The global wild marine fish harvest increased fourfold between 1950 and a peak value near the end of the 20th century, reflecting interactions between anthropogenic and ecological forces. Here, we examine these interactions in a bio-energetically constrained, spatially and temporally resolved model of global fisheries. We conduct historical hindcasts with the model, which suggest that technological progress can explain most of the 20th century increase of fish harvest. In contrast, projections extending this rate of technological progress into the future under open access suggest a long-term decrease in harvest due to over-fishing. Climate change is predicted to gradually decrease the global fish production capacity, though our model suggests that this is of secondary importance to social and economic factors. Our study represents a novel way to integrate human-ecological interactions within a single model framework for long-term simulations.