Fig. 2. Relaxation to a fitness maximum does not generate a logarithmic fitness trajectory.

(A and B) Without epistasis (J = 0) (blue curves), the fitness reaches the global maximum quickly and follows a power law $F=F_{\text{max}}-\frac{F_{\text{max}}-1}{{(1+\mathit{bt})}^{\mathrm{\gamma }}}$ with γ = 2. With maximum epistasis (h = 0) (red curves), the fitness trajectory is slower with a power law exponent γ ≈ 0.9 but is still not as slow as a log trajectory if we do not allow escape from local fitness maxima. Here and in all other figures, time t is measured in units of number of mutational attempts (other parameters: L = 200, initial rank = 100, ρ = 0.05, Δ = 0.003).