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

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