Impacts of the nonlinear relationship between abundance and its index in a tuned virtual population analysis

Abstract

The abundance index used in a tuned virtual population analysis (VPA) is usually assumed to be proportional to actual abundance. However, the actual abundance and abundance index do not always have a linear relationship. Such nonlinearity can cause biases in abundance estimates as well as retrospective biases arising from systematic differences in abundance estimates when more data are successively added. Severe retrospective biases can damage the reliability of stock assessments. In this study, we use an approach to estimate an additional parameter that controls the nonlinearity in a tuned VPA. A performance test using simulated data revealed that the tuned VPA was able to accurately estimate the nonlinearity parameter and thus yielded less biased abundance estimates and smaller retrospective biases. We also found that estimating the nonlinearity parameters was effective even under other model misspecification scenarios, such as disregarding historical increases in catchability and time-varying natural mortality. Moreover, we applied this approach to some Japanese fish stocks and evaluated its validity. We found that estimating the nonlinearity parameters in the tuned VPA enhances the reliability of fisheries stock assessments.