Use the NRR (Life Table) tab to enter survivorship (lx) and fecundity (mx, daughters per female) by age class to compute the Net Reproductive Rate (R₀). The Natural Increase tab calculates the crude rate of natural increase from births, deaths, and population size (this is not the same as net reproductive rate).

Net Reproductive Rate Calculator

NRR (Life Table)
Natural Increase

Enter age classes with survivorship (lx) and fecundity (mx, daughters per female). Ages are optional but needed for generation time.

+ Add age class
− Remove last
Results
Net Reproductive Rate (R₀)—
Mean Generation Time (T)—
Approx. Intrinsic Rate of Increase (r)—
Doubling Time (if r>0)—
Interpretation—

Net Reproductive Rate Formula

The following formula is used to calculate the Net Reproductive Rate. 

R₀ = \sum_x l_x m_x
  • Where R₀ is the net reproductive rate (average number of daughters produced per newborn female; dimensionless)
  • lx is survivorship to age x (the proportion/probability of females surviving from birth to age x)
  • mx is age-specific fecundity at age x (daughters per female for that age class/time interval)

To calculate net reproductive rate, multiply lx by mx for each age class, then sum the products across all ages. If ages (x) are provided, mean generation time is T = (Σ x lx mx) / R₀, and a common approximation for the intrinsic rate of increase is r ≈ ln(R₀) / T.

How to Calculate Net Reproductive Rate?

The following two example problems outline the steps and information needed to calculate the Net Reproductive Rate.

Example Problem #1

  1. First, determine survivorship (lx) for each age class.
    • Example survivorship values: l20 = 0.97, l25 = 0.95, l30 = 0.92, l35 = 0.88.
  2. Next, determine age-specific fecundity (mx) as daughters per female for each age class.
    • Example fecundity values: m20 = 0.30, m25 = 0.50, m30 = 0.45, m35 = 0.15.
  3. Next, multiply lx by mx for each age class.
    • l20m20 = 0.97 × 0.30 = 0.2910; l25m25 = 0.95 × 0.50 = 0.4750; l30m30 = 0.92 × 0.45 = 0.4140; l35m35 = 0.88 × 0.15 = 0.1320.
  4. Finally, calculate the Net Reproductive Rate using the formula above: 

R₀ = Σ lxmx

The values provided above are inserted into the equation below and computed.

R₀ = (0.97×0.30) + (0.95×0.50) + (0.92×0.45) + (0.88×0.15) = 1.3120

Example Problem #2

The variables required for this problem are provided below:

age classes (x) = 18, 23, 28, 33, 38 (years)

survivorship (lx) = 0.98, 0.96, 0.93, 0.89, 0.84

fecundity (mx, daughters per female) = 0.10, 0.35, 0.40, 0.20, 0.05

Test your knowledge using the equation and check your answer with the calculator.

R₀ = Σ lxmx = ____