Looking in the rear-view mirror: bias and retrospective patterns in integrated, age-structured stock assessment models

Retrospective patterns are systematic changes in estimates of population size, or other assessment model-derived quantities, that occur as additional years of data are added to, or removed from, a stock assessment. These patterns are an insidious problem, and can lead to severe errors when providing management advice. Here, we use a simulation framework to show that temporal changes in selectivity, natural mortality, and growth can induce retrospective patterns in integrated, age-structured models. We explore the potential effects on retrospective patterns of catch history patterns, as well as model misspecification due to not accounting for time-varying biological parameters and selectivity. We show that non-zero values for Mohn's rho(a common measure for retrospective patterns) can be generated even where there is no model misspecification, but the magnitude of Mohn's rho tends to be lower when the model is not misspecified. The magnitude and sign of Mohn's rho differed among life histories, with different life histories reacting differently from each type of temporal change. The value of Mohn's rho is not related to either the sign or magnitude of bias in the estimate of terminal year biomass. We propose a rule of thumb for values of Mohn's rho which can be used to determine whether a stock assessment shows a retrospective pattern.