Comparison of logistic and generalized surplus-production models applied to swordfish, Xiphias gladius, in the north Atlantic Ocean

Recent assessments of swordfish, Xiphias gladius, in the north Atlantic Ocean by the International Commission for the Conservation of Atlantic Tunas (ICCAT) have included fitting a nonequilibrium logistic (Schaefer) surplus-production model. The logistic model offers simplicity, but concern has been expressed that its fixed model shape may bias estimates of quantities of management interest. Here, I compare results from the logistic estimator used by ICCAT to those from an otherwise equivalent generalized (Pella–Tomlinson) production-model estimator. Following initial estimation with nonlinear least-squares, a resistant fitting method was used to identify statistical outliers, and both models were refit with outliers removed. The estimate of model shape from the generalized model was then close to the logistic, and estimates of stock status from the two estimators were similar. A simulation study conditioned on the trimmed generalized fit suggests that any systematic estimation error caused by assuming logistic shape for this stock is small. Moreover, the generalized estimator was sensitive to outlying observations and thus less precise than the logistic estimator, and it exhibited larger median proportional unsigned error. Sensitivity to outliers and lack of precision in an estimator make it more likely to provide misleading estimates in a given analysis; therefore, if the generalized production model with estimated shape parameter is used in stock assessment, it should be applied with skepticism and in conjunction with the more robust logistic form. Unless a good external estimate of model shape is available, the logistic model appears more suitable for routine assessment use on stocks similar to swordfish.