Because tuna is so prevalent and easily caught in the wild it is rarely farmed, simply because there is no need. Blue-fin tuna however are becoming rarer and have been farmed inside by certain people. Bigeye tuna is also sometimes farmed, though you will find that most fisherman simply catch it in the wild because there is so much of it in the ocean.

Usually fish that are farmed tend to be rare and difficult to catch in the wild but this is not the case with most tuna. There are different types of tuna fish though and some of them are indeed scarce enough to where farming is a better option than trying to go out in the wild and catch them.