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

risk-based approaches from EM. Complementary approaches also provide consistency checks on one another in the same way that they have done for sea level rise predictions from global climate models [12]. The multiple model paradigm is a way to provide more robust risk analy- ses and overall science advice and quickly provide a means of conditioning advice to the CC reality. When developing EMs for CC impacts on fish stock it is necessary to think clearly on what climate-driven environmental (E) variable to use and define a hypothesis for how fish stock production should change with E. Good choices will be case specific and require appropriate experts and/or resource users familiar with the stock and environment and the amount of information available, to make a wise choice for E. Some of the necessary characteristics of an appropriate E variable is that it should be hypothesised or demonstrated to have some impact on stock production and therefore could affect the achievability of stock objectives. The E vari- able should also have a hypothesized or demonstrated link to how climate change is affecting the general area, or to some other environmental forcing factor considered by experts to be potentially important to changes in the marine ecosystem. For the Greenland halibut in the Gulf of St. Lawrence, we selected water temperature in the central Gulf at 150 m depth as the E variable. This area is not the main region where Greenland halibut is concentrated and fished in the Gulf (Fig 1); however, northward flowing water in the Gulf branches at the central Gulf

and feeds both the main eastern and western Greenland halibut fishing areas [41]. Therefore, the central Gulf temperature does have bearing on all the main Greenland halibut fishing areas and it is a measure that is likely to have a bearing on what the majority of the fish experience. This choice of E variable was also based on considerations of explanatory power (AIC value) and the expectation of a mono-modal-type relationship between Greenland halibut produc- tion and temperature since the species is adapted to a relatively narrow range of temperature conditions [42] (S2 Appendix). E variable selection may take into account consequences of a variety of processes including physiological and ecological adaptation, it may consider time lags, and it may relate to other driving forces on stock production such as recruitment or mor- tality. Therefore, it is important to consider that E may not be a direct driver but could poten- tially behave as a meta-variable pertinent to the productivity of a particular stock. The shape of the production vs E relationship should also be considered. The E variable here showed a dome shaped relationship with E (Fig 3) which is the logical shape one might expect for a pop- ulation adapted to a range of conditions where its productivity decreases outside that range. Nonparametric approaches model fitting approaches like GAMs can be used to try to quantify empirical relationships that may be present. GAMs are particularly useful because of their relaxed assumption however, there must be an ability to infer plausible interpretations of rela-

tionships that are found, and if possible, suggest more targeted analyses or experiments to improve understanding of the bases for the relationships useful in these tasks because they develop a central tendency for the relationship within interpolated ranges while still allowing considerable freedom in the form of the P/B vs E relationship. We also tried fitting just a parabola to the relationship which forced a dome like relationship and this is a much stronger hypothesis. This resulted in a stronger CC effect, thus the GAM is a more conservative approach in this case. When information is adequate, one can take into account more than one E variable and their combined impact on the P/B ratio of the stock. Multivariate GAMs are also easily fitted if there is a sufficient amount of data. However, as the number of E vari- ables increases, plausible future scenarios are needed for each one and the potential interac- tions and non-linearities among scenarios for different E variables must be considered. Thus, we recommend the KISS (keep it simple and straightforward) principle in choosing E variables for this empirical approach, and interpreting E variables as capturing an ensemble of environ- mental forcing processes rather than very specific mechanisms. PLOS ONE Climate-change conditioned risk-equivalent fisheries advice PLOS ONE | https://doi.org/10.1371/journal.pone.0239503 February 19, 2021 18 / 22