Correction: This article has been updated to correct a reference to Jaelyn Delshaun Young's background. We regret the error.

Most people can tell you who the potential jihadists are, especially the ones in Europe and the USA. You can point them out in a group: they are immigrants, or more often, the children of immigrants, who came from the Middle East or North Africa. They often converse among one another in Arabic. Many want to join the Islamic State and other terror groups in Syria, or have gone and since returned. They are mostly men, usually around age 20 or less, and have grown up feeling alienated from the societies in which they live.

Most of this is wrong.

In fact, the UK-based Henry Jackson Society has found that "those who convert to Islam are four times more likely to become terrorists than those who are born Muslims." And in 2015, the Washington Post warned that converts have emerged "as some of the most dangerous and fanatical adherents to radical Islam."

Now a recent study in the Netherlands shows that "the share of converts to Islamist extremism tends to be significantly higher" than those born into the faith. As many as 17 percent of Dutch converts have joined the caliphate, the study's authors claim – seven times more than the percentage of converts to the entire Dutch Muslim community. And most of those are women.

That study is supported by previous reports that show that as many as 25 percent of the French Muslims who have made hijrah to Syria are converts from other faiths. Figures are slightly lower – one in six, or about 17 percent– in Germany. In the UK, according to the Economist, though converts comprise fewer than 4 percent of all Muslims, they account for 12 percent of "home-grown jihadists." And in America, while one-fifth of Muslims are converts, two-fifths, or 40 percent, of those arrested on suspicion of ISIS ties in 2015 had converted.

A review of recent attacks confirms this. Converts were involved in the attempted 2015 Garland, Texas attack on a contest to draw the prophet Mohammed; the killing of four people outside London's Houses of Parliament; and the London July 7, 2005 bombings. Samantha Lewthwaite, the "white widow" said to be responsible for the deaths of more than 400 people – including those killed in the 7/7 attack, is a convert, as was the Belgian Muriel Deguaque, who blew herself up in Iraq in 2005. And in America, Colleen La Rose, aka Jihad Jane, collaborated with another convert, Jamie Paulin-Ramirez, in a failed plot to murder Lars Vilks, the Swedish cartoonist who had drawn cartoons of Islam's prophet Mohammed.

The number of women among them is notable: according to the BBC, unlike the men, the "vast majority" of women who join ISIS from the West are converts. Similarly, according to the Dutch report, of the Dutch converts who have joined the Islamic state, 61 percent were women – a figure that seems consistent with other countries, as well. Among the more well-known: Jaelyn Delshaun Young, then a Mississippi State University chemistry student, apprehended en route to the Islamic State in 2015; Fatima Az Zahra, neé Maria Giulia Sergio, an Italian Roman Catholic convert whom the Italian media now calls "Lady Jihad"; and British ex-punk-rocker Sally Jones, whom counter-terrorists consider an active, effective, and therefore dangerous recruiter.

To read more about social media and recruiting women, click here.

Also of note in the Dutch study is the age of the individuals who have gone to Syria: they are on average 23 (though according to other analyses, the average German and American who makes the trip is 26). The average ISIS-jihadist, in other words, is older than many believe these young radicals to be.

None of this is accidental, according to Mubin Shaikh, a former Muslim radical turned counterterrorism professional and the author of Undercover Jihadi: Inside the Toronto 18. In the early days of the Islamic State, he said in a recent phone interview, ISIS recruiters "would get a bonus if they brought women over. There were units dedicated to recruiting Western women to use as propaganda, specifically targeting converts."

All of which suggests that our current "profile" of your average radicalized Muslim may need updating. And perhaps, too, we should be tweaking elements of counter-terrorism approaches worldwide. Shaikh believes the primary focus needs to be on "human intelligence" and better monitoring within the (Muslim) community. "That's where the best tips come from," he said. "But it's a sensitive topic. Do we need to send more spies into the community? Then the community feels they can't trust anyone anymore. But that's the price you pay. If a threat is coming from a particular community, you need to convince them to come forward."

That community includes converts' families, who often are too uninformed about Islam, and rarely pay attention to what or who has influenced the new convert's decision. And the problem, he said, is that many of these younger converts "don't actually convert to Islam. They convert to extremism." Hence families, especially parents, "need to be vigilant. Identify what they are converting to. People need to know who these groups are. Who are Salafis? Who are Sunnis? Sufis? You need to find out what their ideology is."

But this alone is not enough. "I'm a big believer in sting operations," Shaikh said, "because you often can't talk them out of it. They continue to go down the route of extremism to the road of terrorism." And even if the community goes to the authorities, he pointed out, "how often do we hear 'he was known to the police'? Two of the three London attackers were 'reported to the police.' But what does that mean? So you need more human intelligence. You need spies."

At the same time, Bart Schuurman, an assistant professor at Leiden University's Institute of Security and Global Affairs and co-author of "Converts and Islamist Terrorism," a policy brief produced by the International Center for Counter Terrorism in The Hague, cautioned in a recent interview, "We don't want all converts to be seen as a terror threat. The vast majority do not get involved in terrorism whatsoever." Hence, despite the "overrepresentation of converts" among terrorists and extremists, he said, "conversion itself should not be seen as a risk factor for violence."

Yet the number of violent, radicalized converts to Islam also shows that many current counterterrorism initiatives may be misplaced. Both Schuurman and Shaikh point to popular proposals for Muslim bans in the United States and several European countries. Those bans are especially ineffective, noted Shaikh, if they only involve specific Muslim regions of the Middle East and North Africa. "It's too quickly expanding," he said, referring to radical Islam. "And ultimately it doesn't work anyway, because the majority threat is coming from the inside." Similarly, Schuurman observed, "If you want to prevent people from doing harm to your society, it helps to understand what makes them do harm in the first place; and if you have a 'Muslim travel ban,' if you feed into the narrative that the West is at war with Islam, it doesn't help security in Amsterdam or Chicago."

What does help, said Shaikh, who practices Sufism – a mystic, spiritual movement within Islam – and whose wife converted to Islam from Catholicism, is to create a different narrative, both for those born Muslim and for converts. "I don't think we can stop the conversion. But there is a pro-Western argument to be made that the Muslims who are flourishing in the world are doing so in non-Muslim countries, expressly because of their interfaith, secular cultures. Where in the world has radical Islam brought wealth, or success, or dignity? Name me one place, and I'll sell up and go live there. Because it doesn't exist."

Abigail R. Esman, the author, most recently, of Radical State: How Jihad Is Winning Over Democracy in the West (Praeger, 2010), is a freelance writer based in New York and the Netherlands. Follow her at @radicalstates