? a pattern into which the Madrid bombings, on commuter train stations at the morning rush, fit neatly. This trend also seems to point to an eventual suicide attack using chemical or nuclear weapons.

So what can we do? Traditional top-heavy approaches ? strategic bombardment, invasion and other large-scale forms of coercion ? will not be any use against border-hopping jihadist swarms, and they would only add to their popular support.

Surprisingly, however, pinpoint responses may not be the answer either. Kathleen Carley, a professor at Carnegie Mellon University, has used intelligence data and computer modeling to monitor changes in jihadist networks, including the cell responsible for the suicide bombing of the American Embassy in Tanzania. She found that eliminating the "central actors" ? that is, cell members who have the most ties to other cell members and to other groups ? has actually spurred terrorists to adapt more quickly, and has been less effective in the long run than eliminating less-central foot soldiers. Thus assassinations of leaders (a favorite Israeli tactic) may be counterproductive, in addition to causing public revulsion.

Rather, destroying terrorist networks requires what David Ronfeldt, a RAND analyst, calls "netwar." This is, in effect, mimicking the swarming tactics of the enemy. It involves long missions by smallish, mobile military units that can quickly descend on terrorist groups.

This approach also requires a sort of global spider web ? a set of international and interfaith alliances bonded by mutual trust and purpose. Such a true coalition of the willing would have the collective intelligence and resourcefulness needed to stop the swarms. While Spain's incoming prime minister, José Luis Rodríguez Zapatero, intends to pull Spanish troops out of Iraq, he has said he would back efforts in Iraq and elsewhere as part of a United Nations enterprise. So would much of the world. Just as Hercules needed the help of his nephew Iolaus to kill the Hydra, the United States will not conquer the Islamic terror without the popular support of its allies. The jihadists are betting America will try to go it alone.

Scott Atran, a research scientist at the National Center for Scientific Research in Paris and the University of Michigan, is author of "In Gods We Trust: The Evolutionary Landscape of Religion."