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14In the Barents Sea and adjacent water, fishing grounds are closed for shrimp

A general spatio-temporal abundance index model is introduced and applied on a case study for North East Arctic cod in the Barents Sea. We demonstrate that the model can predict abundance indices by length and identify a significant population density shift in northeast direction for North East Arctic cod. Varying survey coverage is a general concern when constructing standardized time series of abundance indices, which is challenging in ecosystems impacted by climate change and spatial variable population distributions. The applied model provides an objective framework that accommodates for missing data by predicting abundance indices in areas with poor or no survey coverage using latent spatio-temporal Gaussian random fields. The model is validated, and no violations are observed.

The North Sea cod stock assessment is based on indices of abundance-at-age from fishery-independent bottom trawl surveys. The age structure of the catch is estimated by sampling fish for otoliths collection in a length-stratified manner from trawl hauls. Since age determination of fish is costly and time consuming, only a fraction of fish is sampled for age from a larger sample of the length distribution and an age–length key (ALK) is then used to obtain the age distribution. In this study, we evaluate ALK estimators for calculating the indices of abundance-at-age, with and without the assumption of constant age–length structures over relatively large areas. We show that the ALK estimators give similar point estimates of abundance-at-age and yield similar performance with respect to precision. We also quantify the uncertainty of indices of abundance and examine the effect of reducing the number of fish sampled for age determination on precision. For various subsampling strategies of otoliths collection, we show that one fish per 5-cm-length group width per trawl haul is sufficient and the total number of fish subsampled for age from trawl surveys could be reduced by at least half (50%) without appreciable loss in precision.

The state-space assessment model (SAM) is extended by allowing a functional relationship between observation variance and the corresponding prediction. An estimated relationship between observation variance and predicted value for each individual observation allows the model to assign smaller (or larger) variance to predicted larger log-observations. This relation is different from the usual assumption of constant variance of log-observations within age groups. The prediction–variance link is implemented and compared to the usual constant variance assumption for the official assessments of North East Arctic cod and haddock. For both of these stocks, the prediction–variance link is found to give a significant improvement.