Estimating individual growth variability in albacore (Thunnus alalunga) from the North Atlantic stock: Aging for assessment purposes

• Use of back-calculation methods to obtained the individual growth histories derived by reading fin ray sections of first dorsal fin of albacore (Thunnus alalunga) North Atlantic stock.
• Estimates of growth parameters of von Bertalanffy function were fit by incorporating random effects on L∞ and K.
• Application of a Bayesian hierarchical modelling approach.
• Test of different hypotheses on the back-calculation method and impact of size f, the sample and length coverage on the albacore vB growth model function of North Atlantic albacore.

Length-frequency data and derived catch at age matrices are used in north Atlantic albacore (Thunnus alalunga) stock assessment conducted within the International Commission for the Conservation of Atlantic Tunas (ICCAT). Growth is assumed to follow the von Bertalanffy model with the assumption that growth parameters are constant over time and the same for all fish. However, individual growth variability is an important factor not considered and affecting the input into the modelling of the population. This study describes a Bayesian hierarchical model applied to model the individual variability in the parameters asymptotic length (L∞) and growth rate (K) of the von Bertalanffy growth model for North Atlantic albacore. The method assumes that the L∞ and K values for each individual fish are drawn from a random distribution centered on the population mean values, with estimated variances. Multiple observations of spine diameter at age for individual fish were obtained by direct reading of spine sections collected in 2011 and 2012. A suite of back calculation methods were then applied to the measurements of annuli diameters in the aged individuals observed to back-calculate lengths at each age. The von Bertalanffy model was fitted to the measured and back-calculated lengths. Models with and without individual growth variability were compared using the deviance information criterion (DIC) to find the best model. Normal and log-normal error distribution models were used to analyse the data. Additionally, subsamples of the data were used to evaluate whether an unbalanced age-distribution in the data affects estimates of growth parameters. It was found that North Atlantic albacore asymptotic length (L∞) varies significantly between individual fish but not individual rate growth (K), for all back-calculation methods. Furthermore, negatively correlated relationships between von Bertalanffy growth parameters of asymptotic mean (L∞) and growth rate (K) were estimated for North Atlantic albacore with the array of models explored. The overall estimated values of K and population mean L∞ parameters were similar to values estimates in previous north Atlantic albacore growth studies.