Evaluate the power of a modified continuous time D-DM model, using BSPM and ASPM as benchmarks：a case study of a slow-growing tuna species (Thunnus alalunga Bonnaterre, 1788)

Delay-difference type models (D-DMs) represent a theoretical bridge between classical surplus-production models and data-rich age-structured models. However, periodic changes of recruitment, growth, and mortality rates can also be accounted for in the continuous time delay-difference models (CTDDMs). Such models incorporate biological processes by considering continuous time delays. In the present study, CTDDMs produced realistic outputs for yield, biomass, and biological reference points (BRPs) based on using data from the southern Atlantic albacore fishery. Simulations of predicted biomass or numbers were carried out using fully age-structured information (covering 30 years) and compared with more complicated age-structured production models (ASPMs). The performance of the CTDDMs was also compared with that of a Bayesian surplus production model (BSPM). BSPM estimates of the BRPs, e.g., r, k and MSY, were used as benchmarks for the respective CTDDMs estimates. The assessed maximum sustainable yields by the two models were approximately 21,600 t and 23,500 t, respectively, while the CTDDMs produced more population parameters estimation. The CTDDMs provided reliable prediction of BRPs for sustainable fisheries management and required fewer data than ASPMs. This study have evaluated the applicability and sensitivity of the continuous-time-type D-DM model. The scalability of these models will be discussed in further research.