Growth models in aquaculture for hybrid and natural groupers based on early development stage

Grouper has been highlighted as current hot species for marine aquaculture in China, so it is vital to master its growth performance in early development stage and understand growth trend of it. However, there are few detailed reports on the growth model and biological parameters in the early growth of grouper. The aim of this study is to discuss and compare the applicability of growth indexes and 10 biological growth models in larval and juvenile stage of hybrid and natural groupers, then to evaluate the optimum model. Pearl gentian grouper (PG) and kelp grouper (KG) were selected. The growth data of grouper larvae and juvenile were chosen. Absolute growth (AG), relative growth rate (RGR) and specific growth rate (SGR), and the thermal-unit growth coefficient (TGC) were calculated. Ten nonlinear models, such as Logistic, Gompertz,Von Bertalanffy, Generalized Weibull, Janoschek, Schnute and et al., were used to fit growth. Models were evaluated and selected by Akaike information criterion (AIC) method, the values of RMSE, MAE and R2, parameter significance level and iterations. Fitting results showed that compared with AG, RGR and SGR, TGC has higher fitting degree, especially for fitting weight (R2 > 0.99). In larval stage, Schnute model had the highest best fit ratio (75%), and minimum number of iterations (< 71), with more than two significant parameters (P < 0.001). In juvenile stage, the beat fitting ratio of Janoschek model evaluated by AIC was 25%, and that by RMSE, MAE and R2 was 50%, which was higher than other models. It also had low iteration times and high significant level (P < 0.05). For model evaluation, best fitting result evaluated by AIC method was different from that evaluated by RMSE, MAE and R2. It is more reliable to combine the two methods for model evaluation. The growth curves generated by optimum models showed that the growth characteristics of larvae is exponential, and in juvenile stage, PG maintained accelerated growth but the growth rate of KG gradually decreased. In summary, the optimum model of larval stage was Schnute model and that of juvenile stage was Janoschek model; 4-parameter models have high robustness and accuracy for fitting growth; Compared with KG, PG grows faster and is more suitable for aquaculture.