Figure 3.

Rescue probability. (A) Rescue probability p_r of a W population in a deteriorating environment by G or S mutants, vs. mutation probability μ upon division. Different Hill coefficients n characterizing the steepness of the environment deterioration (see Equation 1) are considered. Here, S mutants satisfy m = n, i.e., they have the same sensitivity to the environment as W organisms (see Equation 2). Vertical dash-dotted line: Kμ = 1. (B) Rescue probability p_r by different types of mutants vs. mutation probability μ upon division. A fixed Hill coefficient n = 10 characterizing the decay of f_W (see Equation 1) is chosen, but G mutants and S mutants with different Hill coefficients m (see Equation 2) are considered. In both panels, markers correspond to averages over 10⁴ replicate stochastic simulations (“Simulation”). Dashed and solid lines correspond to numerical integrations of Equation 9 (“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.