A Decision-Theoretic Approach to Setting Buffers Between Fishery Management Targets and Limits

The usefulness of including a buffer between fishery management targets and limits has frequently been acknowledged. This paper shows how decision theory can be used to set both targets and limits. Decision theory uses expected utility as the objective function to be maximized, and thus requires specification of a utility function. The utility function assumed here exhibits constant absolute risk aversion in the sense of Pratt and Arrow. Maximizing expected utility is shown to be equivalent to maximizing an order mean of antilog relative yield (=exp(yield/msy)) in the stationary distribution. Fishery management targets and limits are computed by assuming different levels of absolute risk aversion in the utility function. It is suggested that the limit be associated with an absolute risk aversion of zero (i.e., risk neutrality), and that the target be associated with some positive level of absolute risk aversion. A simple example model is used to illustrate the theory. Although simple, the model permits examination of the effects of control (implementation) error, estimation error, and process error. The simple example model is used to conduct an experiment where the optimal buffer between the target and limit is computed for each possible combination of parameter values within a factorial design, and the resulting data are used to estimate the coefficients of a set of regressions. The regressions provide an idea of the ranges of buffer sizes that might be expected under various levels of absolute risk aversion, and can be used as a first approximation when data, time, or other resources are insufficient to conduct a full, case-specific analysis. The decision-theoretic approach is compared and contrasted with the “probability-only” approach. Insights are also gained into the process of management strategy evaluation and the relationship between risk aversion and the tradeoff between the mean and variance of long-term yield. This is a draft document and does not necessarily represent agency opinion or policy. 2 Table of