Cairns, D. K. (1992). Bridging the gap between ornithology and fisheries science: use of seabird data in stock assessment models. Condor, 811-824.
I am not an ornithologist but I love birds, fish and nature in general.... I think it might make sense to say for example get a census of birds who prey on fish and identify which ones are the top predators(birds, or maybe other species in the area...; carnivorous fish... . ) maybe you can put a weight on all these species..... and if you can find a data about the annual catch of fish in the area and the variety.... and also say maybe the maturation right before they can reproduce...
I think lots of possibilities to measure the a possible correlation but to measure and ISOLATE the EFFECT of a particular phenomenon that you are observing is more complicated in nature and in an ecosystem....
Maybe you can create an experiment in an aquarium :) with only say for example PREDATORY versus PREY fish :) This way you can first start for example in the WATER inhabitants before taking into account the seabirds and the human fishing....
Or try experimenting in a Pond or an Aviary with birds and pond.....