DAYTON, Ohio >> As cities like this one try to reinvent themselves after losing large swaths of their manufacturing sectors, they are discovering that one of the most critical ingredients for a successful transformation — college graduates — is in perilously short supply.

Just 24 percent of the adult residents of metropolitan Dayton have four-year degrees, well below the average of 32 percent for U.S. metro areas, and about half the rate of Washington, the country’s most educated metro area, according to a Brookings Institution analysis. Like many Rust Belt cities, Dayton is a captive of its rich manufacturing past, when well-paying jobs were plentiful and landing one without a college degree was easy.

Educational attainment lagged as a result, even as it became more critical to success in the national economy.

“We were so wealthy for so long that we got complacent,” said Jane L. Dockery, associate director of the Center for Urban and Public Affairs at Wright State University here. “We saw the writing on the wall, but we didn’t act.”

Dayton sits on one side of a growing divide among U.S. cities, in which a small number of metro areas vacuum up a large number of college graduates and the rest struggle to keep those they have.

The winners are metro areas like Raleigh, N.C., San Francisco and Stamford, Conn., where more than 40 percent of the population has a college degree. The Raleigh area has a booming technology sector and several major research universities; San Francisco has been a magnet for college graduates for decades; and metropolitan Stamford draws highly educated workers from white-collar professions in New York like finance.

Metro areas like Bakersfield, Calif., Lakeland, Fla., and Youngstown, Ohio, where less than a fifth of the population has a college degree, are being left behind. The divide shows signs of widening as college graduates gravitate to places with many other college graduates and the atmosphere that creates.

“This is one of the most important developments in the recent economic history of this country,” said Enrico Moretti, an economist at the University of California, Berkeley, who recently published a book on the topic, “The New Geography of Jobs.”

The recession amplified the trend. Metro areas where more than 1 in 3 adults were college-educated had an average unemployment rate of 7.5 percent earlier this year, compared with 10.5 percent for cities where less than 1 in 6 adults had a college degree, according to Edward Glaeser, an economist at Harvard and the author of “Triumph of the City.”

Historically, most U.S. cities have had relatively similar shares of college graduates, in part because fewer people went to college. In 1970, the difference between the most-educated and least-educated cities, in terms of the portion of residents with four-year degrees, was 16 percentage points, and nearly all metro areas were within 5 points of the average. Today the spread is double that, and only half of all metro areas are within 5 points of the average, the Brookings research shows.

“There’s a relentless cycle in which knowledge breeds knowledge, but the flip side is that many places are left out,” said Alan Berube, a senior fellow at Brookings who conducted the analysis using census data from the American Community Survey.

Dayton lost about 1 percent of its college-educated 25- to 34-year-olds between 2000 and 2009, at a time when that group grew by 13 percent nationally, said Joe Cortright, senior policy adviser for CEOs for Cities, an economic development group. In Columbus, Ohio, about 70 miles away, the same group grew by 25 percent.

In a pattern that is part education, part family background, college graduates tend to have longer life expectancies, higher household incomes, lower divorce rates and fewer single-parent families than those with less education, and cities where they cluster tend to exhibit those patterns more strongly. Montgomery County, where Dayton is located, has a premature death rate that is more than double that of Fairfax County, Va., the highly educated Washington suburb, according to Bridget Catlin, a University of Wisconsin researcher.

Now, Dayton is racing to produce, attract and retain college graduates as a badly needed food for its hungry economy. But it is a painstaking process. Kate Geiger, who lost her job at General Motors in 2008, said she would never forget the feeling of sitting in a college classroom for the first time after 24 years on the factory floor.

“I am this 44-year-old old-school union girl,” she said, “and here I am with all these 18-year-old kids who have grown up with computers.”

Kelley Shomaker, 23, who graduated from the University of Dayton this year, said she searched for work in Dayton but ultimately received an offer from Rock Hill, S.C., a suburb of Charlotte, N.C. In August, she and two friends will set off for that city to start teaching careers there.

Charlotte, once a city with very little education, now has a population that is more than a third college graduates. Shomaker estimated that 60 percent of her friends were moving to other cities.

Dayton’s past was rich, but by the 2000s the city was in trouble. It lost half of its manufacturing jobs in 12 years, according to Richard Stock, an economist at the University of Dayton. When the city’s last Fortune 500 company, National Cash Register, left in 2009, residents were jolted into action.

“Our premise is you have to change people’s mind-set,” said Thomas Lasley, the former dean of education at the University of Dayton, who runs Learn to Earn, the city’s effort to increase its share of college graduates. “We have to go from one where people think of themselves as being in a high-school-attending culture to being in a college-attending culture.”

One effort has shown marked success. The Dayton Early College Academy, which opened in 2003 as a public high school, focuses on preparing low-income students for college. It sends 97 percent of its graduates to college, the vast majority to four-year programs.

One of the graduates, Francei Brown, plans to attend Morehouse College in Atlanta in the fall. His father, who for years cobbled together part-time jobs fixing cars and doing plumbing and roofing, even in the worst weather, was resolute about college for his son.

“He said, ‘I want you to have a job, where, if it’s cold outside, you’ll be warm inside,”’ Brown said.

Dayton may be struggling to find a second act, but it has strengths that many industrial cities lack. Wright-Patterson Air Force Base is a major employer in the area. Lexis-Nexis, the research company, has a large operation here.

And the city has an above-average share of people with some college — those who have a two-year degree or who have taken some classes but have no degree. Steven Lee Johnson, president of Sinclair Community College here, argues that the paradigm may be changing to one in which students take bundles of courses instead of spending four years on obscure academic topics. The approach has been popular among students here, who tend to have children and busy lives (about a tenth of students at Sinclair are displaced workers).

“There’s a concern among employers that a degree is not specific enough,” he said. “What will count is competencies — very concrete things that you have achieved.”

Even so, those with four-year degrees still tend to have the biggest impact on economic development, Cortright argues.

Geiger, the former GM employee, graduated with an associate degree in graphic design and is now working on a website and planning events for a Harley-Davidson shop.

The job does not pay very well, and she compares it to “new shoes that don’t really fit right yet.” But she loves the freedom of not having to clock in and out.

“It’s so strange to find that there is life after GM,” she said.

© 2012 The New York Times Company