Updates of provisional stock assessment of Pacific saury in the North Pacific Ocean by using state-space biomass dynamics models

Population analyses were conducted for updating the results in the provisional stock assessment of the North Pacific saury using updated dataset. The models employed in the analysis are the state-space biomass dynamic models, which are same as in the previous provisional stock assessment. The models account for process and model errors in biomass indices such as standardized CPUE series for commercial fisheries by China, Japan, Korea, Russia and Chinese Taipei and fishery-independent surveys by Japan. Given that the biomass indices observed are not necessarily synchronized possibly because of difference in spatial use of fishing and survey grounds, several options were considered for selection of the indices in the analyses. Also, a wide range of models/scenarios were developed for assessing sensitivity to key assumptions such as types of production function, hyperstability/hyperdepletion, and priors. Parameters in the models were estimated via Bayesian methods with Markov chain Mote Carlo. 
The models were diagnosed with respect to shapes of posterior distribution, residual plots, retrospective pattern and predictability of the future population status. Shapes of posterior distributions were generally good. The convergence of MCMC runs was achieved for all the case. In terms of model fitting, standardized residual plots showed that the residuals are almost perfectly within the 95% range and the variance is homogeneous across years although some residuals patterns were observed due to different behaviors of CPUE series over fisheries. The results tend to show that the estimated population dynamics fitted well to the Japanese and Russian CPUE series and tend to be fitted to the biomass indices by Japanese survey. In addition to the types of production model, the presence/absence of hyperstability/hyperdepletion was somewhat influential to the results. Model selection was not conducted formally in this paper partly because the models are not based on the iid observations and therefore use of Bayesian types of information criteria such as WAIC may not be suitable, and partly because Bayes factor may have Monte Carlo errors. Instead, not yet comprehensively conducted, as a way of model checking for management use, a hindcasting approach (in terms of predictability; e.g. Kell et al. 2016) was proposed as an initial attempt for model selection and checking retrospective patterns simultaneously. No remarkable mis-fits were observed. 
As for the reference cases, the current median depletion level was within 37-48 % of the carrying capacity, and the current median B-ratio=B2017/Bmsy was estimated as 0.81-1.11. The current median F-ratio=F2016/Fmsy was evaluated as 0.50-0.68. These results did not suggest that the population is now severely depleted although the uncertainty in the estimation is quite high. For considering management implications, population dynamics were projected for some scenarios with respect to the reduction/status quo/increase from the current catch level. Under the two reference cases, although continuation of current catch level may not cause severe decline in the population size in the next decade, a safer option is of course slight reduction to keep the population size above the MSY level. One of the reference case showed that increase of catch might collapse the population. 
The results dramatically changed when the results of the fishery-independent survey biomass were more weighted for model fitting. The B-ratio was clearly estimated less than 1 (the median range is 0.30-0.44), and the F-ratio is significantly above 1 (its median range is 1.10-1.86). Future projection showed very pessimistic results. 
Given that there is the large uncertainty in the estimation (estimation and process uncertainties) and large variation among the scenarios (model uncertainty) as well as the observed results of biomass surveys, the authors conclude that immediate action may be needed for setting a reduced quota for next a few years, and continued works/efforts for improving data and models would be required toward stock assessment beyond the existing provisional assessment and development of management procedures based on the assessment.