Genetic Drift Simulator

The genetic drift simulator models how the frequency of a single allele wanders randomly from generation to generation in a finite population. Unlike natural selection, which pushes allele frequencies in a predictable direction, genetic drift is pure chance: when only a limited number of gametes form the next generation, the allele frequency in the offspring will rarely match the parents exactly. This sampling error accumulates, and over enough generations every allele eventually drifts to fixation (frequency 1) or loss (frequency 0).

This simulator runs several independent replicate populations at once so you can watch the spread of possible outcomes. You set four values: the population size (N), the starting allele frequency (p), the number of generations to run, and how many replicate simulations to launch (up to 10). Each generation, the tool draws the next allele count by binomial-style sampling from a pool of 2N gene copies, because every diploid individual carries two alleles at the locus. The result panel reports how many replicates ended in fixation, how many in loss, how many remain polymorphic, the mean final frequency, and the decay of heterozygosity.

Population geneticists, evolutionary biology students, and conservation researchers use a genetic drift calculator like this to build intuition for why small populations lose genetic variation so quickly, why founder events matter, and how effective population size shapes the long-term fate of neutral alleles. The same sampling logic underlies the Wright-Fisher model that anchors most theoretical population genetics.

The engine uses the Wright-Fisher idealized population. A diploid population of size N contains 2N copies of the gene. If the current frequency of allele A is p, then the number of A copies that survive into the next generation is drawn from a binomial distribution with 2N trials and success probability p. For computational speed with larger N, the simulator approximates that binomial with a normal distribution that has the same mean and variance, then rounds and clips the count to the valid range of 0 to 2N.

Concretely, each generation the tool computes a mean of 2N·p and a variance of 2N·p·(1−p), takes the standard deviation as the square root of that variance, draws a standard-normal value z using the Box-Muller transform, and sets the next allele count to round(2N·p + z·√variance). The new frequency is that count divided by 2N. Once a replicate hits exactly 0 or 1 it is absorbed — the allele is permanently lost or fixed and the trajectory stays flat.

Because the model has no mutation, migration, or selection, drift is the only evolutionary force at work. That makes the simulator a clean laboratory for the neutral theory: every replicate is equally likely to fix or lose the allele in proportion to its starting frequency.

Two theoretical quantities help you interpret the random replicates. The first is expected heterozygosity, the probability that two randomly chosen alleles differ. It starts at H(0) = 2·p₀·(1−p₀) and shrinks by the constant factor (1 − 1/(2N)) every generation. The smaller the population, the larger 1/(2N) becomes and the faster heterozygosity collapses — that is the mathematical reason small populations purge variation rapidly.

The second is the theoretical variance in final allele frequency across many replicate populations. The simulator computes it as p₀·(1−p₀)·(1 − (1 − 1/(2N))^t), which approaches the maximum possible variance of p₀·(1−p₀) as t grows large and all replicates fix or lose. The tool also reports the observed variance among the handful of replicates you actually ran; with only a few simulations this observed value is noisy and can differ noticeably from the theory, which is itself a useful lesson about sampling.

The probability that a neutral allele ultimately reaches fixation equals its starting frequency, p₀. So if you start at p = 0.5 and run many replicates, roughly half should fix and half should be lost. The mean final frequency across replicates stays near p₀ on average even as individual populations diverge wildly.

Using the genetic drift simulator takes four inputs and a few seconds:

1. Population Size (N): Enter the number of diploid individuals, from 2 up to 10,000. Try small values like 10 or 25 to see dramatic drift, and large values like 1,000 to see frequencies stay nearly stable.
2. Initial Frequency (p): Set the starting allele frequency between 0 and 1. A value of 0.5 gives the most balanced fixation-versus-loss outcome.
3. Generations: Choose how many generations to run, up to 500. More generations give more replicates time to reach an absorbing state.
4. Simulations: Pick how many independent replicate populations to launch, up to 10. Each runs with its own random draws.

The results panel then summarizes the outcomes: counts of fixation, loss, and still-polymorphic replicates, the mean final frequency, the initial and expected final heterozygosity, and both theoretical and observed variance. The trajectory chips at the bottom show each replicate's final frequency, color-coded green for fixation, red for loss, and blue for polymorphic. Re-run with the same settings and the random seeds change, so outcomes differ each time — that randomness is the whole point of drift.

Genetic drift is one of the four core forces of evolution alongside mutation, migration, and natural selection. It dominates whenever populations are small — during a founder effect, after a population bottleneck, or on isolated islands. Conservation geneticists worry about drift because endangered species with few breeding individuals lose alleles, increase homozygosity, and risk inbreeding depression. A genetic drift calculator makes these abstract risks concrete by showing how fast variation disappears at a given effective population size.

Drift also drives the neutral theory of molecular evolution, which holds that most variation at the DNA level is selectively neutral and changes frequency purely by chance. Understanding the random fixation of neutral mutations underpins the molecular clock used to date evolutionary divergences. In medicine and agriculture, recognizing drift helps explain why rare disease alleles can become common in isolated human populations or small breeding stocks.

By experimenting with population size and starting frequency here, you can reproduce textbook results: doubling N halves the rate of heterozygosity loss, low-frequency alleles are usually lost while common alleles often fix, and replicate populations that start identical can end up genetically very different. These are the same insights that population genetics courses build entire problem sets around.