Data shows that fisheries can have direct affects on the genetics of fish populations. In the late 1980s and early 1990s overfishing of the Northern and Atlantic Cod resulted in a shift to smaller sizes and earlier maturation. The graph below shows these changes for three distinct populations of cod over time. This helps give a visual representation of how overfishing can cause fish to start to adapt, breeding earlier before they get caught and staying small because it is the large fish that are most desired by fishermen. However, this shows the significance of letting our oceans be fished unchecked. Without caution we might get rid of the type of fish we like the most, not just because they were caught, but because the fish adapt to avoid our selective pressures.
Source: Maturation trends indicative of rapid evolution preceded the collapse of northern cod. Esben M. Olsen1, Mikko Heino, George R. Lilly, M. Joanne
Another study was done to show average changes in fish sizes over a series of generations. They found that large harvested lines declined significantly in mean weight of the fish caught and total weight of harvest compared to a random harvested line. Interestingly these mean weights actually increased for the small harvested lines, which shows the huge impact of size-selective fishing on a population.
Source: Conover, D. O., & Munch, S. B. (January 01, 2002). Sustaining fisheries yields over evolutionary time scales. Science (new York, N.y.), 297, 5578, 94-6.