Abstract/Summary

Nutrition is fundamental to all living systems. In animals, morphological, physiological, and behavioral adaptations for acquiring and digesting food shape their responses to the environment. While experimental frameworks have advanced our understanding of animal nutrition, methodological tools to address its complexity remain limited. This thesis introduces pioneering analytical methods to explore nutritional trade-offs and optimal diet balances using Geometric Framework for Nutrition (GF) performance landscapes. Chapter 1 traces the historical development of GF, highlighting its independent origins in agricultural sciences and evolutionary ecology. Chapter 2 presents the Vector of Positions approach—the only method capable of analysing n-dimensional performance landscapes—validated using two landmark datasets. Chapter 3, the first study in the Nutrigonometry series, introduces a computationally efficient algorithm to estimate nutritional trade-offs in three-dimensional performance landscapes—the most common in the field. Using the Pythagorean theorem, I demonstrate its robustness across multiple datasets, showing that ordinary linear regression outperforms machine learning models for these calculations. Chapter 4 provides the first systematic test of the GF experimental design, proposing improved methods for high-dimensional nutritional experiments to enhance accuracy in estimating optimal diets and performance landscapes. Chapter 5 applies differential geometry to measure curvature in performance landscapes and introduces the Hausdorff distance for comparing performance landscapes. Chapter 6 integrates previous analytical methods to examine the evolution of optimal diets between sexes in insects. My findings reveal that the protein-to-carbohydrate ratio is more similar among closely related species and that sexual conflict over nutrition is evolutionarily conserved. This study represents the first empirical work in precision comparative nutrition. Chapter 7 applies Thales’ theorem of inscribed triangles to analyse how animals cope with imbalanced diets. By triangulating food intake under suboptimal conditions, I quantify deviations from Thales’ theorem, revealing underlying nutritional strategies. This thesis advances our understanding of nutritional constraints in optimizing fitness. Through a range of methodological advancements, my work provides new insights into how animal nutrition can be studied in its full multidimensional complexity. These methods and applications have broad implications, and I hope they will be extended to other areas of biology to further our understanding of how living organisms interact with their diet and how nutritional responses evolve across the tree of life.