Genetic Drift Calculator

Calculate probability of allele fixation and time to fixation under genetic drift.

Effective population size Ne

Initial allele frequency p

0-1

Number of generations (generations)

Selection coefficient s (0=neutral)

0 = pure drift

Please check your inputs and try again.

Why Fixation Probability Equals Starting Frequency

For a strictly neutral allele, the probability of eventual fixation is simply its current frequency. The reasoning is elegant: every copy in the population is equally likely to be the ancestor of all future copies, so an allele at 30% frequency owns 30% of the lineages and has a 30% chance.

P(fixation) = p Var(Δp) = pq/(2N_e) per generation

Note that fixation probability does not depend on population size — but the time to fixation does, averaging about 4N_e generations. Small populations reach an outcome quickly; large ones take far longer to resolve.

N_e	Variance per generation at p = 0.5	Drift strength
10	0.0125	Very strong
100	0.00125	Strong
1,000	0.000125	Moderate
10,000	0.0000125	Weak

Drift Versus Selection

The decisive comparison is between the selection coefficient and effective population size. When |s| < 1/(2N_e), drift overwhelms selection and the allele behaves as effectively neutral regardless of its fitness effect.

This is why slightly deleterious mutations accumulate in small populations but are purged from large ones — the same mutation is invisible to selection in one context and removed in another. It is central to the nearly neutral theory.

Why N_e Is Smaller Than You Think

Factor	Effect on N_e
Unequal sex ratio	Reduces — harmonic-mean weighted
Variance in reproductive success	Reduces substantially
Population bottleneck	Dominated by the smallest size
Overlapping generations	Complicates estimation

Because N_e across generations is a harmonic mean, a single severe bottleneck dominates the long-term average. A population of 1,000 that crashes to 10 for one generation has an effective size far closer to 10 than to 1,000 — which is why historical bottlenecks leave such lasting genetic signatures.

Worked Examples

Example 1: Neutral allele p=0.5, Ne=100

P(fix)=0.5, P(loss)=0.5

Result: Equal chance regardless of starting frequency

Fixation time=400 generations

Example 2: Small pop Ne=10, p=0.1

Large drift expected

Result: Var=0.1x0.9/20=0.0045 per generation

High risk of rapid loss in small populations

Example 3: When selection stops working

N_e = 100, s = 0.002

Result: Effectively neutral

1/(2N_e) = 0.005, which exceeds s. Drift overwhelms the selective advantage and the allele behaves as if neutral.

Example 4: Bottleneck dominance

N_e of 1,000 for nine generations and 10 for one

Result: Harmonic mean about 92

The single crash generation pulls the long-term effective size down by an order of magnitude, which is why bottlenecks leave lasting genetic signatures.

Common Mistakes

⚠️

Confusing census size with effective size

N_e is typically far smaller, reduced by unequal sex ratios, variance in reproductive success and historical bottlenecks.

⚠️

Assuming selection always overcomes drift

When |s| is below 1/(2N_e), drift dominates and the allele is effectively neutral no matter its fitness effect.

⚠️

Thinking fixation probability depends on population size

For a neutral allele it equals the starting frequency regardless of N_e. Only the time to fixation scales with population size.

⚠️

Averaging N_e arithmetically across generations

It is a harmonic mean, so a single bottleneck generation dominates. Arithmetic averaging badly overestimates effective size.

Frequently Asked Questions

Kimura's neutral theory?

Most mutations are neutral or slightly deleterious, fixed by drift not selection. Rate of neutral evolution = mutation rate (independent of Ne). Molecular evolution mostly neutral: basis of molecular clock.

Ne bottleneck effect?

One generation at Ne=10 has same genetic effect as 100 generations at Ne=1000. Bottlenecks cause random fixation of alleles, loss of heterozygosity. Cheetah, northern elephant seal: evidence of historical bottlenecks.

Why does fixation probability equal starting frequency?

Because every copy of the allele is equally likely to be the ancestor of all future copies. An allele at frequency p owns p of the lineages.

When does drift overpower selection?

When the selection coefficient is smaller than 1/(2N_e). Below that threshold the allele is effectively neutral regardless of its fitness effect.

Why is effective population size smaller than census size?

Unequal sex ratios, variance in reproductive success and historical bottlenecks all reduce it. Ratios of N_e to census size around 0.1 are common.

How long does fixation take?

On average about 4N_e generations for a neutral allele. Small populations resolve quickly; large ones take far longer.