Gentrifying neighborhoods in New York City have seen an influx of relatively wealthy, young, college-educated single people and a jolt of new housing development.

But a report released Monday found limited evidence the shift had brought with it a harmful effect sometimes associated with gentrification: the widespread dislocation of poorer, nonwhite New Yorkers.

The report by New York University’s Furman Center found that the pressure from rising rents and limited incomes was felt in neighborhoods across the city, both rich and poor, and gentrifying or not. This in turn suggested that a broader approach was needed to address housing issues.

The number of people living in poverty in gentrifying neighborhoods fell by 4.9% between 2000 and 2014, providing some evidence for the displacement of poor people, said Ingrid Gould Ellen, the faculty director of the Furman Center.

But even so, the report showed, the number of people living in poverty in these neighborhoods was higher than it was in 1990.