Derivation of the Reach Time Equation—Based on the Arrhenius Equation, a Theoretical Equation Describing the Time Distribution to Reach a Certain Stage, such as Germination, in a Population

抄録

The reach time equation, a sigmoidal equation with the same number of parameters as the logistic equation, is derived by adding a concentration factor to the physically theoretical Arrhenius equation and assuming a normally distributed factor. Because this equation provides a good description of the time distribution to germination, it may be applicable as an equation for the time distribution reaching a certain stage in a population. Moreover, as derived from the Arrhenius equation, this equation can also be used to evaluate the effect of temperature. Using this equation, the skewness in the time distribution reaching a certain stage became proportional to the variation coefficient of the concentration factor, indicating that a high variation coefficient for the amount of relevant substrates, such as nutrients and enzymes, caused the skewness in the distribution. Given the theoretical implications of the parameters obtained by fitting this equation, it is predicted that the growth and development of living organisms, including inorganic changes can be theoretically analyzed by fitting and analyzing the parameter values. In addition, owing to the small number of parameters, it will also be useful for simple fitting as a sigmoidal curve.