Four marine fish species are among the most important on the world market: cod, salmon, tuna, and sea bass. While the supply of North American and European markets for two of these species – Atlantic salmon and European sea bass – mainly comes from fish farming, Atlantic cod and tunas are mainly caught from wild stocks. We address the question what will be the status of these wild stocks in the midterm future, in the year 2048, to be specific. Whereas the effects of climate change and ecological driving forces on fish stocks have already gained much attention, our prime interest is in studying the effects of changing economic drivers, as well as the impact of variable management effectiveness. Using a process‐based ecological–economic multispecies optimization model, we assess the future stock status under different scenarios of change. We simulate (i) technological progress in fishing, (ii) increasing demand for fish, and (iii) increasing supply of farmed fish, as well as the interplay of these driving forces under different scenarios of (limited) fishery management effectiveness. We find that economic change has a substantial effect on fish populations. Increasing aquaculture production can dampen the fishing pressure on wild stocks, but this effect is likely to be overwhelmed by increasing demand and technological progress, both increasing fishing pressure. The only solution to avoid collapse of the majority of stocks is institutional change to improve management effectiveness significantly above the current state. We conclude that full recognition of economic drivers of change will be needed to successfully develop an integrated ecosystem management and to sustain the wild fish stocks until 2048 and beyond.