Population dynamics: theory of stable populations

A population with an age distribution which remains constant over time is referred to as stable. A stable population of constant size is said to be stationary. These concepts are of considerable antiquity. Subject to age-specific mortality and fertility rates which remain unchanged over time a population will eventually develop a stable age distribution which depends on those mortality and fertility rates but is independent of the initial age distribution of the population. This result, due to Sharpe and Lotka (1911), caused renewed interest in stable populations among demographers, and the theory underlying it is outlined. Although demographers usually think of a stable population as one with an age distribution which is unchanging, such a definition is restrictive, because populations can also exhibit stability in respect of other characteristics as well as age and in more general situations. The discrete approach of Bernardelli, Leslie, and Lewis, which readily permits generalizations to a range of population stability situations is therefore described, as well as extensions covering migration, multiregional populations, populations studied by parity of woman, and membership of particular organizations. Applications are discussed only very briefly with cross-references to the relevant article. Limitations of the underlying models are also mentioned, again with a cross-reference.