Bayesian decision analysis and uncertainty in fisheries management

Large variability and estimation errors in data create challenges for estimating risks and identifying appropriate fisheries management strategies. The formal quantitative method of decision analysis, sometimes referred to as statistical decision theory, can help deal with this challenge because it explicitly considers uncertainties in quantities such as parameters of dynamic processes in fish populations or fishing fleets. Field data can be used in conjunction with Bayesian statistical analysis to calculate probabilities associated with different estimates of the uncertain parameters. These probabilities can then be used as part of a decision analysis to identify the optimal management action for each specified management objective. We illustrate this approach of decision analysis with three examples. (1) The optimal decision for opening an in-river sockeye salmon fishery depended, among other things, on the assumed functional form (not just parameter values) of the stock-recruitment relationship, i.e. whether it was a Ricker model or a more flexible Shepherd model, which can take on various shapes, including a Ricker shape. (2) When uncertainties in density-dependent growth and in size-dependent vulnerability to fishing gear were accounted for, the optimal stocking density for juvenile rainbow trout in British Columbia lakes increased considerably compared with the case where uncertainties were ignored. (3) Marine fish stocks such as Atlantic menhaden typically exhibit large uncertainty in estimates of current stock biomass and stock-recruitment relationships. We show that commonly used arbitrary reductions in harvest rate (such as a 20% ‘safety margin’) that qualitatively try to allow for such uncertainties are not necessarily optimal, and can lead to significant reduction in benefits. Instead, optimal safety margins should be estimated for each situation. These examples demonstrate that it is worth explicitly considering uncertainties in analyses of fisheries management options because they can potentially alter the optimal decision.