Use this stable-population relationship for analytical schedules whose fertility, mortality, migration assumptions, and age intervals match the model.

Growth rate r

Intrinsic annual growth rate r of the stable population.

Ages

Age at the start of each group in years.

Weights

Person-years lived or exposure weight for each group.

c(a)

Proportion of the stable population in each group.

Mean age

Mean age of the resulting distribution in years.

Stable-population identities assume fixed vital rates and usually a closed population. Real populations with changing schedules or migration may be far from the implied equilibrium.

Compare the stable-population result with an observed age distribution or a cohort-component model using changing schedules. The difference indicates how strongly the equilibrium assumption shapes the result.

• Intrinsic Birth Rate B Stable Calculator

  Compute the stable-population intrinsic birth rate b as the reciprocal of the growth-discounted person-years sum and derive the intrinsic death rate d = b - r.

• Intrinsic Death Rate D Stable Calculator

  Compute the stable-population intrinsic death rate d as the growth-discounted weighted average of age-specific deaths per person-year, accepting deaths directly or death rates times L(x).

• Stable Equivalent Population Size Calculator

  Compute the stable-equivalent population size as observed annual births divided by the intrinsic birth rate b.