Evolution of ﹩\Delta _{x}﹩. Plotted are the peak value, ﹩\Delta _{x,\mathrm{max}\,}﹩, the scale at which it occurs, ﹩k_{\mathrm{max}\,}﹩, its effective width, ﹩\overline{k}﹩, and the corresponding rms, ﹩x_{\mathrm{rms}\,}﹩, for all simulations, as labeled. We also show the bias, ﹩b( z) ﹩, at large scales of the ionized density with respect to the underlying density field (right axis) and ﹩\overline{k}﹩ (see text for details). The values of ﹩k_{0}/ 2﹩, where ﹩k_{0}﹩ is the value of the characteristic ionized bubble scale, that give a good fit to the ﹩W( k) ﹩ window function at large scales are also indicated for each case (squares; see text for details).