Testing the validity of lognormal likelihoods for abundance indices in stock assessment models using the generalized gamma distribution

Abstract For stock assessments to be accurate, observation models (likelihoods) must accurately reflect data. Many studies have examined age/length composition likelihoods, but few examined abundance indices, which are typically assumed lognormal. Indices from design-based estimators and model-based standardization are sums of positive quantities, but lognormal distributions arise from products of positive quantities, and so lack theoretical justification. We quantified the severity and extent of non-lognormality of indices by fitting the generalized gamma distribution (GGD) to design-based bootstrap biomass estimates across 19 species from Gulf of Alaska survey data. Non-lognormality extent varied by species and year, with less skew than a lognormal common, particularly for species with few zero catches. Age-structured model estimates of spawning biomass using the GGD versus lognormal likelihoods were generally within 5%, with even smaller uncertainty impacts. Overall, we found ample evidence for non-lognormality, but that assessments were not necessarily sensitive to it, particularly for well-sampled species. Impacts may be larger for models without other data (e.g. surplus production models) or for multimodal indices, and corroboration in additional circumstances is critical. Accurately incorporating abundance trends via the index is crucial for fisheries management, and our practical roadmap will help stock assessment authors to test and improve their models.