Evolution of genotype composition x ( t ). (a) Deterministic evolution with fitness difference ΔF
> 0, leading to certain fixation of genotype b (time is shown in units of τ
). (b) Stochastic evolution with selection and genetic drift, leading to fixation of one of the genotypes. The time to fixation (grey shading) is of order τ
= 0.5, time is shown in units of N). (c) Stochastic evolution with selection, genetic drift, and mutations in the regime Nμ ≪ 1, leading to a substitution dynamics with rates ua→band ub→agiven by (49). Substitution events are marked by dashed lines. The typical time between initial mutation and fixation (grey shading) for a given substitution, τ
, is much shorter than the time between subsequent substitutions, 1/ua→bresp. 1/ub→a(N ΔF
= 0.5, Nμ = 0.05, time is shown in units of 1/μ).