Shaping sustainable harvest boundaries for marine populations despite estimation bias

Biased estimates of population status are a pervasive conservation problem. This problem has plagued assessments of commercial exploitation of marine species and can threaten the sustainability of both populations and fisheries. We develop a computer-intensive approach to minimize adverse effects of persistent estimation bias in assessments by optimizing operational harvest measures (harvest control rules) with closed-loop simulation of resource–management feedback systems: management strategy evaluation. Using saithe (Pollachius virens), a bottom-water, apex predator in the North Sea, as a real-world case study, we illustrate the approach by first diagnosing robustness of the existing harvest control rule and then optimizing it through propagation of biases (overestimated stock abundance and underestimated fishing pressure) along with select process and observation uncertainties. Analyses showed that severe biases lead to overly optimistic catch limits and then progressively magnify the amplitude of catch fluctuation, thereby posing unacceptably high overharvest risks. Consistent performance of management strategies to conserve the resource can be achieved by developing more robust control rules. These rules explicitly account for estimation bias through a computational grid search for a set of control parameters (threshold abundance that triggers management action, Btrigger, and target exploitation rate, Ftarget) that maximize yield while keeping stock abundance above a precautionary level. When the biases become too severe, optimized control parameters– for saithe, raising Btrigger and lowering Ftarget–would safeguard against overharvest risk (<3.5% probability of stock depletion) and provide short-term stability in catch limit (<20% year-to-year variation), thereby minimizing disruption to fishing communities. The precautionary approach to fine-tuning adaptive risk management through management strategy evaluation offers a powerful tool to better shape sustainable harvest boundaries for exploited resource populations when estimation bias persists. By explicitly accounting for emergent sources of uncertainty our proposed approach ensures effective conservation and sustainable exploitation of living marine resources even under profound uncertainty. Open Research Statement Data sets and code utilized for this research are available on Figshare. DOI: https://doi.org/10.6084/m9.figshare.13281266

In commercial capture fisheries, assessments of current population status provide a scientific 68 basis for setting a threshold for safe harvest to prevent the decline of fish stocks. This approach 69 may include using biological thresholds such as the population abundance that produces 70 4 maximum sustainable yield (Beddington et al. 2007). The harvest of wild populations is 71 commonly managed by applying decision rules (harvest control rules) based on such predefined 72 thresholds to set a catch limit for the year (Beddington et al. 2007). Accurate population 73 assessments contribute to successful implementation of management measures to sustain long- getting it wrong, we urgently need a procedure that provides practical guidance for explicitly 93 5 evaluating robustness of management strategies and designing alternatives to inform decision 94 making to safely harvest under uncertainty (Punt et al. 2020). 95 We illustrate how closed-loop simulation of resource-management systems (management 96 strategy evaluation) can help prevent estimation bias from derailing effective management of 97 exploited marine populations. Management strategy evaluation is a flexible decision-support tool 98 used in fisheries management Punt 1999, Smith et al. 1999) and has 99 increasingly been applied to conservation planning in marine and terrestrial systems (Milner-  We simulated population and harvest dynamics, surveys, assessments, and implementation of 117 management strategies to explore trade-offs in achieving conservation-oriented (minimizing 118 overexploitation risk) and harvest-oriented (maximizing yield) goals through management 119 strategy evaluation. We made use of the framework developed and adopted for commercially   where SSBy is adult biomass (known as spawning stock biomass, t) in year y, which is the sum of 155 the product of age-specific numbers, masses, and maturity rates, β, b, and α are parameters, and 156 γy is process error in year y. 157 We developed the OM using data and life history parameter estimates taken from the 2018 158 assessment (Fig. 1b, ICES 2018), which represents the best available information on the past 159 (1967-2017) population and harvest dynamics (Fig 1b and Appendix S1). The data sources, masses (g, Appendix S1: Table S3-S4) and maturity rates (proportion of adults, Appendix S1: 163 Appendix S2: Fig. S1) and age-specific (ages three to eight) abundance indices (International 167 bottom trawl surveys in the third quarter, IBTS-Q3, in 1992-2017, Appendix S1: Table S7 and showed little evidence of temporal autocorrelation in recruitment (Appendix S2: Fig. S4c).

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Monitoring and catch surveys 187 We simulated future annual monitoring of the population and harvest, which are subject to where wa,y+1, Na,y+1, Sa,y+1, and Za,y+1 are as above and forecasted for the advice year.

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Population and management measure performance 234 We computed conservation-oriented (risk of stock depletion) and harvest-oriented (median scenario or 1,920,000 unique runs in total) for reoptimization to illustrate our proposed approach. 289 We conducted a restricted grid search in parameter spaces of Btrigger (210,000 to 320,000 t with 290 10,000 t increments) and Ftarget (0.24 to 0.39 with 0.01 increments) for each bias scenario. We 291 computed median catch limits and risk from the simulations and optimized the parameter sets by 292 maximizing median catch limits while maintaining long-term risk ≤ 0.05.

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Performance of harvest measures with estimation bias 295 An increasing amount of estimation bias in annual assessments was found to increase median 296 catch and overharvest risk in the short term. Although median SSBs declined by as much as 30% 297 in the OM (Fig. 2a), with SSB overestimation, median catches rose by 15-44% relative to the 298 14 baseline (Fig. 3a), increasing mean Fs in the OM by 19-80%, which were underestimated in the 299 EM by on average 42% (Fig. 2b). As a result, biased assessments elevated risks as much as 17-300 fold (Fig. 3a). Mean ICV responded nonlinearly to biased estimates, and the distribution was 301 highly skewed (Fig. 3a).

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In the long-term the estimation bias was found to increase ICV and risk but had negligible 303 effect on median catch. Biased estimates reduced median SSB in the OM by as much as 35%

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(resulting in a 37% increase in mean F) relative to the baseline; this reduction was 305 underestimated in the EM by on average 53% (Fig. 2a,b). With overestimated SSBs and largely 306 unadjusted Ftarget, median catches remained unchanged (~113,000 t, Fig. 3b). Also, biased 307 assessments amplified temporal variations (CVs in medians of replicates) in both SSB and mean 308 F in the OM as much as ~71%, thereby increasing ICVs by up to 72%, which, combined with 309 reduced SSBs, elevated risks 2-13-fold (Fig. 3b).

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Harvest control rule optimization 311 The proportion of the select grid search area evaluated through management strategy 312 evaluation that remained precautionary (which we define as safe harvest margin) progressively 313 shrank as more bias was introduced ( Fig. 4 and Table 1). Within the safe harvest margin, the 314 fishery yielded highest catches at lower (by 0.02-0.10) Ftarget and higher (by 10,000-60,000 t)

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Btrigger (Table 1 and Fig. 4). With reoptimization of these control parameters the control rule was 316 projected to produce higher (by 6.7-25%) short-term catches and maintain similar (<3.0% 317 deviation from the baseline) long-term catches under all bias scenarios (Table 1). And both 318 short-and long-term SSBs declined by 3.1-6.9% and long-term ICVs rose by less than 1.5% 319 (Table 1).

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Shifting the focus from assessment to decision making in management strategy evaluation ( Fig.   409 1a), our analysis shows the undesirable outcomes of managing with biased assessments can be  criterion: long-term risk ≤ 5% (ICES 2019c). 625 ‡ The performance was evaluated with short-term and long-term median catch (t), interannual catch 626 variability (%, ICV), median spawning stock biomass (SSB, t), and risk (%). 627 § Scenarios simulate SSB overestimation and mean (averaged across four to seven-year-olds) fishing 628 mortality rate (F) underestimation. 629 ¶ Risk is the maximum probability of SSB falling below B lim (107,297 t) over a given period. Safe harvest 630 margin (SHM) indicates the proportion (%) of the grid-search area with the harvest rules that remain 631 precautionary (Fig. 4). 632  10% 20% 30% 40% 50%