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Each life table is associated to a stationary population, with its own age structure, here called RAS (reference age structure). In this paper we show that the RAS possesses a useful property: it is the set of points (vector of population shares, by age) towards which the actual population structure tends. This property holds for all populations, at all times, and it does not depend on models or assumptions. The strength of the attraction is weak, usually overshadowed by other, more powerful forces (e.g., the demographic transition), and detectable only in the long run: this may explain why the property has gone unnoticed until now.

In the paper, we prove the existence of this tendency, measure the speed of the convergence (of the current on the reference age structure), discuss the mechanisms that may lead to this outcome, and sketch a few possible practical uses of this property.

age structure, stationary population, ECM