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

Abstract

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.

Nutrigonometry III: curvature, area and differences between performance landscapes

“…It is important to mention that the model proposed here, and all previous models developed in the literature which rely on—or estimate properties from—performance landscape assume that the landscape itself can be estimated accurately. This may not necessarily be the case for a standard GF design which relies on nutritional rails and explores a subset of all possible regions in space, leaving large parts of the space unexplored (particularly in regions that correspond to the interactions between nutrients, that is, along the diagonal of the nutrient space) [ 40 ]. The rationale for empirically testing a subset of diets and hence, regions of the nutrient space, is that results are reliable only if ecologically relevant ranges of diets are tested (see Point 4 in [ 51 ]).…”

“…Note that the choice of 1 was arbitrary and does not affect curvature or surface-area.We then used the grid containing the predicted values for each trait to estimate curvature, surface-area and Hausdsorff distances.The algorithm above is needed because standard GF design only explores the nutritional space through rails, which are lines that subdivide the nutrient space. This means that a large portion of the space remains unexplored, and the approach above is needed to cover these unexplored spaces as shown in the second study of the Nutrigonometry series (see [40]). A full coverage of the nutrient space is needed for a global analysis of the properties of the performance landscapes (see also ‘Discussion’ section for more on this topic).…”

Nutrigonometry IV: Thales’ theorem to measure the rules of dietary compromise in animals

“…Flies were given seven P:C ratios (i.e., nutritional rails), namely, 0:1, 1:16, 1:8, 1:4, 1:2, 1:1, and 1.9 14 . This data has been extensively used for GF method development and thus, has gained a important status as a ground-truth in the field 38 – 40 . The second dataset was for two locust species originally presented in Fig.…”