Stable, semi-stable populations and growth potential

Abstract Starting from the definition of a Malthusian population given by Alfred J. Lotka, the author recalls how the concept of stable population is introduced in demography, first as a particular case of stable populations, and secondly as a limit of a demographic evolutionary process in which female age-specific fertility rates and age-specific mortality rates remain constant. Then he defines a new concept: the semi-stable population which is a population with a constant age distribution. He shows that such a population coincides at any point of time with the stable population corresponding to the mortality and the fertility at this point of time. In the remaining part of the paper it is shown how the concept of a stable population can be used for defining a coefficient of inertia which measures the resistance of a population to modification of its course as a consequence of changing fertility and mortality. Some formulae are established to calculate this coefficient first for an arbitrary population, and secondly for a semistable population. In this second case the formula is particularly simple. It appears as a product of three terms: the expectation of life at birth in years, the crude birth rate, and a coefficient depending on the rate of growth and for which a numerical table is easy to establish.