Fig. 4: The coupling between marine benthic δ¹³C and δ¹⁸O/ice volume on the ~100-kyr timescale leads to the ~100-kyr climate cycles.

A The sea level equivalent relative to present (m) of the Antarctic and Northern Hemispheric (NH) ice sheets, estimated based on benthic δ¹⁸O stack of Westerhold et al.^44,45. B The statistically reconstructed 500-kyr mean global mean surface temperatures (GMST) estimated from benthic δ¹⁸O stack following Westerhold et al. (with 50 and 95% credible intervals)^44,84. C Soil carbonate δ¹³C data from Pakistan Siwalik⁶¹, and equid δ¹³C data from North America⁶⁰, act as an indicator reflecting expansion of C4 plants in low and high latitudes, respectively. D Sedimentary accumulation rate (SAR) at Huaitoutala section, NE Tibetan Plateau, indicating tectonic uplift events⁶². E The uplifting rate of Panama Isthmus relative to sea level⁶⁴. F Eccentricity parameter based on La04 astronomical solution (in black)⁷⁴ and the ~2.4-myr filter (in blue). G The evolutionary correlation coefficient between δ¹³C stack⁴⁴ and eccentricity (in vermilion)⁷⁴; and that between δ¹⁸O stack⁴⁴ and eccentricity (in blue); and that between the reversed sea-level equivalent^44,45 and eccentricity (in teal green) on the ~100-kyr timescale. The sliding window was set as 1000 kyr. H The evolutionary correlation coefficient between benthic δ¹⁸O and δ¹³C stack⁴⁴ on the ~100-kyr timescale (the dashed line in blue), and it’s absolute value (the solid line in blue); the evolutionary correlation coefficient between the reversed sea-level equivalent^44,45 and δ¹³C stack⁴⁴ on the ~100-kyr timescale (the dashed line in teal green), and it’s absolute value (the solid line in teal green); the evolutionary ~100-kyr power ratio of benthic δ¹⁸O stack (in black)⁴⁴. I The evolutionary ~100-kyr power ratio of mean daily insolation on 21 June at 65°N, calculated based on La04 solution⁷⁴.