Growth modelling including size heterogeneity: Application to the intensive culture of white shrimp (P. vannamei) in freshwater

• We model the phenomenon of homogeneity and heterogeneity in the growth of Penaeus vannamei.
• The model was applied to intensive cultivation of P. vannamei in freshwater (90–330 shrimp m−2).
• Three mathematical functions were modified to include the effect of the initial density.
• Best fits are obtained by including aspects of variability of sizes (PRMSE decreases from 16% to 12%).
• The results of this study allow the producer to optimise the gradation periods in culture.

This article models the growth of a population in aquaculture, including the phenomenon of size heterogeneity. Experimental observations of six initial densities (90, 130, 180, 230, 280 and 330 shrimps m−2) in an intensive culture of Penaeus vannamei in freshwater were used to fit a growth model. For this, three mathematical functions were analysed (Gompertz, von Bertalanffy and Pütter), which were modified in order to include the effect of initial density. Two models were constructed, one assuming the hypothesis of homogeneous individual growth and the other including size-heterogeneity throughout the culture cycle. For the second case, a stabilisation time was evaluated which defines the future heterogeneity of the cohort. In each initial density, the stabilisation phase was reached at approximately 2 g. However, the time taken for this phase to start increased with increasing initial culture density. The modified von Bertalannfy function was the most effective of the three equations in predicting growth. The weight predictions, assuming homogeneity and variability of sizes, presented low Percentage Root Mean Square Errors (PRMSE). However, the inclusion of size variability in the fit produced better statistical results than when they were not included (PRMSE decreased from 16% to 12%). This confirms the importance of taking into account size heterogeneity at an intensive level. Particularly at the technical level when the aquaculture producer is required to make stocking and harvest plans.