AbstractThe effect of current harvesting on future fish stocks is best captured with a multicohort model. In principle, numerical dynamic programming can be used to determine optimal harvesting for any level of fish stocks. In practice, applications to long-lived species of fish have been limited because of the need to have a state variable for each cohort. The problem is further increased if vessel capacity is included as a state variable. Ignoring excess vessel capacity in a fishery with depleted stocks is likely to lead to recommendations for overly drastic reductions in catch. A method is proposed for finding approximately optimal harvesting policies for a multicohort fishery, taking account of changing harvesting capacity. The method is illustrated for the southern bluefin tuna fishery.