Genetic Drift: Evolution That Happens by Chance Alone

Evolution without selection

Natural selection is not the only force that changes how common a gene variant is in a population. Even when an allele confers no advantage or disadvantage at all, its frequency still wanders from generation to generation, purely because only a finite, random sample of parents' alleles makes it into the next generation. That random wander is genetic drift, and in small populations it can be a far stronger force than selection.

The Wright-Fisher model

The standard mathematical model, developed independently by Sewall Wright and Ronald Fisher in the 1930s, treats each new generation as a random sample of alleles drawn (with replacement) from the previous generation's gene pool — mathematically identical to flipping a biased coin 2N times for a diploid population of size N, where the bias is the current allele frequency p.

p(t+1) ~ Binomial( 2N, p(t) ) / 2N

E[ p(t+1) ]   = p(t)                      // drift has no directional bias
Var[ p(t+1) ] = p(t) . (1 - p(t)) / (2N)   // but variance grows every generation

The expected value does not move — drift has no built-in direction, unlike selection — but the variance grows every generation, and it grows faster the smaller N is. Eventually every allele either disappears entirely (loss, frequency reaches 0) or takes over the whole population (fixation, frequency reaches 1); there is no stable middle ground under drift alone, because 0 and 1 are absorbing states of the random walk.

Why fixation probability equals starting frequency

One of the cleanest results in population genetics falls straight out of this model: for a truly neutral allele (no selective advantage), the probability that it eventually fixes is exactly equal to its starting frequency p0. A brand-new mutation present in a single copy in a diploid population of size N starts at p0 = 1/(2N), so its fixation probability is 1/(2N) — vanishingly small in a large population, but not zero, which is precisely why neutral mutations do occasionally fix even without any selective benefit.

Drift is stronger in small populations

Because the variance term carries a factor of 1/(2N), drift's effect on any single generation shrinks as population size grows — a population of a million individuals barely wanders generation to generation, while a population of twenty can swing wildly. The average heterozygosity in a population, a standard measure of genetic diversity, decays geometrically under drift alone:

H(t) = H(0) . (1 - 1/(2N))^t

Small, isolated populations — after a founder event, a bottleneck, or on an island — therefore lose genetic diversity measurably faster than large ones, independent of any selection pressure. Expected time to fixation or loss for a neutral allele also scales with population size, on the order of 4N generations to fixation for an allele that does eventually fix — small populations resolve to fixation quickly, large populations can carry variation for a very long time.

Drift versus selection

Selection and drift are always acting together, and which one dominates depends on the product Ns, population size times the selection coefficient. When Ns is large (strong selection, or a large population), selection reliably wins and pushes the favoured allele to fixation. When Ns is small — a weak selective advantage, or a small population — drift can easily overpower selection, and even mildly deleterious alleles can drift to fixation by chance, or advantageous ones can be lost. This is the mechanistic core of the neutral theory of molecular evolution, which argues that most differences between species at the DNA level are fixed by drift rather than by selection.

Frequently asked questions

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