The autocatalytic growth model

Summary

Because of the important role which the ‘autocatalytic’ or ‘logistic’ equation has played in determining the direction of a good deal of research both in demography and in the study of individual growth phenomena, a critical and comparative evaluation of those leading ideas inRobertson's (1923) book which pertain to this equation and of some of the criticisms levelled against it seemed to be of interest. The present paper shows that, contrary to common belief,Robertson did not really assume that the autocatalytic reactions to which he compared growth processes, took place in closed systems (viz., cells). On the other hand, he does not seem to have found a satisfactory representation of how the growth phenomena of the individual cells in an organism might interact to yield the overall growth of the organism as a whole. Nor is the manner in which he made his equation account for the openness of the individual cells free from possible criticism. An alternative equation is here proposed, which will be discussed in another paper. The properties of the solutions of this equation are such that the autocatalytic theory might never have gained a foothold if this, more realistic, equation would have been the object of the initial studies.