Figure 4.

Time of appearance of the mutants that fix. (A) Average time τ_af of appearance of a G or S mutant that fixes vs. mutation probability μ upon division. The Hill coefficient characterizing the steepness of the environment deterioration (see Equation 1) is n = 5. Vertical dotted line: Kμ = 1. (B) Average time τ_af of appearance of a G or S mutant that fixes vs. Hill coefficient n. The mutation probability upon division is μ = 10⁻⁵. In both panels, markers correspond to averages over 10³–10⁴ replicate stochastic simulations (“Simulation”). Dashed and solid lines correspond to numerical integrations of Equation 13 (“Theory”) for G and S mutants, respectively. Parameter values: $g_W=g_G=g_S=0.1,$ K = 10³, $N_W^0=10,$ and θ = 10³. Horizontal dotted lines: τ_af = θ.