Simulation Study of Biological Reference Points for the Summer Flounder

F_x% is a commonly used proxy or substitute for MSY (where x is usually set equal to 40).  However, F_x% is not in general equivalent to F_MSY.  In order to investigate the difference between F_x% and F_MSY, we developed a simple simulation model capable of representing the relationship between yield and fishing mortality, %MSP, and the curvature of the stock-recruitment curve for a summer-flounder like stock.  The curvature of the stock recruitment curve was parameterized as b.  The model demonstrated that the dynamic trajectories of the stock were heavily dependent upon b.  The model confirmed the dependence of equilibrium yield on b and produced the specific relationship between the magnitude of yield and the magnitude of b.  A decision-theoretic approach was used to suggest that setting x = 40 reduces yield and that smaller values of x produce greater yields.  The analysis focused attention on the fact that the choice of F_x% as a management tool places extreme reliance on the least known and understood component of fisheries biology — the stock recruitment relationship.  While it was difficult to resolve the shape of the stock-recruitment curve, the b averaging enabled in the decision theoretic approach, and the correspondence of traditionally computed B_MSY with high values of b, as well as the literature, all supported the use of lower values of x as a better proxy than F_40%.