Genetic Drift

How drift happens — the marble jar

Imagine a jar containing 100 marbles, half red and half blue. To make the next generation, you reach in blind and pull out 100 marbles with replacement (so each draw is independent). On average you'll get 50 red and 50 blue, but you might pull 53 and 47, or 45 and 55. That's drift: a random sample doesn't perfectly recover the original frequency.

Now repeat. The new jar starts with 53 red and 47 blue. You draw again — this time perhaps 50 and 50, or 55 and 45. The frequency drifts up and down each generation. Over many draws, eventually one color reaches 100% (fixation) or 0% (loss). Once that happens, the system is stuck: with no input of new colors, you cannot recover the lost variant.

This is the Wright-Fisher model. Replace marbles with gene copies, color with allele, and the jar with a finite population. Each generation samples 2N gene copies (for N diploid individuals) from the previous generation's gene pool. Even with no selection — no allele intrinsically favored — frequencies wander, and given enough time, every allele either fixes or vanishes. Drift is the unavoidable consequence of finite population size.

The Wright-Fisher model and the 1/(2N) result

Sewall Wright at the University of Chicago and R. A. Fisher at Rothamsted, working largely independently in the 1920s and 1930s, gave drift a precise mathematical form. The Wright-Fisher model assumes a fixed diploid population of size N (so 2N gene copies at any locus), discrete non-overlapping generations, random mating, and no selection. Under those assumptions, the number of copies of an allele in the next generation is binomially distributed around the current frequency.

The key results follow directly. The variance in allele frequency change per generation is p(1-p)/(2N) — small populations have larger jumps. The probability that any new neutral allele eventually reaches fixation, starting from a single copy, is exactly 1/(2N). Equivalently, every neutral allele at current frequency p has fixation probability p; the rest of the time it disappears. Time to fixation conditional on fixing is roughly 4N generations.

The 1/(2N) result is striking. In a population of 1,000 diploid individuals, a brand-new neutral mutation has a 0.05% chance of ever spreading to everyone. Most novel mutations vanish in the first few generations, victims of sampling. Yet because mutations arise at every locus all the time, a small but steady stream of them does fix — building up the molecular divergence between populations and species.

Drift vs other evolutionary forces

	Genetic drift	Natural selection	Gene flow	Mutation
Direction	Random	Toward higher fitness	Toward source-population frequency	Random across genome
Strength scales with	1/N (small populations)	Selection coefficient s	Migration rate m	Mutation rate μ (≈ 10⁻⁸/site/gen)
Effect on within-pop variation	Removes (alleles fix or vanish)	Removes (purifying) or maintains (balancing)	Adds (imports new alleles)	Adds (creates new alleles)
Effect on between-pop divergence	Increases (each pop wanders separately)	Increases when local s differs	Decreases (homogenizes)	Increases slowly
Speed	Fast in small pops, slow in large	Visible in tens-hundreds of generations	Immediate	Per-locus tiny, genome-wide cumulative
Typical evidence	Heterozygosity decay, allele loss	Selective sweeps, dN/dS > 1	FST < 0.05 between groups	Standing variation, novel diseases
Wins out when	Ns < 1	Ns >> 1	Nm >> 1 between pops	Always — but slowly

Drift, selection, gene flow, and mutation are the four classical forces of evolutionary change. Real populations experience all four simultaneously. The Wright-Fisher framework was extended through the twentieth century to handle each in combination — diffusion approximations (Kimura), coalescent theory (Kingman, 1982), and modern simulation tools all stack drift onto a backbone of selection, migration, and mutation.

Worked example: heterozygosity decay in a small population

Take a population of N = 50 diploid individuals starting with allele frequencies p = q = 0.5 — maximum heterozygosity. Each generation, expected heterozygosity declines by a factor of 1 − 1/(2N) = 0.99. After 100 generations, expected heterozygosity is 0.99^100 ≈ 0.366 — about 73% of the starting variation has been lost. After 200 generations, only 13% remains.

Now compare the same starting state with N = 10,000. The decay factor is 1 − 1/20,000 = 0.99995. After 100 generations heterozygosity is 99.5% of starting — drift has barely touched it. After 1,000 generations, still 95%.

The lesson: drift is a numbers game. In a population of ten thousand, drift is practically invisible over centuries. In a population of fifty, drift erodes variation in a few hundred generations. This is why conservation biologists worry about effective population sizes (Ne) below a few hundred — drift becomes a serious threat to long-term genetic health below that threshold.

Real-world examples

• Cheetahs (Acinonyx jubatus). Modern cheetahs went through a severe bottleneck around 10,000 years ago at the end of the Pleistocene. Genetic diversity is so low that skin grafts between unrelated individuals are accepted without rejection, like identical twins. Reproduction suffers, sperm abnormalities are high, vulnerability to disease is high. Drift in a small surviving population stripped variation, and the species has not recovered it despite tens of thousands of years.
• Pingelap Atoll achromatopsia. A typhoon in 1775 killed most of the population of Pingelap, a small Pacific atoll. The roughly 20 survivors became founders of the modern population. One survivor carried a recessive allele for total color blindness (achromatopsia). Today around 5-10% of Pingelap islanders are homozygous and completely color-blind — about a thousand-fold higher than the global rate. The high frequency reflects drift acting on a tiny survivor cohort.
• Amish polydactyly. The Old Order Amish of Lancaster County descend from a few hundred founders in the 1700s. One founder carried a rare allele causing Ellis-van Creveld syndrome — short-limbed dwarfism with extra fingers and a heart defect. The condition's frequency among the Amish is far higher than in the global population, again from drift in a small founding group followed by reproductive isolation.
• Ashkenazi Jewish disease alleles. Tay-Sachs, BRCA1/2 founder mutations, Gaucher's, familial Mediterranean fever — multiple alleles are at elevated frequency in Ashkenazi Jews because of drift through historical bottlenecks (medieval European persecutions reducing the population to a few thousand) followed by demographic expansion.
• Galápagos finches and small islands. Each island's finch population is small enough that drift, layered on selection, contributes to the rapid divergence Darwin observed. Population genetics analyses show drift signatures even on islands where ecological selection is also strong.
• Effective population size (Ne) of humans. Genetic diversity in humans is consistent with an effective Ne of around 10,000 throughout most of our species history — strikingly low for a species now numbering 8 billion. Drift over our deep past shaped the variation we see today.

Kimura's neutral theory

By the late 1960s, molecular biologists had begun comparing protein sequences across species. The rate of amino-acid substitutions seemed strikingly constant — a "molecular clock" ticking at roughly the same speed across very different lineages. Motoo Kimura (1968) realized this was hard to reconcile with selection, which should vary in intensity across lineages and lifestyles. He proposed that most molecular changes are neutral or nearly neutral, with their fate set by drift.

The neutral theory makes specific predictions: synonymous substitutions (same amino acid) should accumulate faster than nonsynonymous ones (because most amino-acid changes are slightly deleterious and removed by selection). Substitution rates should be roughly clocklike. Within-species polymorphism should match between-species divergence under drift expectations. All three predictions are broadly confirmed by genomic data.

The neutral theory does not say evolution is random — selection still drives the major phenotypic changes that matter to organisms. But it changed how biologists read DNA. Most of the differences you see between two species' genomes are not adaptive innovations but the accumulated noise of drift, with selection visible as deviations from the neutral baseline.

Variants and refinements

• Effective population size (Ne). The actual census count N rarely matches what matters for drift. Ne is typically smaller — reduced by sex-ratio imbalance, fluctuating size, age structure, and reproductive variance. Bottlenecks crater Ne for centuries afterward.
• Bottleneck events. Sharp transient reductions in population size strip variation and inflate drift. Cheetahs, northern elephant seals, golden hamsters all bear bottleneck signatures.
• Founder effect. A specific kind of bottleneck where a new population is established by a small subset of an original. Drift on the founder cohort sets a new starting frequency. (See the dedicated founder-effect article.)
• Linkage and hitchhiking. Drift acts on entire haplotypes, not single sites. Selection on one site drags neighbors with it; drift erases neighborhoods of variation around any fixed allele.
• Coalescent theory. Run drift backward — every pair of gene copies traces back to a common ancestor. The expected time to coalescence is 2N generations. The whole genealogical structure of a sample emerges from drift run in reverse, the foundation of modern population genomics inference.
• Nearly neutral theory. Tomoko Ohta's 1973 refinement: many mutations have small selection coefficients of order 1/N, so drift dominates in small populations and selection in large ones. Predicts genome-size correlations with population size that match data better than strict neutrality.

Common pitfalls

• Treating drift and selection as either-or. Both act on every allele simultaneously. The relative strength is set by Ns. For weakly selected mutations in small populations, drift can override selection; for strongly selected mutations in large populations, selection swamps drift.
• Conflating drift with bottleneck or founder effect. Drift is the continuous random sampling that happens every generation in any finite population. Bottlenecks and founder effects are episodes of intensified drift; they are special cases, not synonyms.
• Thinking drift only matters for neutral alleles. Drift acts on every allele, neutral or not. Its relative importance falls as |Ns| grows but never disappears. Even strongly favored alleles can be lost by chance in their first few generations.
• Assuming drift increases variation. Within a population, drift removes variation. Between separately evolving populations, drift increases divergence. Both are correct — at different scales.
• Ignoring effective population size. Census size badly overestimates Ne. Sex-biased reproduction, fluctuating numbers, and reproductive variance all reduce Ne — sometimes by orders of magnitude. Conservation genetics calculations must use Ne, not N.
• Interpreting drift outcomes as adaptive. A trait fixed by drift looks like the species "chose" it; it didn't. Just-so stories about every fixed allele assume selection where drift may suffice. Always ask whether the standing population was large enough to make selection visible.