When do marine reserves increase fishery yield?

An age-structured model is developed for analyzing the effects of marine reserves and other long-term closures on fishery yield, assuming larvae are well-mixed and that exchange of adults between the open and closed areas is negligible. A number of analytic results are derived, including a formula for the gradient of yield with respect to fishing mortality and closure fraction. Increasing the closure fraction at equilibrium spawning stock biomass (SSB), B, will increase yield if and only if s'(B) > 1/b(0)(0), where s'(B) is the slope of the stock-recruitment curve at B and b(0)(0) is SSB per recruit at zero fishing mortality. Conditions for the level of closure required to prevent stock collapse are also derived. Applications of the theory to canary rockfish (Sebastes pinniger) and Georges Bank sea scallop (Placopecten magellanicus) illustrate that long-term closures increase yield only at low SSB associated with fishing mortalities greater than F-MSY and with low closure fractions. The theory presented here gives simple analytic and graphical techniques for predicting the effects of long-term closures on yield and stock persistence.