Sensitivity and variance estimators for virtual population analysis and the equilibrium yield per recruit model

Fish stock assessment makes Widespread use of Virtual Population Analysis (VPA) and long-term equilibrium prediction models. Although there have been some statistical investigations about the properties of VPA results, apparently there are no complete analyse about predictions statistical and numerical behaviour. However, management decisions generally rely upon production forecasts. This paper compares stability properties of VPA and the yield per recruit model with regard to various errors concerning all the input parameters. Robustness fis assessed by means of first-ordo sensitivities whereas variances are inferred from delta-method estimators. Sensitivity of yield per recruit appears to be mainly due to terminal mortality rate and age-specific weights, and to a lesser extent, to catches and natural mortality. Mean values of the input parameters were also found to influence the model's behaviour. A complete estimation of variances would require a variance-covariance matrix for weights at age and terminal fishing mortality rates. Sensitivities and variances are complementary in that the first quantify the absolute robustness of the models whereas the second show model robustness in relation to the dimensioned interval of variation of each input parameter. If variances were available for all parameters, yield per recruit estimates could be taken into account for fisheries management decisions