While intuitively appealing, a correct answer (although it sounds hideously like the government talking) is that C&R benefits some fisheries but can actually hinder others.
C&R when effectively practiced - that is, when released fish actually survive - affects fish populations in two ways: abundance of fish and size of fish.
Abundance of fish can only stay the same or increase when anglers practice C&R. Not only do the released fish remain a part of the population, but they also are around to reproduce and contribute to increases in the population.
C&R tends to increase the size of fish. Big fish happen when growth is fast and the fish survive to grow to large sizes. No fish ever grew larger after being harvested, except maybe in the mind of the angler.
C&R is especially effective for building trophy-class fish for longer-lived species such as many marine fish and freshwater fish in the pike, sturgeon and catfish clans.
Now, how can C&R hinder sustaining or improving quality fisheries?
Prolific fish like largemouth bass and crappie can become so abundant that their food supply limits their growth. With slow growth, natural mortality removes fish before they reach large sizes.
Yes, fish remain abundant, but they are small.
Harvest is a way to thin the population and boost growth. Harvesting a fish is a hard thing to do for someone who has bought into C&R and its intuitive appeal.
So how does an angler know when harvest is the right thing to do?
Check the harvest regulations. Low minimum size limits or slot limits and high possession limits are put in place to encourage anglers to harvest fish. Indeed, harvest regulations are a form of C&R - mandatory C&R.
While the simple question might be, "Does C&R really work?" the question that actually leads to better fishing is "When does C&R really work?"
Following is a decision tree to help you make smart C&R decisions and do your part to maintain good fishing opportunities.
1) C&R can improve fisheries when:
Recruitment to the fishery is limited, that is, when spawning is insufficient or survival of young fish is poor. In this case, C&R will increase the abundance of fish.
When big fish are scarce but the fish you catch are heavy-bodied, indicating fast growth rates. In this case, C&R will increase the abundance of large fish.
2) C&R will not improve fisheries, and may even hinder improvement in fisheries, when recruitment to the fishery is good - that is, fish are spawning and juvenile fish are abundant - but fish have slow growth as indicated by fish with poor body conditions (skinny fish.)
A relatively high minimum size limit and possession limit or a slot limit is a fishery manager's way of telling you that recruitment is good and that harvesting fish will improve the fishery.
I foresee another yet-to-be-recognized benefit of C&R. While C&R, when properly practiced, can lead to more and bigger fish, these fish have little value if you can't catch them.
Recently completed research on largemouth bass demonstrated that a bass population is made up of easy-to-catch (catchable) and hard-to-catch (non-catchable) bass.
Further, catchability is heritable - catchable bass spawn catchable bass, while non-catchable bass spawn non-catchable bass. This finding, based on almost 30 years of research and multiple generations of bass, indicates that over time harvest will result in less-catchable bass.
Thus, C&R can help keep catchable bass in the population. Does this hold true for other sport fish? Similar studies are needed for other species, but I would predict that it does.
Of course, this new information about catchability presents management challenges. For example, how do fisheries managers use harvest to improve fish populations and, at the same time, maintain populations with a high proportion of catchable fish?