Fish need food. The basis of the food chain in the ocean is phytoplankton, photosynthetic protista. These creatures require dissolved nutrients which are scarce in most areas of the oceans. The major limiting nutrients are soluble nitrogen and phosphorous compounds.

The best fisheries used to be where continental runoff or deep upwelling brough these minerals to the surface waters where they could be assimilated by phytoplankton. Of course, overfishing can destroy ANY stock, no matter how good the underlying food supply.

These minerals are in a dynamic equilibrium. As phytoplankton (or the animals that eat them) die, the resulting dead tissues slowly drift to the bottom of the oceans, carrying their nitrogen and phosphorous in insoluble form to the bottom. This detritus slowly decomposes, releasing soluble nitrogen and phosphorous in the deep bottom waters. The ocean circulation slowly brings these minerals back to the surface, especially around Antarctica, and a few other places where upwellings of deep water occur. The rest of the ocean is a nutritional desert.

In conclusion, we can not farm fish in the deep ocean because there is nothing for them to eat there, except in certain select areas. These areas have been overfished so completely that their natural populations have collapsed. If we limit fish catches rigidly, the fish stocks in these areas can rebound to their natural levels in only a few decades. However, if we allow uncontrolled fishing again, they will disappear as fast as they did the first time.