American, German and British antecedents to Pearl and Reed's logistic curve

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Abstract
This paper provides a general history of the logistic growth curve and its applications to several biological populations. Curiously, the same curve, in several disguises, was discovered at least four times by independent authors before the work of Pearl and Reed, who are usually credited with the discovery. Two aspects of the history are stressed. First, the paper discussed the apparently wide applicability of the curve to many fields of physiology, biology, and human demography. Second, it emphasizes the different reasons given as to why various populations should approach a maximum asymptotically according to the logistic curve. Biologists hypothesized that either the autocatalytic nature of some growth processes or the fixed food supply available to a single species would produce a time series of the total population of microorganisms and other species that followed the curve. Pearl and Reed's arguments concerning human populations, however, were of a different kind. They relied upon nothing more than the general idea that a fixed area imposed a ceiling to the population. This ceiling was not estimated by means of an aggregate production function or any other production theory. The error of their famous 1920 estimate of 197 million as the maximum population for the United States demonstrates the danger of seeking to apply methods which have been successful in one field to a quite different field.

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