Applying a probability harvest control rule to account for increased uncertainty in setting precautionary harvest limits from past stock assessments

Estimates of current population status, derived from stock assessments and often expressed as spawning output, are uncertain. United States (U.S.) fisheries management has adopted approaches to account for this uncertainty when setting harvest limits with the goal of preventing overfishing, as mandated by the Magnuson Stevens Fishery Conservation and Management Act. For U.S. West Coast groundfish species, the Acceptable Biological Catch (ABC), since 2011, has been set to a fraction of the Overfishing Limit (OFL) based on the uncertainty (a) surrounding the estimated final year spawning output, as a proxy for the OFL uncertainty, or the uncertainty around the OFL itself. However, uncertainty around population size is expected to increase during the projection period when the true population dynamics may differ from the model projected values. Age-structured, data-rich stock assessments for West Coast groundfish species were evaluated for changes in spawning output uncertainty during a ten-year projection period. The spawning output time series from a more pessimistic population projection, termed the "low state of nature", was compared to the spawning output time series from the base assessment model adopted for management, for each of 17 West Coast groundfish species (comprising a total of 21 modeled areas). The standardized median estimated a increased, as measured between the low and base model spawning output, during the projection period for all species evaluated, increasing to a mean of 1.67 times greater than that in the first year after a ten-year projection. Combining the results by species groups used by the Pacific Fishery Management Council (rockfish, roundfish, and flatfish) elucidated that while the a values increased for all species groups, the rockfish species had the smallest median multiplicative increase in a (1.65) and the flatfish species had the largest increase in a (2.66) during the projection period, although only two flatfish assessments were available. Across species, natural mortality was the best life history predictor of the rate of change in a, however, the correlation between the two was low, though greater within species groups. Applying the estimated increase in a by year, across species groupings, combined with an adopted risk tolerance probability for exceeding the true OFL (termed P*) of 0.45 resulted in ABC values that decreased from 93.9 % of the OFL in the first year following the assessment to 90.0 % of the OFL by year ten of the projection period.