Abstract

The debates over the future of human population and the earth’s environment, and similar large issues, usually take place without reference to explicit models. Debate would be clarified if such models were employed. We propose that the logistic equation and its extensions like the generalized logistic and the Lotka-Volterra equations, so familiar to ecologists, can easily be modified to model the important "macro" questions that motivated the three thinkers of our title. The long term rate of population growth must normally be controlled by the rate of improvement in K, the carrying capacity of the earth. K will in turn be controlled by the rate of technological progress. The present situation, in which technological improvement (but also perhaps environmental deterioration) are increasing at rates above r, the Malthusian intrinsic rate of natural increase, is probably unique in human history. Can present levels of human prosperity and population growth be sustained? What processes are most likely to determine the answer to this and similar questions? We here sketch a model that endogenizes technological progress and environmental deterioration in the logistic framework. We discuss extensions of the logistic approach to multiple populations, such as other species, and sub-populations, such as human social classes, using the Lotka-Volterra equations.