Scaling laws in biological thermal performances

Understanding the extent to which genetic correlations change in response to environmental factors, such as temperature, is a poorly explored question, despite the importance of understanding how different processes will change with climate warming. Despite correlations between thermal performance traits having been reported in the literature for a few taxa and performance tasks, such as population growth rate, a comprehensive global analysis of the entire tree of life and multiple performance tasks remains an open challenge. To advance in this open question, we compile a database of 1,300 thermal response curves, encompassing 38 variable types related to individuals’ performance (including per capita population growth rate, photosynthetic rate, among others) and 1,125 different species, ranging from viruses to mammals, encompassing all major lineages of the tree of life. Our analysis reveals that among all possible relationships between traits and optimal performance, four traits form a line with a high goodness-of-fit, while the remaining traits exhibit a polygonal pattern, either a triangle or a tetrahedron. We derive a thermodynamic framework that explains the relationships described by a curve or line (as opposed to a surface or polygon), highlighting the linear relationship between maximum and minimum temperatures, as well as between maximum and optimum temperatures. We also discuss other generic trait evolution models, which could account for the other significant sublinear relationships, as well as the more general model, Pareto optimality theory, which could account for relationships in the form of lines or polygons. Our theoretical framework and empirical evidence suggest that, based on a single data point (e.g., minimum temperature), all critical temperature limits and maximum performance boundaries can be predicted using the estimated parameter from this study. Our results reveal universal scaling relationships in thermal performance, which could be useful for predicting changes in performance under scenarios of climate warming.