Conventional and alternative dose–response models to estimate nutrient requirements of aquaculture species

Despite criticism in the literature, the conventional broken-line model (BLM) and the four-parameter saturation kinetics model (SKM) are the dose–response models most frequently used to estimate nutrient requirements of aquaculture species. This study combines the advantages of both conventional models to produce models that more accurately estimate requirements, the broken saturation kinetics model (BSKM) and the broken-convex curve model (BCCM). Additionally, the feasibility of using other alternative dose–response models is addressed and an equivalence test is introduced as a method to deal with statistical results that are not significant at the plateau of the response curve. The models were evaluated using 24 published cases, considering weight gain and feed efficiency as response parameters. There were significant differences (P < 0.05) in model-fitting performance and parsimony. The BSKM and BCCM fitted better, while some evidence supported conventional models as being more parsimonious. There was significant evidence that fitting performance and parsimony of the models tended to coincide among the cases. There was also significant evidence that estimates of nutrient requirements differed, depending on the model used, and that the models tended to consistently yield low, intermediate, or high requirements among the cases. The BLM produced the lowest estimates and the SKM produced an erratic performance. When the BLM was fitted to a published case, the slope at the plateau was not significant; yet an equivalence test, using the two-one sided procedure, with a similarity level of 5%, indicated that it was not adequate to assume that fish were non-responsive to nutrient inputs. The results indicate that combining the advantages of the conventional models resulted in models that were easy to implement and that more accurately estimated nutrients requirements. Additionally, equivalence tests were shown to be useful for analyzing results that were not significant at the plateau.