Chapter 1: Theoretical Foundations

Extract

The approach to population structure followed in this work is that of stable population theory as developed by A. J. Lotka and others. An early exposition of this theory is found in Lotka (1956); more recently it has been summarized by Coale (1972), Keyfitz (1968), and Shryock and Siegel(1971).

The theory of stable populations requires that a population is infinite in size, has no net immigration or outmigration, and has fixed rates of fertility and mortality at each age. These assumptions are often approximated closely enough by real populations for the theory to be useful. Given the stated conditions, a population is described by its age distribution, or the number of individuals at each age. Since the theoretical population is infinite, the age distribution is defined in terms of relative numbers or percentages rather than finite numbers of individuals at each age.

The age structure is determined by the rates of mortality and fertility. It has been proved by Lotka that, no matter what the initial age distribution, a population under these assumptions approaches a certain age distribution which is determined by those rates. The result is the so-called stable age distribution since it will no longer change if mortality and fertility remain fixed. In fact, a temporary perturbation in these rates will only temporarily disturb the age distribution, which will quickly return to the stable form. Human populations approach the stable age distribution in well under 100 yr after the rates become fixed.