Inbreeding Coefficient Calculator
How much inbreeding accumulates in a small population over generations — the inbreeding coefficient, the heterozygosity that remains, and how long until the 50/500 warning lines are crossed.
In a population with effective size Nₑ, each generation loses a fraction 1 ÷ (2Nₑ) of its heterozygosity to drift, and the inbreeding coefficient grows to F = 1 − (1 − 1 ÷ 2Nₑ)^t after t generations.
How the inbreeding coefficient calculator works
In a population with effective size Nₑ, each generation loses a fraction 1 ÷ (2Nₑ) of its heterozygosity to drift, and the inbreeding coefficient grows to F = 1 − (1 − 1 ÷ 2Nₑ)^t after t generations. Fifty breeding animals lose 1% a generation — the origin of the conservation rule that Nₑ under 50 risks inbreeding depression in the short term and under 500 loses adaptive potential in the long term.
Formula: ΔF = 1 ÷ (2Nₑ); F_t = 1 − (1 − ΔF)^t; H_t = H₀ (1 − ΔF)^t
Worked examples
| Inputs | Inbreeding coefficient after those generations | Note |
|---|---|---|
| Nₑ = 50 for 10 generations | 0.0956 | F ≈ 0.096; 90% heterozygosity retained |
| Nₑ = 10 for 5 generations | 0.2262 | F ≈ 0.226 |
| Nₑ = 500 for 100 generations | 0.0952 | F ≈ 0.095 |
FAQFrequently asked questions
What is effective population size?
The size of an ideal population that would lose genetic variation at the same rate as the real one. It is usually far below the census count — unequal sex ratios, variation in family size and fluctuating numbers all reduce it, often to 10–20% of the head count.
What does F = 0.25 mean?
The inbreeding of offspring from a full-sibling mating — the level at which inbreeding depression (lower fertility, survival and vigour) becomes severe in most species. F = 0.0625 is a first-cousin mating.
Where does the 50/500 rule come from?
Franklin (1980): 50 to keep inbreeding under 1% a generation, the rate animal breeders tolerate; 500 so that mutation replaces the variation drift removes. Later work suggests 100/1,000 is safer.
How do I increase Nₑ?
Equalise family sizes, balance the sex ratio, avoid population crashes, and bring in unrelated individuals — even one migrant per generation greatly slows the loss of variation in a small population.
Where these figures come from
- NCBI Bookshelf — Molecular Biology of the Cell — growth kinetics and molecular conventions
- Wellcome Sanger Institute — a leading UK genomics institute
Last checked: September 2026. Formulas are the standard textbook forms; assumptions are stated on each page because they are where these models break.