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

or the stock. Greenland halibut in the Gulf of St. Lawrence are stenothermic [39]. This lack of adaptability to a large range of temperature conditions of the stock combined with low oxygen conditions of bottom waters in the GSL (that are projected to worsen) means that there is a low adaptive capacity of this stock to compensate production losses with climate change. It has been conservatively predicted that this stock may lose up to 55% of its best habitat over a 20– 40 year period [39] with CC. The relationship between P/B and E used here captures some of this effect concurring that the habitat loss is likely to lead to important productivity losses for the stock and there is little compensatory capacity for adaptation. Development of EMs is an effective way to condition fishery advice to CC in the short- to medium-term. These models are relatively quick to implement and they tend to be robust because they are driven by broad phenomenological relationships and take advantage of emer- gent phenomena and constraints present in the climate forcing feedback system [40]. The EM approach should not be seen as a substitute for detailed mechanistic approaches but comple- mentary. EM methods can incorporate process-based understanding as knowledge increases, and when knowledge is sufficient, mechanistic approaches can take many of the elements of PLOS ONE Climate-change conditioned risk-equivalent fisheries advice PLOS ONE | https://doi.org/10.1371/journal.pone.0239503 February 19, 2021 17 / 22

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

An alternative approach to projecting the stock into the future is to sample the actual sur- plus production values from certain time periods where E conditions had different means, i.e. block sampling or by sampling from particular quantiles of the E distribution. This does free one from forming a hypothesis on the mechanism, which though elegant, can only produce values that have been observed previously and is constraining especially for shorter time series. Implicitly a time blocking approach is a hypothesis about time period impacts on growth and not CC (even though they may be correlated). This block resampling approach limits the range of values of future E in scenarios and the precedents being set in many regions of the world with environmental variables such as temperature with every new year of data suggests that this is likely to be a conservative approach that may well underestimate the impact of cli- mate change on stock production. And although that approach may appear hypothesis-free, it is still making a strong assumption about future production being the same as some part of the past. We also advocate an approach that forces a one to develop an hypothesis on P/B vs E because it is more clearly falsifiable. Density dependence is a key consideration in fisheries models so that stocks do not grow exponentially beyond natural limits. The EM approach used here includes a simple form of density dependence by introducing a carrying capacity parameter (S1 Appendix) in the same

manner as the Schaefer production model [13], i.e. it acts as a reducing factor in growth rate to the point where growth is zero when biomass is at the carrying capacity. The carrying capacity parameter was set at three times the maximum observed biomass since the survey started in 1990, which is arbitrary but does take into consideration that the stock has been fished com- mercially for >50 years [43] and may once have been much larger than biomasses estimated from the survey series. Density dependence did not have an appreciable impact on model out- puts, nor on estimates of the incremental risk associated with the inclusion of CC in stock pro- jections. This lack of influence of density dependence on projections from current stock sizes is a useful result because it means that for stocks assessed as well below their carrying capaci- ties, CC conditioning with EMs can be done without including density dependence parameters in the EM projections. For stocks that are in very depressed states where depensation is consid- ered a plausible hypothesis [44], it may be necessary to include a depensatory process in the model, and for projections that suggest stocks may return to much larger sizes in just one or two decades, monitoring for evidence of density dependence in stock dynamics can be imple- mented as the stock grows. 5 Summary We developed an EM approach that describes how fish production changes as a function of a CC variable and carries that relationship through to a risk assessment and estimation of the

incremental risk for alternative fishing strategies in a context of CC. Using basic time series data that are typically available for exploited demersal fish stocks, the model was parameterised and projected forward, given future climate scenarios inferred from a single environmental variable. The risk assessment required an explicit management objective, which in this case corresponded to a target objective defined by setting a baseline period over which to average stock status. Model projections under different climate scenarios could then be compared to a baseline or ‘average conditions’ climate scenario. The comparisons formed the basis for deter- mining the incremental risk associated with each scenario under a status quo fishing strategy (assuming random or constant environment with no productivity dependence on the environ- mental variable), and the change in fishery exploitation rates required to maintain the risk at a specified tolerance—in this case 50% likelihood of achieving the objective (i.e., risk equivalent fishery exploitation advice). This approach shows how fishing pressure should change in PLOS ONE Climate-change conditioned risk-equivalent fisheries advice PLOS ONE | https://doi.org/10.1371/journal.pone.0239503 February 19, 2021 19 / 22

relation to CC (expressed as E) if the management goal is to achieve the stock objective with the same level of risk. It can also inform managers on the relative change in risk associated with alternative management options under different climate scenarios, fostering transparency into decisions made considering CC-contributed uncertainty. This approach can therefore use previously observed stock productivity dynamics to define a safe operating space for fisheries given the projected future climate, the management objective and timeframe and the risk level considered acceptable. The approach can be used to expand stock exploitation advice to take CC into account, inform managers of the change in risk that can be anticipated under different climate scenarios, and support a transparent dialogue among scientists, managers, and stake- holders on how risk decisions can be altered by CC, by giving a rough magnitude of the changes potentially required in stock exploitation advice if CC is to be considered. Although this risk-based approach was designed to develop advice that considers CC, it can be applied to any ecosystem or environmental driver affecting stock production, for example in cases of habitat loss not caused by CC, or where there is potential for a degree of interdepen- dence between sustainable exploitation rates for a predator and a prey species. The main con- dition to applying this risk-based approach to other potential drivers is the need for a plausible hypothesis on how the external variable affects a stock’s production. At an even higher level

than fish stock production, the risk equivalent principles for altering advice are more universal and can work in any area of natural resource management where status quo advice is consid- ered possibly suspect because of a change in an external factor. Supporting information S1 Appendix. (PDF) S2 Appendix. (HTML) Acknowledgments Johanne Gauthier, Peter Galbraith and Denis Gilbert for providing the stock, temperature and oxygen data, respectively. Important feedback on many of the ideas presented here was pro- vided by participants of the DFO peer review meeting in incorporating CC into stock assess- ment advice in May 2018. Mariano Koen-Alonso suggested that density dependent processes should be explored. Author Contributions Conceptualization: Daniel E. Duplisea, Marie-Julie Roux, Karen L. Hunter, Jake Rice. Data curation: Daniel E. Duplisea. Formal analysis: Daniel E. Duplisea, Marie-Julie Roux, Jake Rice. Investigation: Daniel E. Duplisea. Methodology: Daniel E. Duplisea, Marie-Julie Roux, Karen L. Hunter, Jake Rice. Software: Daniel E. Duplisea. Validation: Marie-Julie Roux. Visualization: Daniel E. Duplisea. Writing – original draft: Daniel E. Duplisea, Marie-Julie Roux, Karen L. Hunter, Jake Rice. PLOS ONE Climate-change conditioned risk-equivalent fisheries advice PLOS ONE | https://doi.org/10.1371/journal.pone.0239503 February 19, 2021 20 / 22

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