Performance of alternative harvest control rules for two Pacific groundfish stocks with uncertain natural mortality: Bias, robustness and trade-offs

Harvest control rules (HCRs) are used in fisheries management to reduce fishing mortality as the level of perceived risk to the fish stock increases. This is typically done by adjusting fishing mortality rates based on estimated stock status relative to operational control points (OCPs). OCPs represent the stock status level at which management responses are taken. OCPs differ from biological reference points (BRPs), which represent biomass targets to be achieved, or low biomass thresholds to avoid. Both BRPs and OCPs can be based on theoretical quantities such as Maximum Sustainable Yield (MSY), Spawning Potential Ratio (SPR), or unfished spawning biomass (B0). However, they can also be based on quantities such as the estimated average spawning biomass and fishing mortality during a productive period. Formal evaluation of the performance of HCRs that account for potential biases in estimated model parameters and stock status relative to OCPs can help managers and stakeholders select HCRs expected to provide acceptable outcomes and trade-offs. We use closed-loop simulation to evaluate the performance of five HCRs for two British Columbian groundfish stocks for which there is considerable uncertainty in underlying productivity: Hecate Strait Pacific Cod (Gadus macrocephalus) and Hecate Strait Rock Sole (Lepidopsetta spp.). Performance metrics representing ecological and economic fishery objectives are reported for two alternative productivity scenarios for each stock, including depensatory mortality for Pacific Cod, and alternative levels of natural mortality (M) for Rock Sole. We present an algorithm for calculating equilibrium M in the presence of density-dependence, and show general effects of uncertainty in M on reference point calculations. Mechanisms for differences in performance among alternative HCRs are explored, and we show that even when model parameters or OCPs are very biased, some HCRs can still produce desirable management outcomes. We show that trade-off considerations are important because differential sources of stock assessment bias between the two species, and between scenarios within a given species, meant that no single HCR performed consistently. We suggest that prospective evaluation of alternative harvest policies using closed-loop simulation could be conducted routinely on a stock-specific basis, and can facilitate choice of HCRs, with a focus on outcomes rather than uncertainty per se.