Questions: Stable Population Theory

Question 1

What does Lotka's ergodic theorem state, and what is its practical significance for demography?

• A. All populations eventually stop growing — they converge to zero growth rate regardless of fertility
• B. Any population subject to constant age-specific fertility and mortality rates will eventually converge to a stable age distribution, regardless of its initial age structure
• C. Populations with identical TFRs will always have identical age structures
• D. The age distribution of a population is determined solely by its current fertility rate

Answer: (B)

Lotka's theorem demonstrates that vital rates, not initial conditions, determine the long-run age distribution. Two populations with identical constant vital rates but very different starting age structures will converge to the same stable age distribution given enough time. This is practically significant because it means current vital rates contain enough information to derive the population's long-run trajectory — the basis for indirect demographic estimation techniques and for understanding population momentum.

Question 2

A stable population has a fixed age distribution. This means its total size must also be constant.

• T. True
• F. False

Answer: False

A stable population has a fixed proportion in each age group, but the total population can be growing or declining at a constant rate (the intrinsic rate r). If r > 0, every age group grows at rate r and the total population grows exponentially, but the age distribution stays the same. Only when r = 0 (a stationary population, where NRR = 1) is total size constant. Stability refers to the shape of the age distribution, not the size of the population.

Question 3

Explain why stable population theory is useful even though no real population has truly constant vital rates.

Model answer: Stable population theory provides a mathematical benchmark for analysis. Its uses include: (1) demographic estimation — in populations with incomplete data, observed age distributions can be compared to model stable populations to estimate vital rates indirectly; (2) understanding momentum — the gap between a population's current age distribution and its stable-equivalent reveals built-in growth or decline; (3) decomposing the effects of fertility vs. mortality vs. age structure on growth rates. The theory is a tool for reasoning about population dynamics, not a claim that real populations achieve stability.

This is analogous to how physicists use frictionless models — the model is never exactly true, but it isolates the essential mechanics. Stable population theory isolates the relationship between vital rates and age structure from the noise of historical fluctuations, migration, and rate changes. The Coale-Demeny model life tables and stable population tables, which are workhorses of applied demography, are direct applications of this theory.