||The abundance of tuna, an important top predator that ranges throughout tropical and subtropical oceans, is now largely determined by fishing activity. Fishing activity, in turn, is determined by the interaction of fish availability, fishing capacity, fishing costs and global markets for tuna products. In the face of overfishing, the continued sustainable supply of tuna is likely to require improved global governance, that would benefit from modeling frameworks capable of integrating market forces with the availability of fish in order to consider alternative future projections. Here we describe such a modeling framework, in which we develop several simple, contrasting scenarios for the development of the tuna supply chain in order to illustrate the utility of the approach for global evaluation of management strategies for tuna and other complex, stock-structured fisheries. The model includes multiple national and multi-national fishing fleets, canneries and fresh/frozen markets, and connects these to global consumers using a network of flows. The model is calibrated using recent data on fish catch, cannery and fresh/frozen production, and consumption. Scenarios explore the control on future outcomes in the global tuna fishery by representing, in a simple way, the effects of (1) climate change, (2) changes in the global demand for tuna, and (3) changes in the access to fishing grounds (marine reserves). The results emphasize the potential importance of increasing demand in provoking a global collapse, and suggest that controlling tuna production by limiting technical efficiency is a potential countermeasure. Finally we discuss the outcomes in terms of potential extensions of the scenario approach allowed by this global network model of the tuna supply chain.