Nutrigonometry II: Experimental strategies to maximize nutritional information in multidimensional performance landscapes.

Animals regulate their nutrient consumption to maximize the expression of fitness traits with competing nutritional needs ("nutritional trade-offs"). Nutritional trade-offs have been studied using a response surface modeling approach known as the Geometric Framework for nutrition (GF). Current experimental design in GF studies does not explore the entire area of the nutritional space resulting in performance landscapes that may be incomplete. This hampers our ability to understand the properties of the performance landscape (e.g., peak shape) from which meaningful biological insights can be obtained. Here, I tested alternative experimental designs to explore the full range of the performance landscape in GF studies. I compared the performance of the standard GF design strategy with three alternatives: hexagonal, square, and random points grid strategies with respect to their accuracy in reconstructing baseline performance landscapes from a landmark GF dataset. I showed that standard GF design did not reconstruct the properties of baseline performance landscape appropriately particularly for traits that respond strongly to the interaction between nutrients. Moreover, the peak estimates in the reconstructed performance landscape using standard GF design were accurate in terms of the nutrient ratio but incomplete in terms of peak shape. All other grid designs provided more accurate reconstructions of the baseline performance landscape while also providing accurate estimates of nutrient ratio and peak shape. Thus, alternative experimental designs can maximize information from performance landscapes in GF studies, enabling reliable biological insights into nutritional trade-offs and physiological limits within and across species.