Selection vs. Drift
When does a beneficial mutation fix?
Selection favors beneficial alleles deterministically; drift loses them stochastically. The single dial that decides which one wins is Ns. Sweep through Ns ≪ 1, Ns ≈ 1, and Ns ≫ 1 — watch the empirical fixation probability slide from p₀ (the neutral baseline) up through the Kimura curve toward 1.
seed 1
Trajectories (80 of 400 shown), s = 0.020, Ns = 1.00
Ns
1.00
empirical Pr[fixation]
0.107
Kimura prediction
0.110
neutral baseline (= p₀)
0.050
Ns ≈ 1 — selection and drift comparable
Sweep s through zero. With Ns ≪ 1 the empirical fixation rate hugs p₀ — selection is invisible to the population. Cross Ns ≈ 1 and selection takes over. A beneficial mutation (s > 0, p₀ = 1/N) fixes with probability ≈ 2s in large populations: most useful mutations still die.