diagrams.ink / population genetics

Drift is just luck, repeated

Two identical alleles, no advantage for either. Watch a finite population forget its variety by chance alone — and see why fewer copies means a wilder walk.

allele A allele a — same fitness, no advantage the population shown above 19 other populations, same start expected drift spread (±1 SD)

Allele A frequency across generationsPress Run: every offspring bead copies a randomly chosen parent bead.

A frequency now0.5010 of 20 copies

Typical one-generation wobble±11.2 pts√( p(1−p) / N ), N = 20

Of 20 populations0 · 0 · 20A fixed · A lost · still mixed

Population size (gene copies) 20 Starting frequency of A 0.50 rarecommon

Speed

Chance, not selection

Both alleles are neutral: a bead of either colour is equally likely to be copied. Each generation, every offspring picks a random parent, so the number of A beads is Binomial(N, p). Its expected value is the old count, but the actual count wanders.

Why small populations drift faster

The spread of one draw is √(p(1−p)/N). Ten beads can easily lurch by a few; two hundred barely move. Try N = 6 against N = 200 with the same start: the small ones hit the walls within a few dozen generations.

Walls that never let go

At frequency 0 (A lost) or 1 (A fixed) there is nothing left to sample from, so the draw returns the same frequency forever. Drift removes variation, and a neutral allele fixes with probability equal to its starting frequency.

Simplified model: haploid Wright–Fisher, N gene copies, non-overlapping generations, no mutation, migration or selection. Diploid organisms have 2 copies per individual.