Abstract Forage fish—small, low trophic level, pelagic fish such as herrings, sardines, and anchovies—are important prey species in marine ecosystems and also support large commercial fisheries. In many parts of the world, forage fish fisheries are managed using precautionary principles that target catch limits below the maximum sustainable yield. However, there are increasing calls to further limit forage fish catch to safeguard their fish, seabird, and marine mammal predators. The effectiveness of these extra‐precautionary regulations, which assume that increasing prey abundance increases predator productivity, are under debate. In this study, we used prey‐linked population models to measure the influence of forage fish abundance on the population growth rates of 45 marine predator populations representing 32 fish, seabird, and mammal species from 5 regions around the world. We used simulated data to confirm the ability of the statistical model to accurately detect prey influences under varying levels of influence strength and process variability. Our results indicate that predator productivity was rarely influenced by the abundance of their forage fish prey. Only 6 predator populations (13% of the total) were positively influenced by increasing prey abundance and the model exhibited high power to detect prey influences when they existed. These results suggest that additional limitation of forage fish harvest to levels well below sustainable yields would rarely result in detectable increases in marine predator populations.