Figure 2.

Fixation probability of mutants. (A) Fixation probability p_fix of G and S mutants vs. their time of appearance t₀ in the deteriorating environment, for different Hill coefficients n characterizing the steepness of the environment deterioration (see Equation 1). Here, S mutants satisfy m = n, i.e., they have the same sensitivity to the environment as W organisms (see Equation 2). Horizontal dashed line: $p_{\text{fix}}=1-g_G/f_G.$ Horizontal solid line: $p_{\text{fix}}=1-g_S.$ Data are shown for t₀ < τ_W, where τ_W is the average extinction time of the W population in the absence of mutation. (B) Fixation probability p_fix of different types of mutants vs. their time of appearance t₀ in the deteriorating environment, for a fixed Hill coefficient n = 10 characterizing the decay of f_W (see Equation 1). G mutants and S mutants with different Hill coefficients m (see Equation 2), corresponding to different sensitivities to the changing environment, are considered. In both panels, markers correspond to averages over 10⁴ replicate stochastic simulations (“Sim.”). Dashed and solid lines correspond to numerical integrations of Equation 4 (“Th.”) 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. Vertical dotted lines: t₀ = θ. Main panels: linear scale; insets: semilogarithmic scale.