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

Annual births

Observed annual births B in the population.

Intrinsic b

Intrinsic annual birth rate b of the matching stable population.

Stable equivalent

Stable-equivalent population size B / b.

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 Age Distribution Proportion Calculator

  Compute the stable-population age composition c(a) proportional to exp(-r a) times the person-year weight at each age, normalized to sum to one, plus its mean age.