Inclusion of ageing error and growth variability using a bootstrap estimation of age composition and conditional age-at-length input sample size for fisheries stock assessment models

Statistical catch-at-age assessment models used for fisheries management integrate multiple sources of information that are statistically weighted in a joint likelihood framework; the relative statistical weighting between these sources of information is an important, yet often subjective aspect of stock assessment. Input sample size (ISS) is a quantity that is used to statistically weight composition data in these types of models. Both design-based bootstrap and model-based estimators have been proposed, however, these methods to determine ISS do not explicitly account for uncertainty from ageing error and growth variability that are inherent to expanded age composition and conditional age-at-length data. In this study, we evaluate the impact of including ageing error and growth variability within bootstrap methods that estimate age composition and conditional age-at-length ISS. We find that for all the stocks evaluated the ISS determined from bootstrap methods decreased as these addition sources of uncertainty were included. The decrease in ISS was species type specific, but generally decreased up to 40% when ageing error was introduced, up to 50% when growth variability was included, and up to 60% when both sources of uncertainty were included. These results indicate that there is more variability within age composition or conditional age-at-length data than would be accounted for with ISS estimates that do not include these sources of uncertainty. The method and results provided here allow for assessment scientists to statistically weight age composition and conditional age-at-length with ISS that takes into account ageing error and growth variability from either fishery-independent or fishery-dependent sources. Including these sources of uncertainty improves bootstrap estimates of ISS to capture all the sources of variability in age composition and conditional age-at-length and will subsequently improve stock assessment model quality.

Automated summary

This study evaluates the impact of considering ageing error and growth variability on the determination of input sample size (ISS) in statistical catch-at-age assessment models. The results show that including these sources of uncertainty decreases the ISS determined through bootstrap methods. This indicates that there is more variability in age composition and conditional age-at-length data than previously accounted for. Including these sources of uncertainty improves the estimation of ISS and subsequently improves the quality of stock assessment models.