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.
Description
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.
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.1
When to use Lotka Intrinsic Growth Rate R Calculator
Use this stable-population relationship for analytical schedules whose fertility, mortality, migration assumptions, and age intervals match the model.
- ASFR
- Female age-specific fertility rates per woman per year for each class.
- L(x)
- Female life-table person-years L(x) aligned with the rates.
- Start age
- Starting age of the first class in years.
- Class width
- Width of each age class in years.
How the method works
- r
- Intrinsic annual growth rate r solving the Lotka equation.
- NRR
- Net reproduction rate NRR = sum of f(x) L(x).
Limitations and assumptions
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.
Alternative or Complementary measures
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.
References
-
Euler–Lotka equation — Wikipedia contributors
Similar or alternative tools
- 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.
- 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).