Evolution Frequency Calculator Drift: What It Means

This calculator works out how much a genetic variant’s frequency drifts over a given number of generations due to random sampling alone. You enter the starting allele frequency, the effective population size, and the number of generations, and you get the expected variance of the frequency change and the standard deviation of that change. The result tells you how much random genetic drift, not selection, is likely to move the allele frequency in your population.

Formula

The standard population-genetics formula for the variance of allele frequency change due to drift over t generations is:

Var(Δp) = p₀(1 − p₀) × [1 − (1 − 1/(2Nₑ))^t]

where:

• pâ‚€ = starting frequency of the allele (unitless, between 0 and 1)
• Nâ‚‘ = effective population size (number of breeding individuals, not the census size)
• t = number of generations
• Var(Δp) = variance of the change in frequency (unitless)

The standard deviation is the square root of that variance. The expected frequency after t generations is still p₀ — drift does not push the frequency in a particular direction on average; it just spreads out the distribution.

Worked Example

Using the defaults: pâ‚€ = 0.5, Nâ‚‘ = 100, t = 10.

1. Compute 1/(2Nâ‚‘) = 1/200 = 0.005.
2. Compute 1 − 0.005 = 0.995.
3. Raise to the 10th power: 0.995¹⁰ ≈ 0.9511.
4. Compute 1 − 0.9511 = 0.0489.
5. Multiply by p₀(1−p₀) = 0.25: variance = 0.25 × 0.0489 = 0.012225.
6. Take the square root: standard deviation ≈ 0.1106.

So after 10 generations, the allele frequency is expected to still be 0.5 on average, but the standard deviation of that frequency is about 0.11. In practice, most populations will end up between roughly 0.39 and 0.61 (one standard deviation either side).

When to Use This Calculator

Use this tool when you want to quantify how much random genetic drift alone might change an allele frequency over a set number of generations. It is especially useful in conservation biology for small populations, in evolutionary biology for teaching drift, and in plant/animal breeding to see how much random loss of variation you might expect.

It is not for predicting the effect of natural selection, mutation, or migration. Those forces change the expected frequency; this calculator only handles the random sampling component.

How to Read the Results

The first output, the standard deviation, is the most intuitive. It gives you a range: about 68% of replicate populations will end up within one standard deviation of the starting frequency, and about 95% within two standard deviations. The variance output is useful if you are combining it with other variance components (e.g., selection variance) in a larger model.

Remember that the expected frequency after t generations is still p₀. Drift is symmetric — it does not systematically increase or decrease the frequency, just makes it more variable over time.

Common Mistakes and Limits

• Using census population size instead of effective size. Nâ‚‘ is usually much smaller than the actual count because not all individuals breed, sex ratios may be skewed, and population size fluctuates. If you use the census size, you will underestimate drift.
• Confusing variance with standard deviation. The variance is in units of frequency squared; the standard deviation is in the same units as frequency. Most people want the standard deviation.
• Assuming drift acts directionally. Drift does not push a frequency up or down; it just adds noise. Selection is what changes the mean.
• Ignoring fixation. This formula assumes the frequency stays between 0 and 1. If the standard deviation is large relative to pâ‚€, the actual distribution will hit the boundaries, and the formula becomes an approximation.

The formula also assumes a constant effective population size and no selection, mutation, or migration. Real populations often violate these assumptions, so treat the result as a baseline.

Why Effective Population Size Matters

The effective population size (Nâ‚‘) is the number of individuals that actually contribute genes to the next generation, not the total headcount. It is often much smaller than the census size due to:

• Unequal sex ratios (e.g., one male with many females)
• Fluctuating population size over generations
• Non-random mating
• Overlapping generations

For example, a population of 1000 animals might have an Nₑ of only 100. That difference changes the drift variance by a factor of 10. If you do not know Nₑ, a rough rule of thumb is that it is often about 10–20% of the census size for many species, but it varies widely.

Comparison with Selection

Drift is often compared with selection because both change allele frequencies, but they act differently. Selection changes the expected frequency in a direction determined by fitness differences; drift adds random noise around that expectation. In a large population, selection dominates because drift is weak (variance scales as 1/Nâ‚‘). In a small population, drift can overwhelm selection, even causing deleterious alleles to increase in frequency.

This calculator isolates the drift component. If you want to include selection, you would need a different model, such as the diffusion approximation or a simulation.

Frequently Asked Questions

What is genetic drift in simple terms?

Genetic drift is the random change in allele frequencies from one generation to the next due to chance sampling of gametes. It is like flipping a coin: even if the coin is fair, you do not always get exactly half heads. Drift is stronger in small populations.

Why is the expected frequency still the same after drift?

Drift is symmetric — it is equally likely to increase or decrease the frequency by a given amount. So the average across many replicate populations remains the starting frequency. But each individual population may deviate, and the variance grows over time.

How many generations does it take for drift to fix an allele?

On average, it takes about 4Nâ‚‘ generations for a neutral allele to go to fixation or loss. For Nâ‚‘ = 100, that is about 400 generations. This calculator does not directly give that time, but you can see the variance growing over time.

What is the difference between effective and census population size?

Census size is the total number of individuals. Effective size is the number that actually pass on their genes, accounting for unequal sex ratios, fluctuating numbers, and non-random mating. Effective size is usually smaller, and it is the one that matters for drift.

Can drift increase genetic diversity?

No, drift tends to reduce genetic diversity within a population over time because it leads to fixation or loss of alleles. It increases between populations, though, as different populations drift in different directions.

Does this formula work for multiple alleles?

No, it is for a single allele with two variants (e.g., A and a). For multiple alleles, the variance-covariance matrix is more complex. This simplified version is still useful for understanding the basic behavior.

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in p0 | Starting frequency | - | 0.5 | 0
in Ne | Effective population size | individuals | 100 | 1
in t | Generations | generations | 10 | 1
out sd | Std dev of freq change | - | sqrt((p0*(1-p0))*(1-(1-1/(2*Ne))^t)) | 4
out var | Variance of freq change | - | (p0*(1-p0))*(1-(1-1/(2*Ne))^t) | 6
out p_after | Expected freq after t gen | - | p0 | 4