"Projections of trends since 1950 suggest a continued depletion of fish and consequent collapse of fisheries."This sentence from the article demonstrates that there are two separate events under discussion; and the distinction needs to be clarified since the article leaves someone not familiar with specific terms to think the discussion is about species extinction.
Definitions of fisheries on the Web:
Generally, a fishery is an entity engaged in raising and/or harvesting fish, which is determined by some authority to be a fishery. ...
en.wikipedia.org/wiki/Fisheries
fishery - a workplace where fish are caught and processed and sold
wordnetweb.princeton.edu/perl/webwn
fishery - the catching, processing and marketing of fish, shellfish etc; a place where fish etc are caught or processed; a fishing company
en.wiktionary.org/wiki/fishery
With that defined, the claim of the article becomes more clear - in general, it is the human impact on food production that is the problem under discussion, not species extinction. Extinction can occur when populations are stressed by fisheries and then they experience another stressor, such as reduced habitat in the areas where spawning occurs. However, that is a relatively rare event and does not underpin the discussion that the OP is pointing towards.
The collapse of a fishery is an economic problem brought about by poor policies controlling the way fishers enter and exit the market based on traditional market signals and the way the resource is exploited by a multinational, unable-to-be-regulated group of profit seekers. When a profit opportunity develops resources are shifted to exploit the fish involved. Without regulation that results in a boom and bust cycle of investment with consequent damaging effects on wildlife populations and human fishing communities alike when the fish "disappear" from the nets.
However, the level at which the bust occurs is usually well above that where most teleost populations (r-selected species) are at risk of extinction from that specific threat. I say "most" because there are some species, particularly those living among coral IIRC, that are able to be fished to extinction.
r- versus K-selected Species
K-selected species usually live near the carrying capacity of their environment. Their numbers are controlled by the availability of resources. In other words, they are a density dependent species. Food availability is one resource that controls population size.
K-selected species have attributes that distinguish them from r-selected species. The attributes of a K-selected species include a long maturation time, breeding relatively late in life, a long lifespan, producing relatively few offspring, large newborn offspring, low mortality rates of young, and extensive parental care. Examples of a K-selected species include elephants, bonobo apes and humans.
On the other hand, r-selected species are the opposite. They are very opportunistic. The attributes of a r-selected species include a short maturation tim, breeding at a young age, a short lifespan, producing many offspring quickly, small offspring, high mortality rates of young, and nonexistent parental care. Examples of r-selected species include waterfleas, insects, and bacteria.
http://www.bioinquiry.vt.edu/bioinquiry/cheetah/cheetahpaid/cheetahhtmls/poprK.htmlI'm not an expert in this area, but I've some exposure to the issues involved because of it is an area of policy I've delved into. Anyone with a background in marine biology could add a lot, I'm sure.