Asymptotic properties of a human age distribution under a continuous net maternity function

Area of Science:

• Theoretical demography
• Mathematical population dynamics

Background:

• The age distribution of a closed population is often assumed to reflect its entire past.
• An alternative view suggests recent demographic history is more influential.

Purpose of the Study:

• To mathematically establish the ergodic principle in population studies.
• To demonstrate how age distributions become independent of their distant past.

Main Methods:

• Developing the mathematical foundations for the ergodic principle.
• Proving the asymptotic independence of age structure from past conditions.
• Illustrating the process of age distribution 'forgetting' its past.

Main Results:

• The age distribution of a closed population is asymptotically independent of its shape in the distant past.
• The current age distribution is exclusively determined by recent fertility and mortality history.
• An unchanging schedule of vital rates leads to a fixed age structure.

Conclusions:

• The ergodic principle provides a robust framework for understanding population age structures.
• Recent demographic trends are the primary drivers of current and future population age distributions.
• This principle has implications for long-term population projections and policy.