The New York Times reports: The portion of American families living in middle-income neighborhoods has declined significantly since 1970, according to a new study, as rising income inequality left a growing share of families in neighborhoods that are mostly low-income or mostly affluent.

The study, conducted by Stanford University and scheduled for release on Wednesday by the Russell Sage Foundation and Brown University, uses census data to examine family income at the neighborhood level in the country’s 117 biggest metropolitan areas.

The findings show a changed map of prosperity in the United States over the past four decades, with larger patches of affluence and poverty and a shrinking middle.

In 2007, the last year captured by the data, 44 percent of families lived in neighborhoods the study defined as middle-income, down from 65 percent of families in 1970. At the same time, a third of American families lived in areas of either affluence or poverty, up from just 15 percent of families in 1970.

The study comes at a time of growing concern about inequality and an ever-louder partisan debate over whether it matters. It raises, but does not answer, the question of whether increased economic inequality, and the resulting income segregation, impedes social mobility.

Much of the shift is the result of changing income structure in the United States. Part of the country’s middle class has slipped to the lower rungs of the income ladder as manufacturing and other middle-class jobs have dwindled, while the wealthy receive a bigger portion of the income pie. Put simply, there are fewer people in the middle.

But the shift is more than just changes in income. The study also found that there is more residential sorting by income, with the rich flocking together in new exurbs and gentrifying pockets where lower- and middle-income families cannot afford to live.

The study — part of US2010, a research project financed by Russell Sage and Brown University — identified the pattern in about 90 percent of large and medium-size metropolitan areas for 2000 to 2007. Detroit; Oklahoma City; Toledo, Ohio; and Greensboro, N.C., experienced the biggest rises in income segregation in the decade, while 13 areas, including Atlanta, had declines. Philadelphia and its suburbs registered the sharpest rise since 1970.