Equivalence between polynomial and extended Arrhenius models. (A) Extended Arrhenius model, where E_o is the activation energy and is the ideal gas constant [ red line] can be fitted with R² > 0.99 to the global polynomial model (; black dotted line; T range of 10–45 °C). The fitted value of lnR_ref differs by less than 2% from a = −2.23, so that E_o(Ref) and the δ-parameter can be predicted with similar precision from b- and c-parameters. GPM, global polynomial R–T model. (B) Nonlinear dependency between T (°C) and reciprocal temperature (1,000/K): . (C) For accurate prediction (±2%) of E_o(Ref) and the δ-parameter from b- and c-parameters, the temperature dependency between T (°C) and x must be accounted for (sensu B). For any given b- and c-parameters, Arrhenius-type parameters can thus be predicted from the midpoint of the T interval under consideration (i.e., 27.5 °C for the global temperature range).

Correlation between parameters for the polynomial model () and an extended Arrhenius model (). All points are based on the data provided by Heskel et al. (). (A) Global polynomial model (T range of 10–45 °C). (B) Extended Arrhenius model, where E_o(Ref) and δ-values were derived from the b- and c-values shown in A. (C) The b- and c-values of the polynomial model derived from measurements within an ecologically relevant T range. (D) Arrhenius-type parameters derived from b- and c-values shown in C. Black stars represent global averages. Tundra and boreal species (blue), temperate deciduous and temperate rainforest and temperate woodland species (green), and highland and lowland tropical rainforest species (red) are also indicated. Each correlation analysis was completed with n = 231 different species [Heskel et al. ()]. Differences in slope of the correlation between exponent variables of the polynomial model versus the extended Arrhenius model result from nonlinear dependency between T (°C) and 1,000/K ().