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

Diet specialists and generalists face a common challenge: they must regulate the intake and balance of nutrients to achieve a target diet for optimum nutrition. When optimum nutrition is unattainable, organisms must cope with dietary imbalances and trade-off surplus and deficits of nutrients that ensue. Animals achieve this through compensatory rules that dictate how to cope with nutrient imbalances, known as 'rules of compromise'. Understanding the patterns of the rules of compromise can provide invaluable insights into animal physiology and behaviour, and shed light into the evolution of diet specialisation. However, we lack an analytical method for quantitative comparisons of the rules of compromise within and between species. Here, I present a new analytical method that uses Thales' theorem as foundation, and that enables fast comparisons of the rules of compromise within and between species. I then apply the method on three landmark datasets to show how the method enables us to gain insights into how animals with different diet specialisation cope with nutrient imbalances. The method opens new avenues of research to understand how animals cope with nutrient imbalances in comparative nutrition.