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.

L(x)

Life-table person-years L(x) per unit radix aligned with the ages.

b

Intrinsic annual birth rate b of the stable population.

d

Implied intrinsic death rate d = b - r.

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 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).

• Generation Length T Intrinsic Calculator

  Compute the intrinsic mean generation length T either as ln(NRR)/r from Lotka's relation or directly as the mean age of mothers at childbirth of the net maternity schedule.

• Lotka Intrinsic Growth Rate R Calculator

  Solve the Euler-Lotka equation for the intrinsic growth rate r from an age-specific female fertility schedule and female life-table person-years, using midpoint ages of equal-width classes.