Hong Life CalculatorsUnderstanding the effective population size calculator — concept and principle
A census tells you how many individuals exist, but genetic change depends on how many actually breed. The effective population size Ne is the size of an idealised population that loses genetic variation at the same rate as the real one. This calculator finds Ne for unequal numbers of breeding males and females, and the heterozygosity lost per generation, for conservation, captive breeding and livestock work.
How it is calculated
- Ne = 4·Nm·Nf / (Nm + Nf), where Nm and Nf are the numbers of breeding males and females.
- Heterozygosity lost per generation = 1 / (2Ne), shown as a percentage.
The principle
Every offspring has exactly one father and one mother, so half of the next generation's genes come from the males and half from the females, however few males there are. When one sex is scarce, its few members contribute a large share of the genes and the population behaves genetically like a smaller one. Wright's formula is twice the harmonic mean of the two sexes and equals Nm + Nf only when the sexes are equal. In an idealised population, genetic drift makes each new generation lose a fraction 1/(2Ne) of its heterozygosity, so after t generations H_t = H₀(1 − 1/(2Ne))ᵗ.
Worked example
- Inputs: Nm = 10 males, Nf = 40 females (census of 50 breeders).
- Ne = 4 × 10 × 40 / (10 + 40) = 1600 / 50 = 32.
- Heterozygosity lost: 1 / (2 × 32) = 1/64 = 0.015625, about 1.56% per generation.
- Over 10 generations: (1 − 1/64)¹⁰ = 0.854, so roughly 15% of the original heterozygosity is gone.
| Breeding males | Ne (sex ratio) |
|---|---|
| 2.5 | 9.411764706 |
| 5 | 17.77777778 |
| 7.5 | 25.26315789 |
| 10 | 32 |
| 12.5 | 38.0952381 |
| 15 | 43.63636364 |
| 20 | 53.33333333 |
How to read the result
Ne is never larger than the number of breeders and falls quickly as the sex ratio becomes uneven: 25 males and 25 females give Ne = 50, while the same 50 animals split 10 : 40 give only 32. Ne / N ratios in wild populations are often well below 1 once unequal breeding success and fluctuating numbers are included. A widely cited rule of thumb from conservation genetics suggests Ne of at least 50 to limit short-term inbreeding and around 500 or more to keep long-term adaptive potential; treat these only as rough guides.
Common mistakes
- Counting all adults rather than those that actually breed.
- Ignoring variance in family size and changes in numbers between generations; both lower Ne further.
Frequently asked questions
Why does one sex matter so much?
Half of all genes in each generation must pass through each sex, so a few males carry as much genetic weight as many females.
How do population crashes affect Ne?
Long-term Ne is close to the harmonic mean of generation sizes, which is dominated by the smallest values, so one bottleneck lowers it for a long time.
Can Ne be estimated from DNA?
Yes, methods using linkage disequilibrium or allele-frequency change between samples estimate it directly.
Sources: S. Wright, "Evolution in Mendelian Populations", Genetics, 1931 · R. Frankham, J. D. Ballou and D. A. Briscoe, Introduction to Conservation Genetics, Cambridge University Press