Fitting Surplus Production Models: Comparing Methods and Measuring Uncertainty

Three approaches are commonly used to fit surplus production models to observed data: effort-averaging methods; process-error estimators; and observation-error estimators. We compare these approaches using real and simulated data sets, and conclude that they yield substantially different interpretations of productivity. Effort-averaging methods assume the stock is in equilibrium relative to the recent effort; this assumption is rarely satisfied and usually leads to overestimation of potential yield and optimum effort. Effort-averaging methods will almost always produce what appears to be "reasonable" estimates of maximum sustainable yield and optimum effort, and the r 2 statistic used to evaluate the goodness of fit can provide an unrealistic illusion of confidence about the parameter estimates obtained. Process-error estimators produce much less reliable estimates than observation-error estimators. The observation-error estimator provides the lowest estimates of maximum sustainable yield and optimum effort and is the least biased and the most precise (shown in Monte-Carlo trials). We suggest that observation-error estimators be used when fitting surplus production models, that effort-averaging methods be abandoned, and that process-error estimators should only be applied if simulation studies and practical experience suggest that they will be superior to observation-error estimators.