Comparison of Thermal Performance Equations in Describing Temperature-Dependent Developmental Rates of Insects: (II) Two Thermodynamic Models

There are many descriptive statistical models describing the temperature-dependent developmental rates of insects without derivation of biophysical processes; thus, it is difficult to explain how temperature affects development from the thermodynamic mechanisms. Fortunately, two mathematical models (the Sharpe-Schoolfield-Ikemoto [SSI] model and Ratkowsky-Olley-Ross [ROR] model) based on thermodynamics have been built to explain temperature-dependent reaction rates. Despite their differences in construction, both models produce similar functions when used to describe the effect of temperature on the probability of a theoretical rate-controlling enzyme that is in its active state. However, the previous fitting method of the SSI model was unable to achieve global optimization of parameter estimates; that of the ROR model usually underestimates the maximal probability of the rate-controlling enzyme that is in its active state, as found in some empirical data sets. In the present study we improved the fitting methods for these two models. We then used these two models to fit 10 data sets from published references. We found the models based on the improved fitting methods agree with the empirical data well and predict that the maximal probabilities of the rate-controlling enzyme that is in its active state are close to 1. The SSI model produces a slightly better goodness-of-fit value for the model than the ROR model, whereas the latter predicts a more symmetrical curve for the probability of the rate-controlling enzyme that is in its active state. If thermodynamic parameters of two or more different species are to be compared, we recommend that researchers use one or the other of these two models and follow the same fitting methods for all species.