Introduction
Fish nutritional requirements are generally estimated through analysis of dose-response studies involving essential nutrients, which condition the nutritional targets of fish feeds during formulation. Due to the high cost of undertaking such studies, they are often performed under simplifying assumptions (e.g., the effects of nutrients on growth are marginally independent) and the implicit notion that nutritional requirements are essentially static: once the requirements of a specific nutrient have been estimated for a specific species, at a specific size and under specific environmental conditions, its value is simply accepted as being universally valid and seldom re-evaluated.
On the other hand, genetic improvement programs of commercial fish species through selective breeding are known to have potential effects on fish traits which directly condition nutritional requirements (e.g., feeding and growth potential, retention efficiencies, body composition). Thus, and given the importance of the genetic-nutrition interaction in the process of fish growth, it seems relevant to be able to quantitatively predict the impact of such changes in fish traits on optimal feed formulation targets.
In this work, we develop analytical formulas that directly relate “relevant fish traits” to “optimal feed formulation” as a way of tackling this question without resorting to (possibly biased) observational data.
Materials and methods
In order to establish general formulas, we start by assuming energy and mass conservation to define a budget for energy, protein and phosphorus (i.e., gain = intake – losses). Then we consider a series of assumption sets with increasing levels of complexity (and realism).
Expanding the budgets under each of these sets of assumptions leads to different closed-form formulas that directly relate relevant fish traits to the optimal feed inclusion levels of energy, protein and phosphorus. The specific effect of each trait on optimal inclusion levels were then obtained and analysed both through an analytical sensitivity analysis and plots of the marginal effects of each trait (under varying conditions).
Results
The formulas obtained under a simplistic assumption of a linear relationship between intake and retention (of energy and nutrients) provide a useful first-order approximation to the effect of changes in fish traits due to genetic improvement on optimal feed formulation targets: the digestible amount of a certain nutrient (or energy) required in the diet is proportional to the relative amount of that nutrient (or energy) in the body of fish, and inversely proportional to FCR and to the retention efficiency of that nutrient (or energy). This implies that the effect of relevant fish traits on optimal feed formulation targets is, in this case, straightforward, since each trait multiplicatively and independently affects the optimal target in the same way.
On the other hand, the more realistic formulas, obtained under an assumption of a saturating (rational) relationship between intake and retention, display a slightly more complicated structure, where (unlike in the previous formulas) both the feeding rate and the growth/anabolic rate play a relevant role (see Figure 1 for an example) , and where the effects of the different traits on the optimal inclusion rates is not necessarily multiplicatively separable. Despite these challenges, these formulas end up being more useful than the previous ones, not just due to the increased realism (e.g., effective retention efficiency should go down at high intake levels), but due to the fact that the nutritional and genetic effects are more clearly separated and identifiable, which is not the case for the first set of formulas (since FCR is not a feed-independent trait).
Discussion and Conclusion
The formulas developed within the traits-to-feed framework seek to help aquaculture stakeholders make more informed decisions: for fish farmers, these formulas can be used to adjust feeding rates to achieve specific growth rates (as a function of fish size, diet composition and environmental conditions); for fish breeders, these formulas can inform them on the relative importance of different fish traits (and the relevance of estimating them within breeding programs); f or fish nutritionists and aquafeed formulators, these formulas can guide the formulation of diets that are adapted to specific fish strains and under specific conditions and growth targets.
Acknowledgements
This work is part of project AquaIMPACT (Genomic and nutritional innovations for genetically superior farmed fish to improve efficiency in European aquaculture), funded by the European Union’s Horizon 2020 research and innovation programme under grant agreement 818367.