Population momentum—A formulation based on a stochastic population process

Abstract

The momentum of population growth is studied within a unifying framework based on a stochastic population process with time homogeneous laws of evolution. After setting down some general asymptotic formulas for mean functions in Section 2, which involve the Fisherian reproductive value, it is shown in Section 3 that a stable initial age structure leads to formulas describing exponential growth when the time variable t is sufficiently larger. An alternative derivation of Keyfitz's formula for mean asymptotic population size, under a regime of replacement fertility and a stable initial age structure, is given in Section 4. Described in Section 5 are six computer simulation runs designed to study the momentum of population growth under various conditions. An example is provided whereby a population would continue to grow for about 30 years even if there were an abrupt change to a fertility regime in which mean family size was one offspring. Among the intellectual lines of descent upon which this paper rests is one initiated by Richard Bellman, during the early fifties, in a stochastic process that subsequently became known as the Bellman-Harris process.