A half-block away from the city hall is Diaz Supermarket, a large store that occupies a former Pantry Pride location. It offered beans, cucumbers, peppers, carrots, tomatoes and oranges — at prices just slightly higher than Winn-Dixie and Publix.

Owner John Diaz said he didn’t understand why anyone would consider the area a food desert that needed a farmer’s market. “It’s like going to a Home Depot parking lot and selling plywood.”

That holds true, too, for Liberty City. Thirteen blocks from the lonely tables of GreenWorks on Northwest 62nd Street is a huge, recently remodeled Winn-Dixie with a large produce department.

“We like to be a pleasant surprise,” said store manager James Morris, who says the store also contributes to a local food bank.

While managers say that Winn-Dixie is profitable, grassroots efforts in Miami’s poor neighborhoods remain iffy, especially when they rely on government support. An Overtown vegetable garden on Northwest Third Avenue flourished for three years — until it lost $100,000 a year in support from the city of Miami.

Organizer Marvin Dunn says it was “a forlorn hope” that Overtown residents could maintain the garden as a unsubsidized source of food, but he hoped to get new funding for an agribusiness venture offering jobs to local residents and selling produce to large purchasers.

On the national level, the Obama administration remains strongly committed to bringing fresh produce to poor neighborhoods. Although Congress last year rejected an administration request for $400 million to help supermarkets set up operations in lower-income areas, White House spokeswoman Joanna Rosholm says the administration “continues to work to ensure that all families have access to healthy and affordable food.”

Last year, the Treasury Department provided $25 million in grants to fund healthy food initiatives and a tax credit program was expected to generate over $400 million worth of activities to improve food access, Rosholm said.

The administration has also funded an interactive map through the U.S. Department of Agriculture that shows census tracts that qualify as food deserts. In South Florida, large areas of Opa-locka and Hialeah fit that category, as well as parts of Biscayne Park, Miramar, Pembroke Pines and a section near Northeast 79th Street and Biscayne Boulevard.

Several local nonprofits are also involved in the obesity battle, led by the Blue Cross and Blue Shield of Florida Foundation, which has put almost $900,000 into anti-obesity campaigns in Hialeah and Opa-locka since 2008, including parent cooking classes, working to change a bus route to put it closer to a supermarket and helping build a recreation center in Opa-locka — “a safe place to help them get healthy,” says foundation vice president Susan Towler.

Sturm, the Rand obesity expert, calls the efforts in poor neighborhoods “well intended” but “really misguided.” He believes the attention should be paid to the larger issue, such as super-sized fast foods, to deal with the fact that all of America, rich and poor, is getting fatter.