These killings, the fear, and the men radicalized by it: They all reflect what some experts describe as the ­evolution of the hate crime in the United States.

Over the past several decades, academic researchers have charted how hate crimes, which have been rising overall, have increasingly gone from sadistic quests to inflict pain on members of minority groups to violence used as an angry defense against rapid ­social and demographic changes.

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The perpetrators of this share of hate crimes are largely white men who hold the belief, exacerbated by rhetoric in politics and media, that they are protecting their culture, race and an endangered way of life that has historically — and, in their view, rightly — placed them at the top. Some belong to white-supremacist groups, but many don’t.

In their version of the story, these men are not the villains, but the heroes, according to those who study them.

“White-supremacist ideology begins with this acceptance that there is this existential threat against the white race, and this gives people license to rationalize doing anything if it will protect or save the white race,” said Mark Pitcavage, an analyst at the Anti-Defamation League. “And this is one of the factors that leads to a lot of violence.”

There are four commonly cited types of hate crimes, conceived by Northeastern University researchers in 2002 and now used by the National Institute of Justice and taught at the FBI Academy.

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One type is thrill-seeking — the perpetrators, often young white men, seek excitement and to show dominance by terrorizing members of minority groups they consider inferior. There are retaliatory hate crimes, to pay back a group for some alleged transgression. A third type consists of mission hate crimes, which are carried out by people so devoted to hatred that it becomes a career.

The rest fall into the “defensive” category. They are committed by people who believe they are protecting themselves or their territory from perceived outsiders. Perpetrators’ motives can sometimes be mixed.

To create the typology, the Northeastern researchers first analyzed 169 hate crimes that had been reported to Boston police in 1991 and 1992. A later study, published in 2002, found that one-fourth of the crimes were defensive and two-thirds were thrill-seeking in type.

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“It was typically a group of young people who would go out together on a Saturday night, looking for someone to bash” as a way to exert power but also to look cool to friends, study co-

author Jack Levin said. “They would look for gays or Muslims or blacks or people with disabilities,” and if they didn’t find their target, they would just go on to the next minority group.

“Hatemongers don’t specialize,” said Levin, co-director of Northeastern University’s Brudnick Center on Violence and Conflict.

The hate crimes at that point were sadistic, but often less extreme, he said. Fewer people ended up dead.

In recent decades, however, a collision of social forces appears to have reshuffled the balance of hate crimes in America, according to research by Levin and others.

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The shift began after the 9/11 terrorist attacks, which “changed everything,” Levin said. The prevalence of defensive hate attacks connected to threatening events began to increase, Levin noted in a 2015 study he co-authored with Ashley Reichelmann, a professor at Virginia Tech, that was published in American Behavioral Scientist.

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Using FBI data in that study, the authors found that the number of crimes targeting Muslims and Arabs quickly skyrocketed, from 28 hate crimes in 2000 to 481 in 2001.

The same happened when Massachusetts became the first state in 2004 to allow gay marriage, the study said, showing the number of hate-motivated assaults against gay people rising from two in 2002 to 24 in 2004.

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The phenomenon repeated itself with crimes against Latinos, the study found. In 2002, only 1 percent of hate-motivated assault victims were Latino. But by 2010, when unemployment from the Great Recession was at its height and immigration was reconfiguring communities all over the United States, they accounted for 40 percent of victims of hate-motivated assaults.

Levin hasn’t reproduced his original study showing the overall composition of hate crimes, so it’s difficult to say for sure how much the defensive category has grown in percentage. But other experts and additional research support the idea that this kind of hate crime has surged.

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James Nolan, an expert on hate crime at West Virginia University, has also studied how the nature of hate crimes and their perpetrators changed after 9/11. Afterward, he found hate crimes were less likely to be perpetrated by young thrill-seekers than by people older than 40 who were defensive and reactive to perceived social threats.

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The study, which is about to be peer reviewed for publication in American Behavioral Scientist, also found a correlation between political rhetoric during the 2016 presidential campaign targeting minority groups and a subsequent spike in hate crimes against them.

“From the FBI hate crime data we can see how the conditions for defensive hate crimes are created by significant events and the discourse surrounding them,” Nolan said.

Brian Levin, a professor and director of the Center for the Study of Hate and Extremism at California State University at San Bernardino, has reported similar spikes after threatening events, including 9/11, passage of the same-sex marriage law, the election of President Barack Obama and the surge in the unemployment rate. He tallied 1,037 hate crimes in 2016, an increase of more than 23 percent over the previous year in the nine areas he researched.

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Other experts say defensiveness fueled by racial anxiety or social changes perceived as threatening has always been a key motivator for hate crime, regardless of the era. “The root of hate crime has not changed,” said Carolyn Petrosino, a professor at Bridgewater State University, who has written extensively on the issue. “The urgency of maintaining control has.”

The factors researchers cite behind recent hate crimes are many: The manufacturing industry collapsed, and economic inequality widened, making life more financially precarious for many white men. Then when they turn on the television, the faces they see are no longer as white as they once were. The United States, meanwhile, elected its first black president. And underlying it all has been the deep anxiety that some whites feel over the prospect of losing their majority status, scheduled to happen sometime around 2045.

“Cumulatively, these threats operate together to create tremendous anger in some Americans who might otherwise be more tolerant toward people who are different,” Jack Levin said. “Now, they’re looking for someone to blame.”

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The FBI recorded 6,121 hate crimes in 2016, which the agency defines as criminal incidents motivated by race, religion, sexual orientation or gender, more than at any time since 2012. Race or ethnicity is the motivating factor in most hate crimes, but among attacks on the basis of religion, anti-Semitism was most prevalent. The FBI declined to comment about the underlying causes of hate crimes.

All of this occurs at a time when the ideological framework of white supremacy has also undergone a transformation. In the Jim Crow era, when the Ku Klux Klan was at its height, white supremacy was rooted in maintaining overt dominance and resisting the proposals of civil rights activists. But with that battle long over, and with white supremacists cast as history’s losers, their pitch has changed. Today, white supremacy is increasingly centered on the perceived victimhood of whites, left defenseless in a multicultural world of widespread immigration, affirmative action and interracial marriage.

“Dylann Roof thought he was saving the world,” said Heidi Beirich, a project director at the Southern Poverty Law Center. “They’ve come to believe they’re saviors of the white race. . . . I’m doing this to protect my race.”

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Then add the accelerant of political demagoguery exploiting fear and division, amplified by social media communities.

“When I hear the word ‘caravan’ I reach for my gun!” one person wrote on Monday on 4chan, where conspiracy theorists and members of the far-right congregate, when another user shared a picture of a tweet in which President Trump called the migrant caravan headed to the Mexican border an “invasion” rife with “Gang Members.” “RIP humanity,” another user worried.

“The rhetoric coming out of the White House is giving people license to target these people,” said Daryl Johnson, former senior analyst for domestic terrorism at the U.S. Department of Homeland Security, who left the agency in 2010.

There was a time when it was more lonely being an extremist, when similar-minded people were accessible only through newsletters or in-person meetings. Now, all it takes is a computer and an Internet connection to access an online chat room, where the narrative is always easy to understand — it’s all their fault. The communities not only provide an addicting sense of righteousness and superiority, but also an inflated sense of numbers.

“The feeling is that you’re part of a large like-minded cause,” Pitcavage said. “It’s not just a bubble, but an echo chamber, where people are constantly exposed to views — and not moderating views, but views that are just as extreme, if not more extreme, than their own.”

But what makes an extremist a murderer? What tips them into violence?

These are questions that researchers still haven’t been able to answer. “We have no idea what shifts someone from ideology to violence,” Beirich said. “There is no way to know what is the moment of breaking.”

Not all extremists are perpetrators of violent hatred. But most perpetrators, she said, are extremists.

That’s why on Saturday, when news of the Pittsburgh synagogue shooting was first washing across the Internet, she didn’t have to wait for the details to know who the alleged killer was.

“Within three minutes of the CNN story being posted, the first thing that came to mind was member of the radical right, raging anti-Semite, and I bet he’s active online. It’s just the case with so many of these people lately.”

Hours later came the first stories of suspect Robert Bowers’s prolific online history, which included rants against Jews, refugees and African Americans.

“We can not let the . . . get any kind of foothold here,” he wrote in one post weeks before the shooting, using an anti-Semitic word.