CONVERGENCE OF A HUMAN POPULATION TO A STABLE FORM
The sequence of births occurring in a closed female population subject to constant schedules of fertility and mortality can be represented as where only one coefficient (Q0) and one exponent (r0) are real. Convergence to a stable population occurs a few years after all complex components in B(t) have become negligible relative to the one real component. The rate of convergence of B(t) to a real exponential function depends on the age schedules of fertility and mortality, and on the initial age distribution. Methods of determining the coefficients and exponents of the terms of B(t) by use of a large computer are described in this paper, and various significant characteristics of the terms are given. Methods are described for visualizing how convergence would occur in a particular human population on the basis of recorded features of its fertility, mortality, and age composition.