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

(0.5˚C warming and cooling scenarios), and by increasing its standard deviation by a factor of 1.5 (sd x 1.5 scenario) and resampling 20000 times for each year in the future projection. Increase variance unders climate change is expected in the 21st century [32]. While a factor of 1.5 multiplying the sd of the normally distributed temperature series is a large increase in vari- ance, down-scaled atmospheric climate projections suggest this could be realistic (climateatlas. ca). A ‘mean’ climate scenario (corresponding to average observed temperature conditions) was considered, which consisted of resampling the distribution fitted to the E series. A ‘null’ model (i.e., model without temperature-dependence on production) was also projected by resampling the observed P/B distribution without regard to the E variable, i.e. the P/B values were simply treated as an empirically derived series and sampled independent of any climate scenario. In all cases but the null model, realisations of future E values were used to determine the population growth rate (P/B) using the GAM model described above with additional vari- ance included by adding a resampled residual from the fitted GAM each year of the projection. 2.3.3 Risk analysis and risk-based advice. The risk analysis required specification of three aspects of a healthy stock in a well-managed fishery: (1) a management objective, such as a biomass target from the observed range of biomass values (e.g., B during a given time period); (2) the time by which the management objective must be achieved; and (3) the risk

tolerance which is the acceptable probability level for not achieving the objective. The manage- ment objective for Greenland halibut was established based on a period of relative stability in the survey biomass index and catches from 1995–2000 (Fig 2). The average biomass (B) (aver- age of annual survey biomass values) over this “baseline” period was used as the biomass target or management objective for the stock. The relatively stable catches during this period (Fig 2) suggests that the selected biomass objective may have characteristics of a biomass at maximum sustainable yield which is a common management target (DFO 2006). The time period required to achieve the objective was set at 10 years and the maximum acceptable risk of failure to achieve the target within that time was set at 50% (which is the de facto risk tolerance for a target). The annual probability of achieving the objective over the 10-year period given status quo fishing and plausible climate scenarios was determined from the outputs of EM projections, as the proportion of the Monte Carlo projections where the objective was achieved annually or at the end of the 10-year projection. For a given climate scenario, the ratio of the calculated risk under CC forcing relative to the same risk in the null model assuming no productivity depen- dence on the environmental variable is the incremental risk resulting from consideration of CC effects on stock dynamics: RI ¼ Rscenario Rnull Where incremental risk (RI) is the risk under the climate change scenario (Rscenario) minus

the risk under a null model where climate was not considered (Rnull). For each projection scenario, we can also determine the fisheries exploitation rate that will allow the objective to be achieved at the end of 10 years at the acceptable risk level (50% in the case with a target). The ratio of this exploitation rate in the null model to that in any of the CC scenario is the risk equivalent CC adjustment factor (multiplicative) that would need to be applied to exploitation re or catch to compensate for CC, we term this the climate change con- ditioning factor (CCCF): CCCF ¼ Fscenario=Fnull PLOS ONE Climate-change conditioned risk-equivalent fisheries advice PLOS ONE | https://doi.org/10.1371/journal.pone.0239503 February 19, 2021 8 / 22