Applying a separability assumption in a length-based stock assessment model to evaluate intra-annual effects of recruitment process error of small-pelagic fish

A key factor in population models, the temporal scale, should both reflect intra-annual biological processes and avoid over-parameterization. We applied the separability assumption to model recruitment process error as additive effects of random annual deviates and quarterly fixed effects (QFEM) to improve our understanding of intra-annual recruitment patterns and, at the same time, minimize the impact of over-parameterization. We formulated a length-based model with a quarter-year temporal resolution and applied it to the anchovy (Engraulis ringens) fishery off northern Chile and southern Peru, using data from 1984 to 2015. Model performance was compared to that of a larger model in which the process error is treated as an interaction of quarter-year effects (QYIM). QFEM proved to be most adequate only when the variability of population processes and the fishery are determined by a clear seasonal pattern. In those cases, QFEM characterized recruitment seasonality as well as inter-annual trends. Under these conditions, the separability hypothesis of recruitment process error substantially reduced the number of parameters in the stock assessment model, the bias of estimated population variables, and uncertainty when the most recent data were incomplete or non-informative. QFEM provides an alternative way to improve assessments and fishery management for fast-growing and short-lived species such as small pelagic fish.