An Equation-Based Systems Approach to Modeling Punctuated Equilibria Apparent in the Macropattern of Urbanization over Time


Author: Harper, Tony
Almanac: History & Mathematics:Economy, Demography, Culture, and Cosmic Civilizations

Abstract

This paper presents a detailed description and explanation of a model of punctuated growth as that pattern of growth is related to population size, carrying capacity, and level of technology. General limits to modeling are introduced to give context to the results of the model, and the model itself is a set of differential equations representing the relationships between the aforementioned variables. It is noted that the pattern of punctuated equilibrium, first introduced by Eldridge and Gould as it applies to speciation, occurs throughout natural processes. A description of the construction of the model, an intuitive construction, is given, the model is then used to generate results consistent with the occurrence of both punctuation and stasis, and a simple mechanism is proposed to explain the interaction between population size, carrying capacity, and level of technology that would then produce the pattern of punctuation over time. Finally, further modifications of the model to give greater reality to the results are presented.

Keywords: punctuated equilibrium, stasis, macropattern, complex system.