Figure 6.

ER probability in the presence of standing genetic variation. In each panel, stress only affects the decay rate $r_D$ (shifting optimum). In both panels, blue solid lines show the theory for de novo and standing variance (“DN”+“SV”) computed numerically [Equation (5)] and the gray lines correspond to an equivalent theory without the FGM (named context-independent model as described in the Methods section, “CI”) modified from Orr and Unckless (2008). This last model was computed using a fixed proportion of resistant mutations equal to the one in Equation (5) for a rescue probability of $0.5$ (which explains why the two curves cross exactly at $P_R=0.5$). The dashed red line gives the simpler expression for the overall rescue rate: $\begin{array}{c}\omega \approx {\omega }_{DN}^{*}/\sqrt{\mathit{ϵ}}\end{array} .$ [Equation (11)] with $\mathrm{ϵ}$ given in Equation (10) and ${\omega }_{DN}^{*}$ by Equations (7a) and (7b). (A) ER probability in the presence of standing genetic variation as a function of $r_D.$ The dots give the results from simulations. (B) Proportion ${\phi }_{SV}$ of rescue from standing variance as a function of $r_D.$ The black dashed-line give the approximate theory from Equation (10) and the dashed red line $\max \left({\phi }_{SV}^{*}\right)\approx 1-\sqrt{\mathit{ϵ}}$ from Equation (11). The shaded area shows the range of $r_D$ for which the ER probability drops from $0.99$ to ${10}^{-3}.$ Other parameters as in Figure 2.