Nutrigonometry III: curvature, area and differences between performance landscapes

Optimum ratio of dietary protein and carbohydrate that maximises lifespan is shared among related insect species

Animals often regulate the intake and quantity of nutrients to maximise fitness through life-history traits such as lifespan, but we still lack a proper understanding of how specific nutrients influence these traits. Here, I developed an algorithm which allowed me to create a nutrient-specific database from literature data, and investigated how the requirements of protein (P) and carbohydrate (C) needed to maximise lifespan evolved across nine insect species. I found moderate evidence of a phylogenetic signal on the optimal ratio of protein to carbohydrate ratio (PC ratio) that maximised lifespan, suggesting that optimal PC ratio for lifespan could have evolved non-independently among related species. I also found evidence for weak-to-strong sex-specific optimal PC ratios for lifespan, suggesting that sex-specific nutritional needs to maximise lifespan can emerge and persist in some species. Although limited in the number of species, the approach adopted here is portable to experiments withn number of nutrients and, thus, can be used in complex comparative precision nutrition studies for insights into the evolution of animal nutrition.

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.

Nutrigonometry III: curvature, area and differences between performance landscapes

Nutrition is one of the underlying factors necessary for the expression of life-histories and fitness across the tree of life. In recent decades, the geometric framework (GF) has become a powerful framework to obtain biological insights through the construction of multidimensional performance landscapes. However, to date, many properties of these multidimensional landscapes have remained inaccessible due to our lack of mathematical and statistical frameworks for GF analysis. This has limited our ability to understand, describe and estimate parameters which may contain useful biological information from GF multidimensional performance landscapes. Here, we propose a new model to investigate the curvature of GF multidimensional landscapes by calculating the parameters from differential geometry known as Gaussian and mean curvatures. We also estimate the surface area of multidimensional performance landscapes as a way to measure landscape deviations from flat. We applied the models to a landmark dataset in the field, where we also validate the assumptions required for the calculations of curvature. In particular, we showed that linear models perform as well as other models used in GF data, enabling landscapes to be approximated by quadratic polynomials. We then introduced the Hausdorff distance as a metric to compare the similarity of multidimensional landscapes.