Scarcity of wild-caught seafood has incentivized innovation and growth in aquaculture, especially for species that compete directly with wild alternatives. In the global tuna industry, the most pronounced scarcity is associated with bluefin tuna species (Atlantic, Pacific, and Southern, which serve similar markets). Supply-side factors including overfishing and governance challenges together with high demand for bluefin as an ultra-premium sushi product have contributed to bluefin scarcity with associated high prices and considerable environmental concerns about the sustainability of the fish stocks. The lucrative bluefin market and limited availability of these tuna from capture fisheries have triggered substantial investment in technologies to farm bluefin tuna. Will technological advances in bluefin tuna farming and market penetration from these operations ultimately alleviate pressure on wild stocks? This paper develops a numerical bioeconomic model of Atlantic bluefin tuna harvest and links the outcomes to developments in the aquaculture industry. We derive a backward-bending supply curve for fish in an age-structured population and show conditions under which technological advances in aquaculture will steer the fishery back to the upward-sloping region of supply.