Capturing uncertainty when modelling environmental drivers of fish populations, with an illustrative application to Pacific Cod in the eastern Bering Sea

Decision makers are increasingly requesting that environmental and climate drivers be included in stock assessments and subsequent projections that provide managers with advice on the consequences of applying harvest control rules. Another key direction in stock assessment science is to capture the full range of uncertainty (model, process, and estimation). However, multiple sources of uncertainty are rarely accounted for when conducting projections based on environmental and climate drivers. We describe a framework for conducting projections that allows for structural model uncertainty (in the structure of the population dynamics model on which the assessment is based, and the Earth System Models and emission scenarios used to drive future recruitment and growth), for process error in future recruitment, and for uncertainty in the parameter estimates of the population dynamics model. We then apply the framework to data for Pacific cod, Gadus macrocephalus, in the eastern Bering Sea, with projections based on a harvest control rule that attempts to maximize the difference between revenue and variable costs based on the current growth and recruitment dynamics of the stock. Increases in temperature are found to increase weight -at -age but reduce recruitment. However, the negative effects on recruitment outweigh the positive effects on weight -at -age. In many cases, the harvest control rules considered in this paper, particularly those based on the assumption of no future environmental effects on population parameters, fail to conserve the stock if the inferred catch limits are taken, which suggests that declines in biomass and catch will take place if the current harvest control rules continue to be used. The strategies that lead to reductions in catch and biomass also lead to much lower profits for the fishery, particularly over the long-term. However, basing future catches on the environmental scenario that leads to the poorest outcomes (GFDL ssp585) generally keeps the stock above the threshold of 20 % of unfished spawning biomass under most climate scenarios and also achieves long-term profits at or greater than those expected in the next ten years.