All politics is local, as the saying goes. The same might be said for produce in Cambridge. Residents have developed an increased appetite for locally grown food in recent years, according to the administrator of the city’s 12 community gardens. “I think it’s primarily due to Cambridge residents wanting to grow their own vegetables and really have a place of tranquility for themselves,” said Jennifer Wright, director of the Cambridge Conservation Commission. About 460 Cambridge residents are using community gardens this year — an increase of more than 100 since 2003, Wright said. “People try some unusual things,” said Kathy Gardner, coordinator at the Peggy Hayes Memorial Garden at 16 Watson St. in Cambridgeport. “Community gardens are a great place to experiment.” The Hayes garden has 13 individual plots. Gardeners grow a range of fruits and vegetables, including tomatoes, green beans, onions, lettuce, peas, herbs and raspberries. Area residents sometimes pick raspberries from bushes lining the fence. The Hayes growing season lasts from spring to late fall. Most gardeners shovel snow during the winter months, among other maintenance duties. Each spring, they prepare the soil in a process known as amending, adding elements such as compost, manure and peat moss to their plots. “It’s not just putting seeds in the ground,” Gardner said. She cited the so-called “locavore” movement — where people grow their own food on small plots, often a ...