Genetic Drift | PopGeneJS

What is Genetic Drift?

Genetic drift is the random change in allele frequencies from one generation to the next due to chance events in reproduction. Unlike natural selection, drift is not driven by differences in fitness — it's the result of random sampling when gametes form the next generation.

Key insight: Drift is most powerful in small populations. In an infinite population, random fluctuations cancel out. In small populations, they can dramatically change allele frequencies.

The Wright-Fisher Model

The standard model of genetic drift, developed by Sewall Wright and R.A. Fisher, treats each generation as binomial sampling from the previous generation's allele frequencies.

P(i → j) = C(2N, j) × p^j × (1-p)^(2N-j) Transition probability: i alleles → j alleles

Where N is the population size and p = i/2N is the current allele frequency. This binomial sampling causes allele frequencies to fluctuate randomly each generation.

Interactive Simulation

Watch how drift affects multiple populations starting at the same allele frequency. Each colored line represents an independent population. Smaller populations show more dramatic fluctuations.

Population Size (N) 20

Generations 50

8 populations with p₀ = 0.5. Dots mark fixation (p = 1) or loss (p = 0).

Key Properties of Drift

Expected Frequency Unchanged

Despite random fluctuations, the expected allele frequency remains constant:

E[p(t)] = p₀ Drift doesn't bias allele frequencies

Variance Increases Over Time

While the mean stays constant, the variance in allele frequency across replicate populations grows:

Var[p(t)] = p₀q₀[1 - (1 - 1/2N)^t] Variance approaches p₀q₀ as t → ∞

Fixation is Inevitable

Given enough time, drift will eventually fix one allele (p = 1) and lose the other (p = 0). The probability of fixation equals the initial frequency:

P(fixation) = p₀ Probability of allele A eventually fixing

Time to Fixation

How long does drift take? Using Kimura and Ohta's (1969) diffusion results, an allele starting at frequency p (with q = 1 − p) takes on average:

t̄(absorption) ≈ −4N[p ln p + q ln q] generations Mean time until the allele is either fixed or lost

t̄₁(p) ≈ −4N q ln q / p generations Mean time to fixation, counting only populations in which A fixes

Starting from p = 0.5, both expressions give 4N ln 2 ≈ 2.8N generations. For a brand-new mutation (p = 1/2N), the alleles that do fix take about 4N generations, but most new mutations are lost within a few generations, so the mean absorption time is only about 2 ln(2N) + 2.

This means larger populations maintain genetic variation longer. A population of 1000 individuals starting at p = 0.5 would take roughly 2800 generations to fix or lose an allele by drift alone. (Here N is the effective population size, Nₑ.)

Heterozygosity Decline

Drift causes heterozygosity to decline over generations. Starting with expected heterozygosity H₀ = 2p₀q₀:

H(t) = H₀(1 - 1/2N)^t Deterministic heterozygosity decay

Each generation, heterozygosity declines by a fraction 1/(2N) of its current value (it is multiplied by 1 − 1/2N), so it halves about every 1.4N generations. Small populations lose variation quickly; large populations retain it longer.

Effective Population Size

Real populations often don't match Wright-Fisher assumptions. The effective population size (Nₑ) is the size of an idealized population that would experience drift at the same rate.

Nₑ is reduced by:

Unequal sex ratios: Nₑ = 4NₘNf / (Nₘ + Nf)
Variance in reproductive success: populations with unequal contribution
Population fluctuations: bottlenecks have lasting effects
Inbreeding: reduces the number of independent lineages

Effective population size is often much smaller than census population size. Humans have a long-term Nₑ of roughly 10,000 despite a census size of billions. Long-term Nₑ is close to the harmonic mean of past population sizes, so it is dominated by the long periods of small size and the bottlenecks in our history; the recent expansion has had little time to raise it.

Drift vs. Selection

When is drift important relative to selection? The key parameter is the product Ns, where s is the selection coefficient:

|Ns| << 1: Drift dominates — selection is effectively neutral
|Ns| ≈ 1: Both forces matter — complex dynamics
|Ns| >> 1: Selection dominates — drift is negligible

In small populations, even moderately selected alleles can be lost by chance. In large populations, even tiny selective differences eventually determine outcomes.