Statistical behavior of retrospective patterns and their effects on estimation of stock and harvest status

• Retrospective patterns are problematic for stock assessment models.
• We provide a bootstrap method to estimate variance of retrospective patterns.
• We conducted simulation study with retrospective patterns from natural mortality change.
• Simulation study suggests that terminal estimates should always be adjusted by Mohn's ρ.
• Which estimates to use for stock status depends on future natural mortality.

The presence of retrospective patterns in stock assessments is problematic for determining stock and harvest status because current estimates of stock size or fishing mortality are consistently lower or higher than those when the assessment model is updated with new data. A statistical measure of evidence for retrospective patterns is needed, but a requisite method to estimate variance of retrospective patterns is lacking. We evaluated the statistical behavior of a parametric bootstrap-based variance estimator for retrospective patterns that arise due to a change in natural mortality using a simulation experiment patterned after an assessment of yellowtail flounder on Georges Bank. We also evaluated effects of retrospective patterns on accuracy of stock assessment results and adjustments to terminal stock attributes intended to correct for retrospective patterns. We focused our analyses on Mohn's ρ, but the bootstrap approach could be used with any measure of retrospective pattern. We found that coverage for confidence intervals of Mohn's ρ were adequate, particularly for commonly specified percentage levels near 95%. We also found increased statistical efficiency of terminal year stock attributes that are adjusted for estimated retrospective patterns when the model structures used to simulate observations and estimate the parameters were inconsistent. Furthermore, this increase in efficiency was generally greater than the decrease in efficiency of adjusted stock attributes when models for simulated data and parameter estimation were consistent. However, the utility of adjustments for estimating stock and harvest status depended on our expectation for future productivity of the stock and using confidence interval coverage of Mohn's ρ to determine whether to adjust terminal stock attributes provided no greater benefit than simply always adjusting.