An Investigation of the Logistic Model of Population Growth

Abstract

This article examines the popular logistic model of growth from three perspectives: its sensitivity to initial conditions; its relationship to analogous difference equation models; and the formulation of stochastic models of population growth where the mean population size satisfies the logistic relationship. The results indicate that the appealing sigmoid logistic curve is sensitive to initial conditions and care must be exercised in developing difference equation models which display the same appealing long term behavior as the logistic growth curve. It is shown that although the logistic model is appealing in terms of its simplicity its realism is questionable in terms of the degree to which it reflects demographically accepted assumptions about the probabilities of individual births and deaths in the growth of a population. In particular this lack of realism has serious implications for the computer simulation of stochastic birth and death processes where the mean population size satisfies the logistic.