Extinction on biophysical fitness landscape.

<p>All finite populations eventually go extinct. The mean number of generations until extinction (<i>τ</i>) increases with population capacity (<i>N</i>) and decreases with mutation rate (<i>U</i>). <b>A</b>: <i>τ</i> versus <i>N</i> at various fixed <i>m</i>; notice the double logscale. Curves for <i>U<2.5</i> or so have an inflection point, signaling a qualitative transition from extinction to survival as <i>N</i> increases. Solid curves correspond to <i>δ = </i>0, while dashed curves correspond to <i>δ/W* = 0.</i>1. <b>B</b>: Coefficient of variation in time until extinction (<i>CV_τ</i>) for the same parameters as panel A. <i>CV_τ</i> increases towards one in the survival phase and decreases toward zero in the extinction phase, as <i>N</i> increases. Curves “peel off” toward <i>CV_τ = 1</i> at the critical population capacity (<i>N_crit</i>), shown approximately with dashed lines. When , both simulation results and general arguments (see main text) show that curves do not peel off, i.e. <i>N_crit</i> does not exist. <b>C</b>: Heuristic cartoon “phase diagram” summarizing the behavior from panels A,B. In panels A,B <i>τ</i> values are reported only in cases where extinction occurred within 10⁵ generations in each replicate. See main text and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002609#pcbi.1002609.s005" target="_blank">fig.S5</a> for a quantitative sense of how <i>N_crit</i> depends on <i>U_crit</i>. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002609#s4" target="_blank">Methods</a> for averaging procedures. <i>Γ = 20</i> throughout this paper.