Nutrigonometry I: using right-angle triangles to quantify nutritional trade-offs in performance landscapes

Animals regulate their food intake to maximise the expression of fitness traits but are forced to trade-off optimal expression of some fitness traits due to differences in nutrient requirements of each trait (‘nutritional trade-offs’). Nutritional trade-offs have been experimentally uncovered using the Geometric Framework for Nutrition (GF). However, current analytical methods to measure such responses rely on either visual inspection or complex models of vector calculations applied to multidimensional performance landscapes, making these approaches subjective, or conceptually difficult, computationally expensive, and in some cases inaccurate. Here, we present a simple trigonometric model to measure nutritional trade-offs in multidimensional landscapes (Nutrigonometry), which relies on the trigonometric relationships of right-angle triangles and thus, is both conceptually and computationally easier to understand and use than previous quantitative approaches. We apply Nutrigonometry to a...