Non-stationarity in population parameters requires careful interpretation of equilibrium reference points

A key reference point in fisheries management is the limit reference point (LRP), which represents a biomass threshold below which serious harm to the fish population is believed to occur. Reference points are often based on equilibrium quantities such as unfished spawning biomass (SB₀) or spawning biomass at maximum sustainable yield (SBMSY), which are calculated using parameters that are assumed constant over time. When equilibrium assumptions are not met within a stock assessment (e.g., when natural mortality (M) is changing over time), there is a question of how to define reference points, especially when changes in productivity parameters cause reference points to change in scale. In this study, we develop simulation models based on recent stock assessments for three Pacific herring (Clupea pallasii) stocks for which M is estimated to have increased on average over the past 50 years. We explore relationships between M, SB₀ and stock-recruit parameters under typical assumptions used in stock assessments. We pose two questions: (1) Are equilibrium-based reference points meaningful for Pacific herring stocks when productivity is changing rapidly? and (2) How do different derivations of the LRP impact perceptions of stock status and the relationship of the LRP to serious harm thresholds? We show that when productivity is changing rapidly, the calculation of SB₀ using typical analytical approaches can violate equilibrium assumptions. Moreover, when M is increasing, the strong negative relationship between M and SB₀ means that LRPs based on dynamic recent values of M can be substantially lower than LRPs based on historical or long-term average values M. Allowing LRP thresholds to decrease with increasing M results in more optimistic assessments of stock status and potentially allows LRPs to drop to levels below serious harm thresholds. We invite practitioners to take a more thoughtful approach to the question of whether LRPs should be lowered in the presence of increasing natural mortality.