A comparison of regression models for defining EPA plus DHA requirements using the gilthead seabream (Sparus aurata) as a model species

Carnivorous marine fish species such as gilthead seabream (Sparus aurata) require dietary eicosapentaenoic (EPA) and docosahexaenoic (DHA) acids for optimal growth and wellbeing. The rapid growth of global aqua -culture, along with increased proportions of dietary oil to increase growth rate of farmed fish, has meant that the supply of marine oils used in aquafeeds has become limited. The shortfall has been satisfied by using vegetable oils that lack EPA and DHA and, therefore, EFA (essential fatty acid) requirements of juvenile marine fish require reassessment. A dietary trial was carried out with gilthead seabream (~25 g) that were fed diets with six EPA + DHA levels ranging from 0.2% -3.2% diet as fed. For each pellet size, the biometric data (weight gain, daily growth index and feed conversion ratio) were analysed by four different regression strategies, namely split linear, quadratic, the Gompertz function, and the four-parameter logistic function. Over the whole experimental period (two pellet sizes) data suggested the current published requirement (1% of diet) was low and should be increased to at least 1.2%. However, when the first pellet size for fish of 25-80 g was considered, the apparent requirement was at least 1.4% of diet. This demonstrated in a single trial that EFA requirement was a function of fish mass, decreasing as the fish grows. If FCR is considered, the requirement may be as high as 2%. The suitability of different regression models varied, as the data for the first pellet was best fit by curves but, over both pellet sizes, the split linear fit the data best. For asymptotic models (Gompertz and four-parameter logistic functions), a novel way of defining the requirement was presented, the "elbow " calculation as a method to bisect an asymptotic function. Therefore, using the raw data, we illustrate how a range of regression approaches could be explored when determining nutrient requirement estimates as no single model was an ideal fit for all response curves.