Admissible dissimilarity value (ADV) as a measure of subsampling reliability: case study North Sea cod (Gadus morhua)

The shape of the length frequency distribution (LFD) is an important input for stock assessments and one of the most important features in studies of fish population dynamics, providing estimates of growth parameters. In practice, oversampling may occur when sampling commercially important species. At times of more and more limited resources, the length sample size can be optimized at some stages of national or regional sampling programmes, without reducing the quality of stock assessments. The main objective of this study is to demonstrate a general distribution-free methodological approach for an optimization of sample size developed as an alternative to both analytical and bootstrap approaches. A novel framework to identify the reduced but still informative sample and to quantify the (dis) similarity between reduced and original samples is proposed. The identification procedure is based on the concept of reference subsample, which represents a theoretical minimal representative subsample that despite smaller sample size still preserves a reasonably precise LFD for certain species. The difference between the original sample and the reference subsample called admissible dissimilarity value (ADV) serves as the upper threshold and can be used to quantify the reliability of derived subsamples. Monte Carlo simulations were conducted to validate the approach under various LFD shapes. We illustrate in case studies how ADV can support to evaluate adequate sampling effort. The case studies focus on length samples from the German commercial vessels fishing for North Sea cod (Gadus morhua).