a, With supercooling, BE (purple dots with red line) and WC (grey crosses with black line) for global maximum (top solid), minimum (bottom solid), average (dashed) and median (dotted) O2 solubilities in Ca-perchlorate brines with varying obliquity (for a climate model without a perennial south polar CO2 cap; blue dots are BE results (from top to bottom: maximum, average, median, minimum) for modern Mars with a perennial south polar CO2 cap as in Fig. 3; for WC, there is no difference between south polar cap and no south polar cap cases). b, Predicted obliquity variation across time22. c, Using a and b, we plot global maximum (top) and average (bottom) [O2]aq values for BE (red lines) and WC (black lines) across time for Ca-perchlorate brines. Dashed brown lines highlight the aerobic breathing limit for sponges and grey shaded boxes obliquities/times where we find atmospheric collapse. Comparable results for Mg-perchlorate.