Effective Population Size Calculators
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Ne Formulas
Equal sex ratio: Ne = N
Unequal sex ratio: Ne = (4 × Nm × Nf) / (Nm + Nf), where Nm = males, Nf = females. Example: 10 males, 90 females: Ne = (4 × 10 × 90) / 100 = 36 — just 36% of census size.
Variance in reproductive success: Ne = (4N − 2) / (Vk + 2), where Vk = variance in offspring number per individual. High variance reduces Ne drastically.
Fluctuating population size (harmonic mean): Ne ≈ t / Σ(1/Nᵢ), where t = generations and Nᵢ = size in generation i. Small bottleneck generations dominate.
Why Ne < N in Real Populations
- Unequal sex ratios (polygyny, harem-based mating)
- High variance in reproductive success (some individuals have many offspring, others none)
- Population bottlenecks (a single small generation reduces long-term Ne dramatically)
- Overlapping generations and age structure
Genetic Consequences
Drift removes alleles at rate 1/(2Ne) per generation. Ne < 50 leads to significant inbreeding depression. Ne < 500 may be insufficient for adaptive evolution. The 50/500 rule in conservation biology: minimum Ne of 50 to avoid inbreeding; minimum Ne of 500 for long-term evolutionary potential.
Glossary
Frequently Asked Questions
Effective population size (Ne) is the size of a theoretical ideal population that loses genetic diversity at the same rate as the actual population. Ne is almost always less than the census size (N) due to unequal sex ratios, variance in reproductive success, and bottlenecks. Ne determines the rate of genetic drift (allele loss: 1/(2Ne) per generation), inbreeding accumulation, and whether selection or drift shapes evolution. In conservation, maintaining adequate Ne is critical for the long-term viability of endangered species.
Formula: Ne = (4 × Nm × Nf) / (Nm + Nf). When the sex ratio is skewed, Ne is pulled toward 4 times the rarer sex. Example: elephant seal herd with 1 breeding male and 99 females: Ne = (4 × 1 × 99) / 100 = 3.96 — an effective size of just 4, despite 100 individuals! This extreme reduction happens in polygynous species where one or few males sire all offspring. The variance in male reproductive success is the key driver.
The 50/500 rule (Franklin 1980) provides Ne guidelines for conservation: Ne ≥ 50 to limit inbreeding depression to <1% per generation (inbreeding coefficient F < 0.01 per generation); Ne ≥ 500 to maintain evolutionary potential by keeping mutation input (new variation) equal to drift loss. In practice, the threshold for long-term viability has been revised upward — some researchers recommend Ne ≥ 1000 for adaptive potential given modern genomic insights. The 50/500 rule is a useful starting point, not a firm threshold.
The effective size across fluctuating generations is approximately the harmonic mean of the sizes over time: Ne ≈ t / Σ(1/Nᵢ). The harmonic mean is dominated by the smallest values — one generation of N = 10 in an otherwise large population reduces the long-term Ne dramatically. Example: 4 generations with N = 1000, 1000, 10, 1000: Ne ≈ 4 / (0.001+0.001+0.1+0.001) ≈ 39 — the bottleneck generation of 10 dragged Ne from thousands to just 39.