WASHINGTON — 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.