A Bayesian hierarchical approach to estimate growth parameters from length data of narrow spread

Estimating fish growth from length frequency data is challenging. There is often a lack of clearly separated modes and modal progression in the length samples due to a combination of factors, including gear selectivity, slowing growth with increasing age, and spatial segregation of different year classes. In this study, we present an innovative Bayesian hierarchical model (BHM) that enables growth to be estimated where there are few distinguishable length modes in the samples. We analyse and identify the modes in multiple length frequency strata using a multinormal mixture model and then integrate the modes and associated variances into the BHM to estimate von Bertalanffy growth parameters. The hierarchical approach allows the parameters to be estimated at regional levels, where they are assumed to represent subpopulations, as well as at species level for the whole stock. We carry out simulations to validate the method and then demonstrate its application to Indian Ocean longtail tuna (Thunnus tonggol). The results show that the estimates are generally consistent with the range of estimates reported in the literature, but with less uncertainty. The BHM can be useful for deriving growth parameters for other species even if the length data contain few age classes and do not exhibit modal progression.