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

than being the direct driver of Greenland halibut production. A functional relationship between P/B and E was defined using a generalised additive model (GAM). Uncertainty about the relationship was added by resampling the GAM residuals. S2 Appendix provides a more complete explanation of developing the P/B vs E relationship including choosing the variables. 2.3.2 Model projections. The P/B vs E relationship formed the basis for projecting the Greenland halibut biomass into the future under different fishing climate scenarios. EMs were implemented as per Eq 2. The density dependent model was implemented under the assump- tion that the maximum unexploited biomass for the stock was equivalent to 3x the largest index biomass observed. This roughly corresponds to the Bmsy/K value from a Fox surplus production model [31]. Most fish stocks that have been exploited for several generations usu- ally have biomass values at or below Bmsy and therefore we considered the Bmsy/K value of 3 to be realistic and suitable for sensitivity test of the inclusion of a density dependent process. We emphasise that the density dependent version of the model is simply a sensitivity test and the reality is that it makes little difference from the density independent model for a fish stock that has been commercially exploited for many years. We used the status quo relative exploitation rate in all projections, corresponding to the average relative exploitation rate (Catch/Biomass in year t) observed in the last five data years

in our case study (2015–2019). This corresponded to a relative exploitation rate of about 0.05 (i.e. 5% of the population biomass of Greenland halibut >40 cm). This assumption allowed us to investigate how stock production and the probability of achieving a management objective will change under plausible future climate scenarios, if exploitation stays the same. Climate scenarios were specified by first fitting a normal distribution to E, treating E as a representative of the underlying distribution of observations. In this particular case, a normal distribution captured the observed temperature series well (Shapiro-Wilks test P = 0.51). Cli- mate conditions were then simulated by shifting the mean of that distribution by ± 0.5 degrees Fig 2. Time series data for Gulf of St Lawrence Greenland halibut used to fit the production model. The temperature time series depicted is the annual average temperature of the Central Gulf of St Lawrence water at 150 m. https://doi.org/10.1371/journal.pone.0239503.g002 PLOS ONE Climate-change conditioned risk-equivalent fisheries advice PLOS ONE | https://doi.org/10.1371/journal.pone.0239503 February 19, 2021 7 / 22