Sustainable fishing could go on indefinitely. The present levels of commercial fishing cannot be sustained though. Stocks are being exploited far beyond what they can cope with, and one fish species population after another will crash. Some already have. Instead of turning to more sustainable practices the fishing industry has simply turned to different species of fish, with the inevitable result that these too will disappear. Eventually the oceans will run out of fish altogether.
Fish is a renewable resource but not an infinite one. You simply cannot increase the biological productivity of the ocean. Over the last fifty years the technology has evolved to catch more and more fish. Nothing short of a miracle however can make the oceans produce more and more fish.
Our ability to catch fish exceeded the fish available to catch a few decades ago. Some of the fishing methods are unsustainable in themselves. An example is bottom trawling, which destroys the entire seabed. Couple this with the simple problem of taking too many fish and the result is stocks of every species in every ocean are declining.
Just how long commercial fishing can continue before there are no fish to catch is debateable, but we are not talking about long periods of time. If things continue as they are then seafood as we know it will become a memory within one generation or less. The populations of all the seafood we now eat have been forecast to hit near zero by the middle of this century.
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