The question deals with over-consumption, and can be answered much in the same way as "what about the trees" and "who will protect animals?" The answer is, as usual: property rights and the non-aggression principle. Using GPS and latitude/longitude, let people parcel out and own a piece of the ocean like they would own a piece of land. Or, let people claim/buy the fishing/mining/whatever rights for a certain parcel of ocean. The point is: private property.
"But won't greedy corporations and people alike just abuse their part of the ocean and over-consume the resources in it?"No. Lets say a logging company owns a forest, and a fishing company owns some "sea-land." It would be a horrendous use of their investment if the logging company, in their lust for riches, completely wiped out its own forest, rendering their investment - land - completely useless for their purposes. It would be make much more sense for them to limit their own production, adjust prices to reflect stretch supply when necessary, replant trees, and otherwise conserve their land and otherwise .
protect their investment
The same concept applies to the fishing company. If a fishing company lets other people dump toxic waste onto its parcel of sea-land and fishes its supply to near-extinction, they're rendering their investment useless. Instead, they might only fish seasonally and actively protect their property.
If a company buys a sea-plot and begins dumping hazardous chemicals which eventually affect the resources/etc. of its neighbors, it would be a violation of the NAP and they could actually be held accountable for damaging the private property of others. Instead, a company can currently throw down a cool couple-hundred grand in front of a handful of bureaucrats and get a tiny, unnoticeable clause hidden in some budget bill to allow the ability to dump toxic waste in "public" rivers and oceans. This affects the lives of billions of people who simply aren't allowed assert property rights over the majority of the earth's population.
certain nations who are typically seen as over-fishers sailing around the whole of the world fishing the ever-loving crap out of everything because, well, why not? It's not their problem. There's no one to say, "get the hell off my property." The simple fact is that people care more for their property than they do that of others. It's not a bad thing, it's human nature: you're going to be more upset if someone breaks your window rather than your neighbor's. It turns out that the profit motive can be used for good as well, so why not give it a chance?
by Murray Rothbard
by Lew Rockwell