Figure 3. Extinction on biophysical fitness landscape.

All finite populations eventually go extinct. The mean number of generations until extinction (τ) increases with population capacity (N) and decreases with mutation rate (U). A: τ versus N at various fixed m; notice the double logscale. Curves for U<2.5 or so have an inflection point, signaling a qualitative transition from extinction to survival as N increases. Solid curves correspond to δ = 0, while dashed curves correspond to δ/W* = 0.1. B: Coefficient of variation in time until extinction (CV_τ) for the same parameters as panel A. CV_τ increases towards one in the survival phase and decreases toward zero in the extinction phase, as N increases. Curves “peel off” toward CV_τ = 1 at the critical population capacity (N_crit), shown approximately with dashed lines. When , both simulation results and general arguments (see main text) show that curves do not peel off, i.e. N_crit does not exist. C: Heuristic cartoon “phase diagram” summarizing the behavior from panels A,B. In panels A,B τ values are reported only in cases where extinction occurred within 10⁵ generations in each replicate. See main text and fig.S5 for a quantitative sense of how N_crit depends on U_crit. See Methods for averaging procedures. Γ = 20 throughout this paper.