This paper provides a comparison of methods to estimate von Bertalanffy growth parameters for Patagonian toothfish (Dissostichus eleginoides) in Subarea 48.3. Here, we have extended growth estimation methods presented in previous studies (Marsh et al. 2022a, b) to fit and compare a series of growth models with the aim to determine a method appropriate for these data. Following recommendations from WG-FSA-2022 (CCAMLR 2022, paragraph 4.28), we: i) explored implementing the Candy conditional-on-age approach using alternative selectivity functions (plateau and constant selectivity probabilities); ii) allowed for additional uncertainty in the linear predictor for older ages using a growth model fit in a Bayesian framework; and iii) presented model residuals. Growth models were fitted to three sex categories (combined sex; females; males) and to the same time periods used in previous studies for consistency (2009 to 2010; 2011 to 2015; 2016 to 2020; 2021).
Comparison of the estimation methods suggested that the Bayesian growth model allowing for additional uncertainty for older ages had the best fit to the data and least bias when examining model residuals. Using the data relevant for the stock assessment, i.e. combined sex and all years of data, we explored the sensitivity of this growth model to inclusion of young fish (≤6 years) using survey data. Our results showed that including the youngest age-classes of fish (ages 2 to 3) from survey data had a large influence on the model estimates, suggesting that the von Bertalanffy model could be inappropriate to capture growth at early ages. While we acknowledge the importance of accounting for data sampling strategy in estimates of growth parameters, our results highlighted the sensitivity of the Candy method to the selectivity function used, and at present, we do not consider the selectivity functions utilised here to be sufficiently representative of the length distributions of the catch or the sampled otoliths.
Based on the results, we propose to use the Bayesian growth model for future estimation of von Bertlanffy growth parameters to be used in assessments for Patagonian toothfish in Subarea 48.3, and to include survey data in the age dataset, with the exception of the age 2-3 fish, given their large influence on model estimates.