According to the most recent data for 2007 from the U.S. Census, 8.4 million boys under 18 were living with a single mother. That's 22 percent of all boys in that age group in the USA.
Lamb says children do better if they have a good relationship with the in-home parent, as well as if the parents have low conflict; if the parent has economic resources; and if children have individual resilience to adverse circumstances.
"What's important is not whether they are raised by one or two parents. It's how good is the relationship with the parent, how much support they're getting from that parent and how harmonious is the environment.
"In the case of Obama, his mother was not particularly well off, though she was well-resourced intellectually and had been to college and had supportive parents," Lamb says.
Michael Kimmel, a sociologist and gender studies expert at Stony Brook University in New York, says the resident parent has a huge effect.
"We see constantly children of single-parent families who thrive because the parents are so devoted because they're compensating for the absence of the other parent," he says.
But Biblarz says the idea "that boys in particular need fathers in the way girls need mothers" doesn't hold true.
"I can tell you there's almost no evidence supporting that," he says. "For a variety of reasons, children who grow up with single fathers, for example, are at higher risk than those who grow up with single mothers for either sex."
In the case of swimmer Phelps, mothers such as Debbie Phelps have the right approach, says Peggy Drexler, author of the 2005 book Raising Boys Without Men.
"Phelps was born with a gift that his mother nurtured," says Drexler, an assistant professor of psychology at Cornell University's Weill Medical College in New York City.
Such mothers "don't hold them back," she says. "They encourage their talents, and drive and encourage independence and a sense of adventure."