Ridge virtual population analysis to reduce the instability of fishing mortalities in the terminal year

Tuned virtual population analyses are widely used for fisheries stock assessments. However, accurately estimating abundances and fishing mortality coefficients in the terminal year using tuned virtual population analyses is generally difficult, particularly when there is a limited number of available abundance indices. We propose a new method of integrating the tuned virtual population analyses with a ridge regression approach. In our method, penalization in the ridge regression is applied to the age-specific fishing mortalities in the terminal year, and the penalty parameter is automatically selected by minimizing the retrospective bias. Therefore, our method is able to simultaneously obtain a stable estimation of fishing mortality coefficients in the terminal year and reduce retrospective bias. Simulation tests based on the northern Japan Sea stock of walleye pollock (Gadus chalcogrammus) in the Sea of Japan demonstrated that this method yielded less biased estimates of abundances and avoided overestimations of fishing mortality coefficients in the terminal year. In addition, despite limited abundance indices, our method can perform reliable abundance estimations even under hyperstability and hyperdepletion conditions.