Evaluating the Consequences of Adjusting Fish Stock Assessment Estimates of Biomass for Retrospective Patterns using Mohn's Rho

A retrospective pattern exists when estimates of some assessment parameter for a given time period (e.g., biomass in a given year) trend in a systematic way as additional periods of data (i.e., typically a year) are added. Causes of such patterns are difficult to determine, and the pattern does not necessarily indicate the direction of the parameter bias. Mohn's rho measures the severity of retrospective patterns and has been used to adjust estimates of biomass and quotas. The consequences of applying Mohn's rho rather than ignoring the pattern are unclear. I used an age-structured simulation based on Atlantic Herring Clupea harengus to evaluate the consequences of ignoring retrospective patterns versus applying Mohn's rho. When the application of Mohn's rho produced more accurate estimates of biomass, subsequent spawning stock biomass and yields were near target levels. When the use of Mohn's rho produced less-accurate estimates of biomass, the results depended on the direction of the pattern. With a positive retrospective pattern (i.e., estimates of biomass for a given year decline as additional years of data are added), the application of Mohn's rho lowered the estimates of biomass, producing little cost in long-term yield relative to the subsequent increases in biomass but resulting in a short-term cost of lower annual quotas. With a negative retrospective pattern (i.e., estimates of biomass for a given year increase as additional years of data are included), the use of Mohn's rho increased the estimates of biomass, thus generating long-term costs in yield and biomass but with a short-term benefit of higher annual quotas. The decision of whether to ignore retrospective patterns or apply Mohn's rho should depend on the direction of the pattern and the relative weight of short- and long-term fishery objectives. Performance may also depend on the shape of the control rules that are used to define annual quotas. Received May 14, 2013; accepted January 2, 2014