Sensitivity and variance estimators for virtual population analysis and the equilibrium yield per recruit mode1

Fish stock asscssment makes widespread use of Virtual Population Analysis (VPA) and long-term cquilibrium prcdiction modcls. Although thcrc have becn somc statistical investigations about thc propcrties of VPA rcsults, apparcntly thcre arc no completc analyse about prcdictions statistical and numerical bchaviour. However, management dccisions gencrally rely upon production forccasts. This papcr compares stability propcrtics of VPA and the yicld per rccruit modcl lvith regard to various errors conccrning al1 the input parameters. Robustncss is asscsscd by mcans of first-ordcr scnsitivitics uhcreas vsrianccs arc infcrrcd from delia-method cstimators. Sensitivity of yicld pcr rccruit appears to bc mainly duc to terminal mortality rate and age-spccific wcights, and to a lcsscr entent, to catchcs and natural mortality. Mcan valucs of the input parametcrs tvcrc also found to influence the modcl's bchaviour. A complctc estimation of varianccs would rcquire a variance-covariance matrix for wcights at agc and terminal fishing mortality ratcs. Scnsitivitics and variances arc complcmcntary in that the first quantify the absolutc robustncss of the models tbhcrcas thc sccond show modcl robustncss in relation to thc dimensioned intenal of variation of csch input parametcr. If varianccs were available for al1 paramcters, yicld pcr rccruit estimates could bc taken into account for fisheries managcmcnt decisions. Keynords: Virtual I'opulation Analysis, yield pcr rccruit, scnsitiviiy, variance cstimation, Dclta-mcthod