MIAMI — Florida freshwater turtles are being illegally caught and exported live in increasingly large numbers to keep up with demand for their meat, their supposed medicinal purposes and their value as pets, state wildlife officials said this month.The black market trade is putting a strain on the state’s already vulnerable fresh water and terrestrial turtle populations, and officials say they expect demand to grow along with the dollar amount poachers in Florida can fetch.Depending on the species, harvesters can make anywhere from $300 to more than $16,000 for a single turtle, officials say.T…