Major U.S. urban centers that became more racially diverse in the wake of the Civil Rights Movement are facing significant re-segregation, a recent analysis shows.

Michael Bader, an assistant professor of sociology at American University, analyzed census data from 1970 to 2010 in more than 10,000 neighborhoods across four major metropolitan areas: New York, Los Angeles, Chicago, and Houston. Maps showing the racial makeup of those neighborhoods can be found here.

He claimed that previous studies had underestimated segregation in many neighborhoods because they did not measure gradual, long-term racial succession.

“The transition models on which they rely measure only whether a group that was not previously present becomes present; or, alternatively, whether a group that was present in a neighborhood is no longer present. But measuring only the presence of racial groups means that they do not measure how the racial composition of various neighborhoods changes over time,” Bader and his co-author wrote.

In fact, over one-third, 35 percent, of all the neighborhoods examined by Bader had experienced “steady resegregation.”

Unlike the traditional method of segregation—White flight—prevalent in the 1970s, the mechanism creating the gradual divides is Whites’ avoidance of neighborhoods with more than a few minorities, according to the study.

“Whites’ tolerance of integration that occurs when minorities move to their neighborhoods does not extend to a desire for integrated neighborhoods,” the researchers wrote. “Whites know less about and are resistant to considering neighborhoods with more than a token number of minorities.”

The study, “The Fragmented Evolution of Racial Integration since the Civil Rights Movement,” can be found on the website of the Sociological Science journal.