Effective Population Size Calculator
The genetically effective size of a population — from an unequal number of breeding males and females, and from fluctuations over generations — with the rate at which it loses genetic variation and how it measures against the 50/500 rule.
A population of a thousand animals in which ten males sire every offspring behaves, genetically, like a population of forty.
How the effective population size calculator works
A population of a thousand animals in which ten males sire every offspring behaves, genetically, like a population of forty. The effective size accounts for the sexes that actually breed, and across generations it is the harmonic mean of the sizes — so one bottleneck generation drags it down for good. Heterozygosity is lost at one over twice the effective size each generation, which is the number a conservation plan is judged on.
The 50/500 rule of thumb says an effective size of 50 avoids inbreeding depression in the short term and 500 keeps evolutionary potential.
Formula: Nₑ = 4 Nₘ N_f / (Nₘ + N_f); across generations: Nₑ = harmonic mean; ΔH = 1 / (2 Nₑ) per generation
Worked examples
| Inputs | Effective population size Nₑ | Note |
|---|---|---|
| 20 males, 80 females | 64 | Nₑ of 64 |
| Equal sexes | 100 | Nₑ equals the breeders |
| A past bottleneck | 64 | the harmonic mean is dragged down |
FAQFrequently asked questions
What is effective population size?
The size of an idealised population — equal sexes, random mating, constant numbers — that would lose genetic variation at the same rate as the real one. It is almost always smaller than the head count.
Why does the sex ratio matter?
Because every offspring has one mother and one father, so the rarer sex contributes half the genes however few they are. Ten males and a thousand females have an effective size of under forty.
Why the harmonic mean?
Because genetic drift in a small generation is not undone by a large one afterwards. The harmonic mean weights small values heavily; a single bottleneck dominates.
What is the 50/500 rule?
Franklin's 1980 rule of thumb: an effective size of 50 keeps inbreeding below 1% a generation, 500 balances drift against new mutation. Modern estimates argue for 100/1000.
How is Ne measured in the wild?
From the sexes and numbers that actually breed, from variance in family size, or from genetic data — linkage disequilibrium or temporal change in allele frequencies.
Where these figures come from
- NCBI Bookshelf — Molecular Biology of the Cell — growth kinetics and molecular conventions
- CSIRO — Australia's national science agency
Last checked: September 2026. Formulas are the standard textbook forms; assumptions are stated on each page because they are where these models break.