Calibrating virtual population analysis for fisheries stock assessment

Virtual population analysis (VPA) is often used for assessing freshwater and marine fisheries resources. One important component in VPA is to calibrate abundance estimates with a time series of abundance indices. One of the commonly used calibration processes usually includes simultaneous estimation of cohort sizes across all ages and years. This reduces the flexibility of the model in accounting for age- and year-effects, in particular in the presence of an age- specific curvilinear relationship between abundance index and stock abundance. In this study, we compared this simultaneous method tuning approach with a stepwise approach which calibrates abundance age by age in tuning VPA. The simulation study suggests that the stepwise procedure tends to perform better with no obvious retrospective errors in the estimated stock biomass compared with the simultaneous method which tends to have large positive retrospective errors. In applying the stepwise procedure and simultaneous method to a cod fishery data set, we found large differences in the stock sizes estimated for the most recent year using these two methods, with the current stock size estimated using the stepwise method being substantially smaller than that estimated with the simultaneous method. Considering the likelihood of the presence of curvilinear relationship between abundance index and stock abundance, we conclude that the stepwise method yields more reliable results, and is less risk-prone in using VPA for fisheries stock assessment.