Arroyo, Jose Ignacio; Beatriz Diez; Chris Kempes; Geoffrey B. West and Pablo A. Marquet

Temperature affects all biological rates and has far reaching consequences from bioengineering [1] to predicting ecological shifts under a changing climate [2-3], and more recently, to pandemic spread [4]. Temperature response in biological systems is characteristically asymmetric and nonlinear, with an exponential phase of increase followed by a concave up-ward or downward phase [5]. Current models for quantitatively describing the temperature response include simple but empirical equations (such as Arrhenius’) or models derived from first principles which are often overly complicated (i.e. with many parameters). Moreover, their theoretical framework does not include how parameters vary, nor their applicability across multiple scales and taxa, or whether they exhibit universality [1-7]. Here, we derive a new mechanistic, yet simple, model for the temperature dependence of biological rates based on the Eyring-Evans-Polanyi theory governing chemical reaction rates, which is applicable across all scales from the micro to the macro. Assuming only that the conformational entropy of molecules changes with temperature, we derive a model for the temperature dependence which takes the form of an exponential function modified by a power-law. Data for a wide variety of biological rates from molecular to ecological scales and across multiple taxonomic groups agree well with our predictions. Furthermore, our framework predicts values for the thermodynamic parameters, and leads to a single parameterless universal scaling curve on which data across all scales and taxa collapse.