Net Reproductive Rate Calculator

Calculate net reproductive rate, mean generation time, and natural increase rate from life table values, births, deaths, and population.

Net Reproductive Rate Formula

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

R₀ = Σₓ lₓ mₓ

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

To calculate net reproductive rate, multiply l_x by m_x for each age class, then sum the products across all ages. If ages (x) are provided, mean generation time is T = (Σ x l_x m_x) / 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

First, determine survivorship (l_x) for each age class.
- Example survivorship values: l₂₀ = 0.97, l₂₅ = 0.95, l₃₀ = 0.92, l₃₅ = 0.88.
Next, determine age-specific fecundity (m_x) as daughters per female for each age class.
- Example fecundity values: m₂₀ = 0.30, m₂₅ = 0.50, m₃₀ = 0.45, m₃₅ = 0.15.
Next, multiply l_x by m_x 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.
Finally, calculate the Net Reproductive Rate using the formula above:

R₀ = Σ l_xm_x

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 (l_x) = 0.98, 0.96, 0.93, 0.89, 0.84

fecundity (m_x, 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 l_xm_x = ____

Net Reproductive Rate Calculator screenshot