Evaluating the Consequences of Adjusting Stock Assessment Estimates of Abundance for Retrospective Patterns Using Mohn's Rho

A retrospective pattern is a systematic trend in a time series of stock assessment estimates (e.g., abundance, fishing mortality) that emerges as additional years of data are included.  Treating retrospective patterns is challenging because their causes are difficult to determine and they do not necessarily trend towards the true value for the given parameter.  Mohn’s rho is a statistic that quantifies the degree of a retrospective pattern and has been used to make post-hoc adjustments to stock assessment estimates under the assumption that this leads to an improved estimate and the pattern will persist in the future.  I used a simulation model to compare the consequences of two analytical alternatives: 1) ignoring retrospective patterns and 2) adjusting terminal year estimates of abundance using Mohn's rho.  With a positively biased retrospective pattern (i.e., estimates of abundance for a given year decline as additional years of data are included), adjusting terminal year estimates of abundance using Mohn’s rho cost little in long-term yield relative to the subsequent increases in abundance, regardless of whether the pattern trended towards the true abundance.  Such adjustments, however, came at the costs of lower quotas and yield in the short-term relative to ignoring the retrospective pattern.  Ignoring the retrospective pattern produced benefits of higher quotas and yield in the short-term relative to making adjustments using Mohn’s rho, but if the retrospective pattern trended toward the truth, this benefit came at the cost of long-term yield and even greater losses in abundance.  Deciding whether ignoring retrospective patterns or adjusting terminal year estimates of abundance using Mohn’s rho is the preferred course of action will partially depend on the relative weight given to the competing fishery objectives of maximizing short-term yield versus maintaining long-term abundance.