Calculate effective population size, Ne, from breeding sex ratio, family-size variance, bottleneck history, and expected heterozygosity loss. The calculator helps genetics students, conservation biologists, and breeding-program planners compare census size with the genetic size that controls drift.
Change any input and the sex-ratio model, family-size variance model, bottleneck estimate, and heterozygosity projection update instantly.
Start with a conservation, breeding, or classroom example, then adjust the values for your population.
Unequal breeding males and females reduce Ne even when census size looks large.
Higher variance in offspring number lets a few parents dominate the next generation.
Ne ≈ (4N − 2) / (Vk + 2)
Vk = 2 behaves like an ideal diploid population. Larger Vk reduces the genetic contribution of census size.
Enter population sizes across generations. The harmonic mean gives heavy weight to the smallest bottleneck.
Live Ne result
The smallest model estimate usually drives drift risk. This scenario shows high genetic drift pressure.
Census N
100
Ne/N
99.5%
ΔF/gen
0.503%
H retained
90.4%
Compare the sex-ratio, family-size variance, and bottleneck estimates before choosing a biological interpretation.
Initial heterozygosity H₀
0.4200
Projected heterozygosity Ht
0.3797
Heterozygosity lost
0.0403
Effective population size describes how many ideal breeding individuals would produce the same rate of genetic drift as the real population. Census size, written as N, counts bodies. Effective size, written as Ne, counts genetic contribution.
Sewall Wright introduced the concept while building the mathematical basis of random genetic drift. A skewed sex ratio, unequal family size, population subdivision, selection, and bottlenecks all push Ne below census size. Nature Education gives the sex-ratio equation Ne = 4NmNf / (Nm + Nf) for non-equal breeding sexes. Read the Nature Education explanation.
The same idea sits beside our genetic drift simulator. A smaller Ne makes allele-frequency paths wobble more strongly, so rare alleles reach loss or fixation faster.
Type the number of reproductive males and reproductive females to calculate sex-ratio effective size.
Enter census size and variance in offspring number to estimate how reproductive skew changes Ne.
Enter population sizes across generations as a comma-separated list to calculate harmonic mean Ne.
Use the projected heterozygosity graph to estimate genetic diversity retained after the selected generations.
The preset buttons load common biological scenarios. A balanced population demonstrates the ideal case, while the skewed sex-ratio preset shows how a few breeding males can reduce genetic size.
The sex-ratio card calculates Ne from breeding males and breeding females. This section answers the common question, “Why does the genetic size shrink when one sex is rare?”
The family-size variance card estimates how unequal reproductive success changes effective size. Use it when one adult pair, founder line, or brood contributes more descendants than others.
The bottleneck input accepts a comma-separated time series. The output uses the harmonic mean, which gives strong weight to the smallest generation in the history.
The result banner highlights the limiting Ne, Ne/N, inbreeding rate, and heterozygosity retained. The chart then turns those values into a visible diversity trajectory.
Each formula answers a different biological question. Use the table to choose the model that matches your data before interpreting the smallest estimate.
Sex ratio
Ne = 4NmNf / (Nm + Nf)
Unequal breeding males and females
Family-size variance
Ne ≈ (4N − 2) / (Vk + 2)
Unequal offspring number among breeders
Bottleneck history
Ne = t / Σ(1/Ni)
Population size changes through time
Heterozygosity retention
Ht = H0(1 − 1/(2Ne))ᵗ
Genetic diversity loss across generations
A population has 12 breeding males and 88 breeding females. Census size equals 100, but the sex-ratio formula gives Ne = 4 × 12 × 88 / 100 = 42.24.
The genetic population behaves like about 42 ideal breeders. This result helps explain why wildlife managers track breeding adults by sex, not just total headcount.
A population changes through 400, 60, 40, 250, and 600 breeding individuals. The arithmetic mean equals 270, but the harmonic mean gives about 88.9.
The two small generations control the genetic outcome. After the population rebounds, lost rare alleles do not automatically reappear unless mutation or migration restores them.
Conservation geneticists use Ne to compare management options before diversity declines. A breeding plan that balances families can preserve more heterozygosity than a plan that lets one lineage dominate offspring production.
Population-genetics classes often pair this calculator with a Hardy-Weinberg calculator. Hardy-Weinberg expectations describe genotype proportions when drift, selection, migration, and mutation do not disturb allele frequencies. Effective size explains one major way that real populations break that ideal.
Long-term genomic diversity also depends on mutation. When you want to connect diversity loss with new variant input, compare Ne with the estimates from the mutation rate calculator.
Ne/N compares genetic size with census size. A ratio near 1 means breeding contribution looks close to ideal. A ratio far below 1 means the census count overstates how many independent allele copies pass into the next generation.
Heterozygosity loss translates Ne into a diversity outcome. If initial heterozygosity is 0.50 and the retained value after 50 generations is 0.39, the population lost 0.11 units of expected heterozygosity under the model. This does not identify which alleles vanished, but it shows the expected genetic erosion.
This calculator uses classroom models. Real populations may have overlapping generations, age structure, migration, selection, population subdivision, related parents, and changing survival rates. Those details can move genomic estimates away from the simplified values shown here.
Treat the output as an educational estimate. For conservation or breeding decisions, combine pedigree records, field demography, genome-wide markers, and expert review.
Use these tools to connect effective size with allele-frequency change, genotype proportions, and population-level assumptions.