Figure 4.

Simulations and analytic predictions for evolutionary rescue in high-density scenarios. The probabilities of observing rescue via soft selective sweeps, rescue via hard selective sweeps, or extinction as a function of the decline rate α (logarithmic scale) measured over 1000 simulations (see Methods) for each combination of model parameters are indicated as stacked bar plots. The color key indicates shading for simulation outcomes. Population-scale mutation rate increases between plots from bottom to top, and unscaled per-capita mutant birth rate increases between plots from left to right. The analytic predictions for each parameter combination show $P_{\text{soft}}$ (bottom red points) and $P_{\text{rescue}}=P_{\text{hard}}+P_{\text{soft}}$ (top orange points). For analytic predictions of $P_{\text{soft}},$ points where adaptation $w*\mu \ge 1$ are shaded. Our analysis has high concordance with the observed probability of rescue for each parameter combination. As in the low-density scenario, our analysis has good concordance with the observed probability of rescue via soft sweeps for most parameter combinations, except in instances where our independence assumption breaks down $\left(w*\mu <1\right)$ and for low decline rates (bottom and middle rows, leftmost α values). Evolutionary rescue is less likely for more parameter combinations in the high-density scenario because the wild-type population must decline before establishment of mutants is likely (see Figure 2).