51. Why a Population Converges to Stability
- Author
-
W.B. Arthur
- Subjects
education.field_of_study ,Fundamental theorem ,Age structure ,General Mathematics ,010102 general mathematics ,Short paper ,Population ,Full view ,01 natural sciences ,0103 physical sciences ,Quantitative Biology::Populations and Evolution ,Ergodic theory ,Age distribution ,010307 mathematical physics ,0101 mathematics ,education ,Mathematical economics ,Smoothing ,Mathematics - Abstract
A large part of mathematical demography is built upon one fundamental theorem, the "strong ergodic theorem" of demography. If the fertility and mortality age-schedules of a population remain unchanged over time, its age distribution, no matter what its initial shape, will converge in time to a fixed and stable form. In brief, when demographic behavior remains unchanged, the population, it is said, converges to stability. This short paper presents a new argument for the convergence of the age structure, one that is self-contained, and that brings the mechanism behind convergence into full view. The idea is simple. Looked at directly, the dynamics of the age-distribution say little to our normal intuition. Looked at from a slightly different angle though, population dynamics define a smoothing or averaging process over the generations -- a process comfortable to our intuition. This smoothing and resmoothing turns out to be the mechanism that forces the age structure toward a fixed and final form.
- Published
- 1981