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On the logistic law of growth and its empirical verifications in biology

, : On the logistic law of growth and its empirical verifications in biology. Acta Biotheoretica 5(2): 51-66

A mathematical analysis of the extent to which the empirical verification of the logistic differential equation [image] as an expression of the biological growth approaches actual proof. By a series of practical evaluations the degree of approximation to be expected, if the equation [image] is replaced by any other group of sigmoid curves with 3 parameters, is determined. The logistic curve does not fit the biological data accurately; they agree equally well with entirely different hypotheses. The same is true of the experiments of Gause (in which the validity of equation [2] was to be proved by observation of bacterial colonies in a disturbed medium). This does not at all impair the special capacity of equation [1] to describe biological growth processes, since this depends partly upon the mathematical properties and even more so on the highly plausible nature of the fundamental conceptions leading to equation [2]. Empirical data constitute no proof in themselves, and it is not permissible in any individual case to draw conclusions about the inner nature and the acting forces from an agreement of a growth process with equation [1].


DOI: 10.1007/bf01602862

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