SAN FRANCISCO — Before the massacre of 50 people in New Zealand mosques last week, the suspect released a document called "The Great Replacement." The first sentence was: "It's the birthrates." He repeated it three times.
If the phrase about replacement sounded familiar, perhaps that was because it echoed what white supremacists bearing tiki torches shouted in Charlottesville, Va., in 2017: "You will not replace us." It is also the slogan of the neo-Nazi group Identity Evropa.
Behind the idea is a racist conspiracy theory known as "the replacement theory," which was popularized by a right-wing French philosopher. An extension of colonialist theory, it is predicated on the notion that white women are not having enough children and that falling birthrates will lead to white people around the world being replaced by nonwhite people.
And like so many fundamentalist ideologies, the foundation of this one requires the subjugation of women.
"For people in the white power movement, everything is framed through reproduction and gender," said Kathleen Belew, a history professor at the University of Chicago who has studied these groups.
As far-right groups have grown across the world, many of their members have insisted that the most pressing concern is falling birthrates. That concern, which they see as an existential threat, has led to arguments about how women are working instead of raising families. The groups blame feminism, giving rise to questions that were unheard-of a decade ago — like, whether women should have the right to work and vote at all.
The obsession with birthrates is both shaping policy goals within the far right and serving as a rallying cry for recruitment. Experts tracking these movements say they are alarmed by the speed and strength with which the idea is spreading, especially among young radicals.
"In their minds, in this clash of civilization, white men are in a weaker position because their women are not doing the work of reproducing," said Arun Kundnani, a professor at New York University and author of "The Muslims Are Coming! Islamophobia, Extremism and the Domestic War on Terror." "They are saying, 'Look, Muslims have got their women where they need to be, and we're not doing a good job at that.'"
The concern over birthrates has hit a fever pitch in part because of recent studies showing sperm counts and testosterone declining. Some men are buying sperm counters to use at home, and some are turning to testosterone replacement therapy, convinced that modernity has feminized them. These have given old fears a new scientific sheen and led many in these communities to more apocalyptic, violent politics.
"It's all related to lower sperm counts and increasing sexual dysfunction," said Paul Elam, the leader of A Voice for Men, a men's rights group. "In my community right now, there's almost this nihilism and cynicism that says, 'Let it burn.'"
And so an old rallying cry is getting refurbished for a new generation.
"The way that emotion gets engaged in the right wing today is almost always around questions of fertility," said Paola Bacchetta, a professor at the University of California, Berkeley, who serves on the board of the Center for Right-Wing Studies. "It's about their anxieties about their male others. They fear that they will overproduce them and eliminate them."
Though these fears fester in online message boards, they are spreading to more mainstream right-wing conversations. The Fox News host Tucker Carlson, for one, has engaged in some of these conversations. In January, he opened his show with a segment he said was "the biggest issue facing this country going forward," bigger than wars and G.D.P.: the collapse of families. The major cause of that collapse, he said, was that some women now out-earn some men.
(Mr. Carlson's discussion of the topic attracted fierce criticism, something he addressed on his show the next night. "This is why important science is no longer being conducted," he said of the response. "It's why art isn't being made and comedy is dying.")
The birthrate panic has been bubbling back up for some time. In a 2012 book by the French philosopher Renaud Camus, he argued that all Western countries were reckoning with erasure by birthrate. That has helped fuel nativist campaigns like the one by the Dutch politician Geert Wilders. It became the animating philosophy in the Charlottesville, Va., attack. And Representative Steve King, the Iowa Republican, tweeted in 2017, "We can't restore our civilization with somebody else's babies."
Many of these groups have seized on statistics showing a slowing birthrate in some Western countries. In the United States, the total fertility rate is now about 1,765.5 births per 1,000 women, according to the Centers for Disease Control and Prevention, which is below the level necessary to keep the population stable without immigration.
The birthrate conversation — and the question that goes with it, of women's continued freedom — has become a key recruitment tool for white supremacists. It is often the first political point of agreement a white supremacist recruiter online will find with a target, especially with young people.
"In gaming and comic books and all these things that aren't politically related, anti-feminism is an easy access point to make your case and then begin people's journeys," said Annie Kelly, a doctoral student at the University of East Anglia in Britain who is researching the impact of digital cultures on anti-feminism and the far-right.
Clifford Leek, a professor of sociology at the University of Northern Colorado and the president of the American Men's Studies Association, said the recruiters would focus on teenagers who were experiencing insecurities and who had already been exposed to some of these ideas online.
That has made old debates new again. And in the loose collection of anti-feminist blogs known as the "manosphere," basic ideas around gender equality that have long been taken for granted are now being relitigated. Ideas like banning women from the workplace are bandied around casually in these communities. And most of it is presented amid memes and jokes, as was the case throughout the New Zealand suspect's manifesto.
"Good-faith proponents have this naïve understanding that bad ideas can be defeated by the power of argument," Ms. Kelly said. "Bad-faith proponents have a vested interest in the idea being back on the table."
Once a group of people in an online forum agree that declining white birthrates are an existential threat, then the conversation turns to policies. In some cases the response is that nonwhites should be killed. Often the response is white women need to be re-educated.
"What's gaining more of a foothold is the idea of reversing a woman's right to vote," she said. "That was something I used to see in the overtly neo-Nazi spaces, but now I'm seeing it introduced in less extremist spaces. First introduced as a joke, of course, then as an acceptable policy that maybe not all users agree with but is worth discussing."
An earlier version of this article placed certain comments by the Fox News host Tucker Carlson out of context. The comments, "This is why important science is no longer being conducted. It's why art isn't being made and comedy is dying," referred to the quick and broad criticism he received for saying on his television show that a major cause of the collapse of families was that some women now out-earn some men. The comments did not refer to his own remarks about the impact of women out-earning men.