The law of total effective temperature, which has been conventionally used by many researchers, and the thermodynamic model based on enzymatic reaction, which was presented by previously, are representative models used to express a relationship between temperature and the development rate of poikilotherms. The former is a very simple and highly descriptive linear model. In contrast, the latter is very complex because it is a nonlinear model, but it has fine descriptive power. In a previous paper, I discovered the existence of a common temperature (Tc) and a common duration (Dc) of development among closely related members of arthropods during the course of comparatively analyzing many estimated values of constants of the linear model and succeeded in explaining the significance of Tc−Dc in an evolutionary process. This study was focused on an extended application of Tc−Dc to the nonlinear thermodynamic model. One of the practical difficulties in using the nonlinear thermodynamic model results from the vexatious complication of estimating simultaneously the values of seven unknown constants. In particular, there were no means to estimate the values of the constants of reference temperature (T0) and development rate (ρ) at T0, which are defined in the nonlinear thermodynamic model. Here, I determine a suitable replacement of the constants T0 and ρ by the common temperature (Tc) and inverse of the common duration (1/Dc), respectively, resulting in reasonably successful curve fitting for data. Therefore, Tc (=T0) could be considered in principle to be common in the two models. I suggest that Tc and T0 be conferred a new definitive concept, that is, the intrinsic optimum temperature for development that tends to be fixed for a taxon, and that they exhibit the minimum effects on enzyme inactivation at low and high temperatures.
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