Age-specific growth rates: the legacy of past population dynamics

Recent developments in population mathematics have focused attention on a function that is widely available but rarely examined: the set of age-specific growth rates in a population. In particular, this set of rates is sufficient for translating the current birth rate and age-specific mortality rates into the current age distribution. This growth-rate function contains all of the pertinent features of a population's demographic history that are required to relate major demographic functions for a particular period to one another. This article presents an expression for the age-specific growth rate and uses it to derive an equation for age distribution. We show how the value of the age-specific growth rate is determined by a population's demographic past and present various sets of growth rates corresponding to stylized demographic scenarios. Several noteworthy sets of growth rates observed in human populations are discussed. Finally, we explain why age-specific growth rates make it possible to determine the age distribution solely from information on current demographic conditions.