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

just above 3.1˚C it becomes impossible to achieve the biomass objective in 10 years with a 50% risk tolerance simply by adjusting the fishery exploitation rate if we consider median tempera- ture at 150 m in the Central Gulf to be the essential E variable capturing Greenland halibut production. Keep in mind again, that temperature in the central Gulf at 150 m is a meta-vari- able reflecting a suite of environmental variables that are impacted by CC and that affect Greenland halibut production. The track of the actual relative exploitation rate and the observed temperature (Fig 8, trace line) shows that even though the relative exploitation rates are not large compared to most demersal species (e.g. < 10%), the median temperature already has increased beyond the range where Greenland halibut production is maximised. The observed 2019 temperature and the relative exploitation rate placed on the stock in 2019 places the risk to the stock of not achieving its objective in 10 years of fishing at this rate at >90%. The history of exploitation and temperature shown by the trace line suggests that the stock has often been outside the safe operating space but it has shown a systematic movement outside that space (in the temperature dimension rather than in exploitation) in the past several years. This suggests that the stock productivity state has shifted or continues to shift directionally to a poorer state. Thus, the con- tour lines can be used for showing how fishery removals have to be adjusted to maintain the

desired probability of achieving a specified management objective and/or to provide risk equivalent advice on fishery exploitation conditioned on temperature (or “E” more generally), which is a surrogate variable for directional change (i.e. Climate Change conditioned advice). 4 Discussion Decisions in the management of fisheries are always risk-based decisions, although both risk and fishery objectives may not always be explicitly described as part of the management sys- tem. A growing emphasis on transparency and rule-based management is increasing the use of both explicit objectives and explicit risk tolerances in fisheries management [33,34]. Managing fish stocks in a changing environment or ecosystem increases the value of risk analyses and a risk-based approach to management, if the risk quantification can capture added uncertainty due to the changing environment [35]. Because fisheries are already implicitly or explicitly independent and density dependent models to determine the impact of the density dependent assumption on risk. A status quo fishing strategy (mean exploitation rate from 2014–2018) was applied for all scenarios. https://doi.org/10.1371/journal.pone.0239503.g006 Table 1. Calculated relative risk (1-the probability of achieving the biomass objective at the end of the 10-year projection period (2027)) across scenarios, and incre- mental risk corresponding to the risk ratio in mean temperature and CC scenarios (numerator) relative to the null model (no dependence on temperature in projections). CC scenario Risk (2027) Incremental Risk� (Riskscenario-

Risknull) Risk equivalent exploitation rate (@ 0.50 risk threshold) Climate change conditioning factor (CCCF) Density- independence Density- dependence Density- independence Density- dependence Density- independence Density- dependence Density- independence Density- dependence Null 0.494 0.536 NA NA 0.071 0.058 1 1 Mean temperature 0.498 0.541 0.004 0.005 0.069 0.057 0.982 0.971 0.5oC warmer 0.744 0.775 0.251 0.240 NP NP 0 0 0.5oC colder 0.423 0.468 -0.070 -0.067 0.089 0.077 1.269 1.324 High variance 0.733 0.766 0.239 0.230 NP NP 0 0 Risk and incremental risk are calculated under a status quo exploitation rate (5%). NA = Not applicable, NP = Not possible/unachievable. https://doi.org/10.1371/journal.pone.0239503.t001 PLOS ONE Climate-change conditioned risk-equivalent fisheries advice PLOS ONE | https://doi.org/10.1371/journal.pone.0239503 February 19, 2021 14 / 22