Integrating published experimental data and hierarchical bayesian modeling: a model for common cuttlefish (Sepia officinalis Linnaeus, 1758) growth to improve predictions for aquaculture and wild stocks

A mathematical description of sub-adult cephalopod Instantaneous Growth Rate (1–120 days after hatching) was formulated as a multistage function, combining a Gaussian function during the post-hatching stages and an exponential decay function during the transition to the pre-adult stages. A set of candidate mixed effects models was formulated where random parameters derived from a common (hyper)distribution were associated with each experiment and where fixed effects were used to account for dependency on temperature, food type and food amount. The candidate models were fitted to data collected from published aquaculture experiments using a Bayesian hierarchical approach and evaluated using quantitative diagnostics and performance metrics. The results showed that including covariates and random effects improved the ability of the model to fit the data. Growth was found to increase rapidly at low food rations but at a decreasing rate as the food supply becomes abundant. The relationship between temperature and growth transitioned from positive to negative approaching the sub-adult stage. Mixtures of small and medium shrimp were found to lead to higher growth during the first weeks after hatching, while grass shrimp were preferred thereafter. The meta-analytic estimation approach allowed information to be leveraged from multiple studies while accounting for the uncertainty induced by variation in experimental setups. Model posteriors were used to predict growth rate and weight at age, which were compared to out of sample data from aquaculture and wild captured individuals. We discuss how the proposed model can be used to make predictions for the growth of common cuttlefish in aquaculture and fisheries studies.