This is a good idea — with a federal funding stream, at a time when federal money for subsidized housing has been drastically curtailed — but it has had only negligible success. Recently, the city released the results of a study it had conducted, which looked at the outcomes for a sample of 295 families, 150 of them in receipt of Homebase services and a control group of 145 that was not. Between 2010 and 2012, the families receiving services spent about 22.6 fewer nights in shelters on average than those that were not part of Homebase. Though this is a statistically significant result, it is hardly an impressive one, especially in light of the fact that the average stay for a family in the shelter system is now 13 months, up from 9 months in 2011, and the city is experiencing record levels of homelessness with 50,000 people, including 21,000 children, in shelters every night.

Is the current understanding of prevention too narrow? Do neighborhoods need to be stabilized long before so many families find themselves so close to the precipice? Reason would seem to say yes. The city’s self-analysis, conducted by various academics, places little credence in the impact of the housing market on homelessness. But a report released last month by the Institute for Children, Poverty and Homelessness, a research and policy group, presents a convincing set of facts to defend the notion of causality.

Examining demographic data from Bedford-Stuyvesant and neighboring Brownsville, the study illustrates how those living in poverty might lose their ability to exist on limited resources when the fortunes of a neighborhood dramatically change. Between 2005 and 2010, the median rent, adjusted for inflation, swelled in Bedford-Stuyvesant and Brownsville by more than 22 percent, while the median household income of renters over that same period did not remotely keep pace. (In Bedford-Stuyvesant, the figure rose only 4.7 percent and in Brownsville, income decreased.)

What happens in a scenario like this one is that the poor are not simply competing with wealthier newcomers for limited housing; the poor are competing with one another. Given the west to east progression of gentrification in northern Brooklyn, the study concluded some faction of low-income residents priced out of Bedford-Stuyvesant have presumably moved to Brownsville, an even more depressed neighborhood, thus creating intense competition in a housing market for those least able to engage in it. Brownsville continues to rank among the communities sending the greatest number of families into the shelter system; public housing, despite its high concentration in the neighborhood, only serves a minority of residents.

The Democratic candidates running for mayor all understand that the city needs more affordable housing, and some have proposed innovative ways of paying for it. Nearly everyone agrees that the city needs to create more economic opportunity for those who have the least access to it. But there has been less conversation about how important economic diversity is to the health of neighborhoods. It is not simply that the rich are getting richer and the poor are getting poorer, as the aphorism goes. The poor are poorer in isolation — and islands can be scary places.