Evolution of the parameter boundaries p_min, max versus the average metallicity Z_avg for the three inference runs (including [S II] on top, ignoring [S II] in the middle, and replacing [S II] by [O II] in the bottom). For each run, the upper row shows p_min, max in blue and red respectively (with the gray rectangles showing the full parameter range in the grid), while the bottom row shows the difference between p_max − p_min.