Genetic Drift in Small Populations
Wright–Fisher: drift preserves expectation, destroys variance
Small populations lose alleles. Not sometimes — always, eventually. Run hundreds of Wright–Fisher trajectories in parallel; every one is absorbed at 0 or N. The fraction that fixes converges to the initial frequency p₀: the martingale property of neutral drift, made visible.
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Allele frequency trajectories (60 of 300 shown)
Final frequency distribution
fixed (p = 1)
74 / 300
lost (p = 0)
226 / 300
Pr[fixation] empirical vs p₀
0.247 vs 0.300
Wright–Fisher: Xt+1 ~ Binomial(N, Xt/N). Every trajectory is absorbed at 0 or N. Across runs the fraction that fixes converges to p₀ — drift preserves expectation while destroying variance.