Not many people would recognize the persons who produce their food if they ran into them, but Allyson Angelini’s customers do.

“Our families are invested in what we do,” she said. “We run into them at the library or the beach or wherever in town, and it’s always, ‘There’s my farmer! There’s Farmer Henry! There’s Farmer Allyson! And that’s the relationship that we love.”

Angelini, who runs Full Heart Farm in Ledyard, is one of a handful of farmers in southeastern Connecticut who operates a community-supported agriculture program. CSA shares provide farmers with income at the beginning of the season to grow their produce while guaranteeing customers a box of fresh, seasonal vegetables every week.

According to the National Agricultural Library, CSA programs came to the United States in the 1980s from Europe and Japan, where consumers seeking safe food partnered with farmers seeking a stable income.

Hunts Brook Farm in Waterford is in its 10th year of operating a CSA program, and Rob “Digga” Schacht said it has become a critical part of his operation.

“I feel the CSA is the heart and soul of our farm,” he said. The farm also has stands at area farmers markets, but with the CSA pick-up at the farm every week or every other week, customers can see what’s growing and meet their neighbors.

Kerry Taylor, owner of Provider Farm in Salem, said she and her husband Max worked on other farms with CSA programs before coming to Connecticut in 2012 and wanted to start one of their own.

“We named ourselves Provider Farm because that’s how we saw ourselves in the community,” she said. “We’re real vegetable advocates.”

CSA programs vary in distribution depending on the needs of the community. Hunts Brook, for example, offers a box share, in which customers come to the farm or another designated pick-up site to receive a pre-packed box of whatever produce is fresh that week.

Full Heart started a meal-based CSA in 2012 with seasonal vegetables and chicken or pork, and this year Angelini switched to market-style shares, where participants have a certain number of points each week to spend on products from the farm. Provider offers a market share at the farm and a box share out of Terra Firma Farm in Stonington.

Many farms offer different sizes to suit individuals, couples, or families of all sizes. Some offer CSA shares just for meat, flowers or winter crops like root vegetables and greens in the greenhouses in addition to the bountiful summer harvest.

The programs themselves also develop differently. Schacht said he wanted to make sure he had the right infrastructure on the farm before establishing a CSA program. He felt that it was important to ensure a good experience from the start because a bad CSA experience could permanently scare someone away from the idea.

Baylee Drown, who runs Upper Pond Farm in Lyme, said she had managed a CSA program in Vermont, but her farm’s program started informally with family and friends. This is the third year of the formal CSA, and Upper Pond’s box share includes a selection of staples with one or two unique crops such as kohlrabi or microgreens each week.

“We’re really interested in growing exactly what our customers want and already use in their kitchens,” she said. While it can be hard sometimes to determine what her customers consider to be a “staple,” she said the CSA is the most fulfilling way to market her produce.

All four farmers said the benefit of a CSA program is the community that it builds. Families get to know their farmers and their food, local children grow up eating vegetables they might not have tried otherwise, and the farms give back not only through providing fresh ingredients and recipes but also through community service and food pantry donations.

“It’s much more rewarding feeding people that you know than just packing up boxes and shipping them up to wholesalers or grocery stores,” Angelini said. “It really makes my work feel meaningful.”

a.hutchinson@theday.com