Net Reproductive Rate Calculator
Calculate net reproductive rate R0 (average offspring per female per lifetime) from life table data. Find generation time T and intrinsic growth rate r from survivorship and fecundity schedules.
🌳 Ecology📐 R0 = Σ(lx · mx)🧬 Biology
Age class fecundity mx (comma-separated)
Age class survivorship lx (comma-separated)
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Net Reproductive Rate Calculator | — | R0 = Σ(lx · mx) | offspring per female |
Step-by-Step Examples
Example 1
Simple life table
Age-specific: lx=[1.0,0.8,0.5,0.2], mx=[0,2,3,1].
- R0 = Σlx×mx = 1.0×0+0.8×2+0.5×3+0.2×1
- = 0+1.6+1.5+0.2 = 3.3
- T = Σx×lx×mx/R0 = (0+1.6×1+1.5×2+0.2×3)/3.3 = 5.8/3.3 = 1.76
- r = ln(3.3)/1.76 = 1.194/1.76 = 0.678
✓ R0=3.3 (growing 3.3x per generation), r=0.678
Example 2
Stationary population
R0 = 1.0 exactly: births = deaths.
- Generation time T determines turnover rate
- r = ln(1)/T = 0 (no growth)
- Population size constant
✓ R0=1.0: stable population
Example 3
Declining population
lx=[1.0,0.7,0.3], mx=[0,0.8,0.5].
- R0 = 0+0.7×0.8+0.3×0.5 = 0.56+0.15 = 0.71
- R0 < 1: population declining
- r = ln(0.71)/T < 0
✓ R0=0.71: population declining
Real-World Applications
Conservation Biology
R0 < 1 means population will go extinct without intervention. Minimum viable population must have R0 ≥ 1.
Wildlife Management
Life table analysis of harvested populations ensures R0 ≥ 1 after harvest mortality.
Epidemiology
Basic reproduction number R0 in epidemiology (average infections per case) is analogous to ecological R0.
Demography
Human population R0 calculation from age-specific birth and death rates.
Common Mistakes to Avoid
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lx must start at 1.0
Survivorship l0 = 1 by convention (all individuals alive at start). lx decreases with age.
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mx is age-specific female offspring
Fecundity mx = female offspring per female at age x. For humans: mx from fertility tables (children per woman at each age class).
⚠️
R0 = 1 means replacement fertility
Replacement fertility for a human population: ~2.1 children per woman (accounting for child mortality and sex ratio).
Frequently Asked Questions
What is R0 in ecology? ▾
Net reproductive rate: average number of female offspring produced per female over her lifetime, accounting for survivorship. R0 > 1: growing. R0 = 1: stable. R0 < 1: declining.
What is the difference between R0 and r? ▾
R0 is per-generation rate (dimensionless). r is per-unit-time rate. Connected by r = ln(R0)/T where T = generation time. Both measure population growth.
How does R0 relate to age-structured populations? ▾
Euler-Lotka equation: 1 = Σe^(-rx) × lx × mx. R0 = Σlx × mx (integral of reproductive value times survival).
What is the epidemiological R0? ▾
In disease ecology: R0 = average secondary infections from one case in fully susceptible population. R0 > 1: epidemic grows. < 1: dies out. Herd immunity threshold = 1 - 1/R0.
How does age at first reproduction affect R0? ▾
Same lifetime fecundity but earlier first reproduction: higher r (faster growth). Elephant (first offspring at 15 yr) vs mouse (3 weeks): very different r despite similar lifetime R0.