We often hear that the oceans are being overfished and that the populations of many ocean animals are rapidly declining. If society transitioned to vegetarianism as a whole (eg. omnivores would be as populous as vegetarians are now), how quickly would the oceans restore? Could this happen in few human generations?
That's an interesting question.
According to this article fisheries can recover even in ten years, so much faster than "a few human generations":
The team ran computer simulations on a massive database of 4,713 fisheries, representing about 78 percent of worldwide fishing activity. By 2050, global fish populations could double if all countries switched to the best management practices.
This can be achieved by:
well-enforced quota system:
in a catch share system (also called a fishing rights system), each fisherman is entitled to a percentage of the total allocated haul. The catch is set by scientists based on the best evidence at the time. If the number of fish in the ocean rises, the number that can be caught can quickly be revised. That gives all fishermen an incentive to use best practices and police their own waters, says Leland, so everyone's piece of the pie gets bigger.
reduce wasteful bycatch
This is not a direct answer to your question, but we can safely assume that if a large part of humans gives up eating fish, it will produce a similar effect to enforced quotas. So, a few years can be the answer.
This article from Nature is less optimistic:
With the possible exception of herring and related species that mature early in life and are fished with highly selective equipment, my analysis of 90 stocks reveals that many gadids (for example, cod, haddock) and other non-clupeids (for example, flatfishes) have experienced little, if any, recovery as much as 15 years after 45–99% reductions in reproductive biomass.
So, in order to fully answer your question, it is important to know how much the biomass was reduced in certain place and its type (e.g. fish species), to be able to evaluate the recovery period.
Conclusion: putting all the information together, I think the ocean, as a whole, can be largely restored in just few years, if vegetarians are about 50% of the total population. However, some places may need much more than that (up to 15 years) to fully recover.
Note: it is important to note that the premise (which is highly implausible today) is not necessary for the oceans to recover in a relatively short period. Political will can change this, as indicated in the National Geographic article:
In the U.S., since 2000, there has been a 70 percent drop in the number of overfished species. The number of fish with rebuilt populations has risen from zero to 39. At the same time, the number of jobs in fishing has risen by 31 percent in the past three years while revenue has risen 44 percent.
In Belize, which has a small artisanal fishery, fishermen have gone from competing with each other to advocating for more protected areas so that fish have safe spawning grounds. They are reporting illegal fishing activities to authorities, working to reduce wasteful bycatch, and supporting efforts to collect the best science.
There is a lot of uncertainty around marine ecosystem recovery. In some areas, there are concerns that even if all fishing stopped, the ecosystem would never return to it's former state. Part of the reason is that over fishing is not the only factor effecting marine life. Warming waters and increased extreme weather also have a large impact. The Gulf of Maine is one example of this1. Over fishing itself can throw an ecosystem out of balance. After fisheries were shut in Cape Cod in the early 1990s, an explosion in the population of foragers prevented plankton numbers from recovering and predators from reaching maturity. It wasn't until around 2010 that predator populations have begun to recover.
Thanks to the closing of a number of fisheries around the world, we have some data on how quickly marine ecosystems recover. Using the supplementary data from a 2006 report on biodiversity loss, I calculated that 43 marine reserves (areas fully protected from fishing) have experienced an average increase in species richness of 5.28% per year. Results in individual fisheries vary widely however, from a 98.3% increase over 2 years in one part of the English Channel, to a 30.6% decline over 10 years in one South African fishery. Data on catch per unit effort (a measure of species abundance) from nine marine reserves shows an average increase of fish abundance of 15.4% per year. Given the small sample size of this data however, this number is unlikely to be accurate.
Given a 50% decline in fish numbers and assuming population growth of 15% per year fish populations would return to 1970 levels in about 5 years.