Fig. A1.

Fixation probability p_f of a mutant (with growth rate $g_m=1+s_I$) as a function of n, the fraction of type 1 cells in a population of size N = 1,000. Type 1 cells have growth rate $g_1=1$ and type 2 cells have growth rate $g_2=1+s$. a) When $s\ll s_I$ (blue curves: s = 0.005, $s_I=0.05$, red curves: s = 0.01, $s_I=0.1$), $p_f(n)$ is approximately linear in n and is given by the selective advantage of the mutant over that of the population average. Solid lines are exact solutions obtained from Equation (A1) while dashed lines plot the expression in Equation (A14). b) In general, $p_f(n)$ is not a linear function of n (dash-dotted lines, Equation A14), but is well approximated by Equations (A15) and (A18) (dashed lines vs solid lines). [Blue curves: s = 0.03, $s_I=0.05$, red curves: s = 0.05, $s_I=0.1$.]