Comparison between Richards Growth Function, its Family Growth Functions and Basic Growth Function

概要

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This study was designed to make a comparison between Richards growth function, its family growth functions and basic growth function. Each growth function was combined with its first and second derivatives. The results obtained were as follows. Mitscherlich, logistic and Gompertz growth functions, each of which was a special case of Richards growth function, took a common form when combined with first and second derivatives. In the case of Richards growth function, there was an additional m when compared with the common form. The present study showed that Richards growth function resulted in its family growth functions when m = 0, and collapsed into basic growth function when m = 1. These were contradictory to the results by Richards (1959), except Mitscherlich growth function that was given when m = 0. There was a gap impossible to jump over between basic growth function and each of Mitscherlich, logistic and Gompertz growth functions. It was suggested that Richards growth function existed between a group of its family growth functions and basic growth function.