“I come across a lot of people who say, ‘Oh, I was an only child,’ or, ‘I have an only child,’ and they’re concerned about this,” Collins says. “There are certain anxieties that parents have about the only child being deprived of social abilities.”

Even the term itself feels tinged with melancholy, some undercurrent of not-quite-enoughness, but the various alternatives — “singletons,” “onelings,” “one-offspring” — never stuck, and so we are left to ponder the only child. And more American parents are pondering the only child, because more American parents are raising them: The proportion of mothers who had one child at the end of their childbearing years doubled from 11 percent in 1976 to 22 percent in 2015, according to Pew Research Center, and census data show the trend continuing to tick steadily upward.

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Culturally, only-child families — the fastest-growing family unit in the United States — are in the midst of a sea change. Individually, only children are the same as they ever were, which is to say that they are most definitely not all the same, which has never stopped society from branding the cohort with a slew of profoundly unflattering and occasionally contradictory stereotypes. They are spoiled brats, troubled misfits, social aberrations; they’re attention-craving showboats, but also, somehow, reclusive weirdos.

But in recent decades, something has begun to shift. Families are shrinking, and improvements in gender equality have made childbearing more of a question than a given. As Gen X and millennial women prioritize personal and career goals, as couples marry and start their families later in life, more parents find themselves mulling the logistical, financial and philosophical possibilities of a smaller family: What would it mean for them if they had only one child? What would it mean for their offspring?

When they ask Collins, he assures them that he found his circumstances, growing up in New York City in the 1950s, really quite ideal.

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“On weekends, I’d run around with this ragamuffin gang of friends, but at a certain point in the day I would break off and go and hide somewhere. I really enjoyed just being alone,” he says. “What’s wrong with being alone?”

At a child's birthday party a few months ago, Carrie Kilman found herself chatting with a father she'd just met, who had brought his preschooler and his baby to the celebration in their hometown of Madison, Wis. He nodded toward Kilman's 3-year-old daughter and asked: Did she have siblings?

“I said, ‘We’re happily a family of three,’ ” Kilman says, recounting the conversation. “And he gave me this really knowing look that was more than a little patronizing, and he literally just said: ‘Trust me, you’ll change your mind. As she grows up, you’re going to want to give her a sibling.’ ” She sighs. “I’ve gotten this before, several times. It usually comes from men.”

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It’s rare to trace a pervasive social bias to a single source, but experts agree that we can blame the spread of so-called “Only Child Syndrome” — symptoms include social isolation, narcissism and general delinquency — on Granville Stanley Hall, the preeminent child psychology expert of the late 19th century, appointed the first president of the American Psychological Association in 1892. It was Hall’s decidedly unscientific 1896 survey of “peculiar and exceptional children” that led him to famously declare that “being an only child is a disease in itself.”

“His study was done in an era where children were quite isolated, they lived on farms with great distances between them, they had great workloads, and they didn’t interact with other children the way children do today,” says Susan Newman, a social psychologist and author who has researched only children. “He concluded that only children are selfish, they’re lonely, they have more imaginary friends than other children — which is absolutely not true.”

Hall’s theories were ultimately debunked by an onslaught of credible research in the decades that followed. (In the mid-1980s, social psychologist Toni Falbo and researcher Denise Polit examined more than a hundred studies of only children conducted since 1925 and concluded that only children were virtually indistinguishable from other children in terms of personality. Like firstborn children or kids with one sibling, only children were found to have some intellectual and academic advantages.

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While having brothers or sisters can certainly yield benefits for some kids — close, healthy relationships between siblings have been tied to happiness well into old age — the innumerable variables that shape any individual childhood make it especially difficult to draw clear conclusions about siblings vs. singletons as a whole. Overall, Newman says, the existing research simply doesn’t show that only children are at any measurable disadvantage.)

It’s been half a century since “Cheaper by the Dozen” and “The Brady Bunch” were pop culture touchstones. The definition of an American family now spans an incredibly vast and diverse array of possibilities.

And yet.

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“Hall’s ideas just stuck,” Newman says. “As a culture, we became so mired in the stereotype, and it’s very hard to change our thinking.”

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But Newman believes its grip on our collective consciousness is finally loosening. “It’s changing because there are more and more only children, and people are seeing for themselves that only children are not lonely, they’re not odd, they’re not selfish.”

Aimee Taylor, who owns a small marketing company in Ashburn, Va., says she has witnessed this transformation. For years, she believed her first daughter would be an only child — then her second girl arrived unexpectedly when her eldest was 9.

“With my younger daughter, who is 7 now, her friends come from much smaller families; she knows plenty of only children,” Taylor says. “My older daughter really did not; she was alone in not having a sibling. And this is a change in just over a decade or so, living in the same house in the same neighborhood.”

In that decade, prospective parents have struggled to build their careers in the wake of the recession, facing stagnant wages and soaring costs of living. The price tag of raising a child now tops $230,000 (college not included). For those who live and work in cities or wish to preserve the freedom and flexibility they’ve enjoyed well into their 30s, one child may be an appealing solution.

“Purely from a financial standpoint, we live in New York City, in a two-bedroom apartment where my son’s bedroom is the size of a teapot,” says Rachel Nobel Fields, who is raising her 6-year-old son with her husband in Queens. “Logistically, just to try to get to all of his end-of-the-year performances, it’s a lot — and it’s easier to know that he’s the only one I have to worry about.”

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Sometimes, one child is the result of both choice and chance, a result of a narrowing fertility window as parents wait longer to start their families.

“If I was younger, we probably would have had two. But being older, and then with the expense of a child, we are comfortable with one,” says Melissa Wilson, who lives with her husband and 4-year-old daughter in Minneapolis. “We can have fun, we can give her what she needs, we don’t need to worry about it as much as if we had two.”

And sometimes an only child isn’t a question at all.

“It wasn’t so much a conscious decision to not have two children as it just never really came up,” says Beth Carter, who lives in Tacoma, Wash., with her husband and 7-year-old son. “It just was never something that we felt like we needed to do; I just did not have the desire. The question is so often framed as a decision not to have a second instead of a decision to have a second, and I think that’s so interesting, as if that is the default — that you’ll have another.”

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Nonagenarian comedian Betty White loved being an only child: "I did a magnificent job of choosing a mother and father," she has said. "I was the happiest only child in captivity."

Pulitzer Prize-winning author Jane Smiley did not: “I do believe that the children should outnumber the parents,” she once wrote.

People are often drawn to the idea of replicating a childhood model they enjoyed, or avoiding one they didn’t, which means that people who are close to their own siblings — such as Wilson, who moved to Minnesota in part to be nearer to her sister — might feel a bit unsettled at first by the prospect of raising one child.

“I was a little worried about her being an only child,” Wilson says of her daughter, who happily bounces from swimming lessons to gymnastics lessons to quiet time at home, where she likes to paint and practice reading. “But my brother-in-law is an only child, and he has lots of friends, and he did just fine. I just want to make sure she has enough friends that become close enough to be like family to her.”

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Karthika Sasikumar, who is raising her 11-year-old son with her husband in San Jose, has come to feel that only children are uniquely equipped for that challenge.

“Only children are so often accused of being selfish, but in fact what I’ve found is that growing up as an only child makes you more open to the world,” says Sasikumar, who has a sister. “You kind of have to go out and find your people and find your tribe; you don’t have that ready-made for you at home in your family.”

When presented with the question “Do you wish you had a brother or sister?” Carter’s 7-year-old, an avid naturalist, offered “a resounding no,” she says. “He enjoys his friends, but he is an introvert. After school, he needs his quiet time. He’ll say, ‘I’m going to my room,’ or ‘I just want to watch a little David Attenborough.’ ”

Introversion isn’t solipsism; solitude isn’t loneliness. And if loneliness does come for the only child, perhaps it comes much later.

Despite the first line of “Only Child,” Billy Collins did eventually yearn for a sibling, as his parents aged into their 90s. In the poem’s second stanza, he conjures an imaginary sister named Mary, a nurse who helps tend to their elderly parents, and meets him for coffee to reminisce.

“It’s interesting to get together and trade stories with brothers and sisters, probably. What one person forgets, the other person remembers,” Collins says. “There is the burden of memory when it’s just you, and if you forget, it’s forgotten.”

The prospect of such eventual heartache looms for only children and those who raise them, but Fields refuses to be burdened by an unknowable future.

“I’ve heard people say: What about when the parents get older, if you’re an only child?” she says. “But you can’t predict any of that, you can’t predict what’s going to happen.”

What she knows, right now, is that her little son is happy — gregarious, boisterous, the opposite of the shy, reserved only child she once was herself. “He’s very, ‘I’m here! The party has started!’ ” she says, laughing. “It works well for him.”

The only kids are all right, as all right as any of their peers. They’re wallflowers at the school dance, or class clowns, or quiet bookworms. They thrive in their hiding places. They flourish in the spotlight. There will only be more of them.

“The smaller family is definitely here to stay,” Newman says, and adds, emphatically: “One child is a family.”

An earlier version of this story incorrectly listed Eleanor Roosevelt as an only child. This version has been corrected.