Fish harvesting advice under climate change: A risk-equivalent empirical approach

automatically chosen 9 knots which gave it considerable flexibility yet still appeared to be weakly dome shaped. Residuals of the smooth were normally distributed when the three out- lier years were excluded and residuals were not autocorrelated. Outliers were retained how- ever, as these more extreme years in P/B capture important large recruitment events that are important for keeping the stock biomass up (residuals were resampled in each year of projec- tions) and the underlying weak dome for P/B vs E represents the underlying smooth (though weak) dependence of P/B on E. P/B values themselves ranged from about -0.5 to 2 and there was important inter-annual variation in stock production. The P/B vs temperature relationship formed the basis for projecting the Greenland halibut biomass into the future under various climate scenarios under the assumption of status quo fishing. Alternative P/B vs E models can be fitted that may be more appropriate representations of hypotheses on external variable influences on production for different stocks (See additional material in https://github.com/ duplisea/ccca). 3.2 EM projections The climate scenarios represent plausible changes in temperature at 150 m in the central Gulf (0.5˚C warming or cooling) which can be important changes for Greenland halibut in the Gulf of St Lawrence (Fig 4). These scenarios were used to project future P/B distributions under each temperature scenario (Fig 5). It is important to note again that the hypothesis is not that

temperature in the central Gulf at 150 m is what the bulk of the fish are experiencing directly but that this this temperature measure has a larger systemic link to Greenland halibut produc- tivity at several depths and locations in the Gulf, i.e. it is something of a meta-variable for cli- mate change driven productivity changes pertinent to this stock. The resulting P/B distributions for the stock under each future climate scenario exhibit small but important dif- ferences (Fig 5). The probability density function for P/B is more peaked at values of -0.5 for both the warming scenario and increased variance scenario than for the status quo tempera- ture or cooling scenario. This greater density in the lower part of the P/B range will render pro- jections based on sampling the warmer or more variable pdfs much more pessimistic. 3.3 Risk analysis The recent mean temperature and 0.5˚C colder scenarios achieved the biomass objective with 50% probability under status quo fishing pressure (Fig 6). Neither the 0.5˚C warming scenario nor the increased temperature variance scenario allowed the biomass objective to be achieved with 50% probability under status quo levels of fishing. In all scenarios, there was little differ- ence in the ability to achieve the biomass objective (annual probabilities of being at or above the objective) between projections assuming no density dependence vs projections assuming density-dependent stock dynamics. The incremental risk of not achieving the biomass objec-

tive after 10 years increased with the mean temperature over the scenarios (Table 1). There was a minimal decrease in risk (1%) when production-dependence on temperature was con- sidered (mean temperature scenario) relative to the null model without temperature-depen- dence. The risk increased by 50% (from about 0.5 to 0.75) in the warming scenario compared to the null model and was similar with or without density-dependence. In cooling scenarios, the risk decreased by about 14% relative to the null model. The scenario where temperature variance was increased while the mean temperature remained the same was almost identical to the warming scenario, i.e. the incremental risk of not achieving the stock objective while fish- ing at status quo increased by 50% (Table 1). For both the warming and increased variance sce- narios, the target was unattainable with any level of fishing given the 50% risk standard associated with a target objective (Fig 7). PLOS ONE Climate-change conditioned risk-equivalent fisheries advice PLOS ONE | https://doi.org/10.1371/journal.pone.0239503 February 19, 2021 10 / 22