1. Lear, C. H., Elderfield, H. & Wilson, P. A. Cenozoic deep-sea temperatures and global ice volumes from Mg/Ca in benthic foraminiferal calcite. Science 287, 269–272 (2000).

2. Zachos, J. C., Dickens, G. R. & Zeebe, R. E. An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics. Nature 451, 279–283 (2008).

3. Bijl, P. K. et al. Early Palaeogene temperature evolution of the southwest Pacific Ocean. Nature 461, 776–779 (2009).

4. Pearson, P. N. et al. Stable warm tropical climate through the Eocene epoch. Geology 35, 211–214 (2007).

5. Inglis, G. N. et al. Descent toward the Icehouse: Eocene sea surface cooling inferred from GDGT distributions. Paleoceanography 30, 1000–1010 (2015).

6. Evans, D. et al. Eocene greenhouse climate revealed by coupled clumped isotope-Mg/Ca thermometry. Proc. Natl Acad. Sci. USA https://doi.org/10.1073/pnas.1714744115 (2018).

7. Huber, M. et al. Eocene circulation of the Southern Ocean: was Antarctica kept warm by subtropical waters? Paleoceanography 19, PA4026 (2004).

8. Anagnostou, E. et al. Changing atmospheric CO 2 concentration was the primary driver of early Cenozoic climate. Nature 533, 380–384 (2016).

9. Kennett, J. P. Cenozoic evolution of Antarctic glaciation, the circum-Antarctic Ocean, and their impact on global paleoceanography. J. Geophys. Res. 82, 3843–3860 (1977).

10. Bijl, P. K. et al. Eocene cooling linked to early flow across the Tasmanian Gateway. Proc. Natl Acad. Sci. USA 110, 9645–9650 (2013).

11. PALAEOSENS Project Members. Making sense of palaeoclimate sensitivity. Nature 491, 683–691 (2012); erratum 494, 130 (2013).

12. Hollis, C. J. et al. Early Paleogene temperature history of the Southwest Pacific Ocean: reconciling proxies and models. Earth Planet. Sci. Lett. 349–350, 53–66 (2012); erratum 374, 258–259 (2013).

13. Sijp, W. P., England, M. H. & Huber, M. Effect of the deepening of the Tasman Gateway on the global ocean. Paleoceanography 26, PA4207 (2011).

14. Huber, M. & Caballero, R. The early Eocene equable climate problem revisited. Clim. Past 7, 603–633 (2011).

15. Lunt, D. J. et al. A model–data comparison for a multi-model ensemble of early Eocene atmosphere–ocean simulations: EoMIP. Clim. Past 8, 1717–1736 (2012).

16. Mascle, J. et al. Proceedings of the Ocean Drilling Program Initial Reports Vol. 159 (ODP/TAMU, College Station, 1996).

17. Wagner, T. Late Cretaceous to early Quaternary organic sedimentation in the eastern Equatorial Atlantic. Palaeogeogr. Palaeoclimatol. Palaeoecol. 179, 113–147 (2002).

18. Kim, J.-H. et al. New indices and calibrations derived from the distribution of crenarchaeal isoprenoid tetraether lipids: implications for past sea surface temperature reconstructions. Geochim. Cosmochim. Acta 74, 4639–4654 (2010).

19. Tierney, J. E. & Tingley, M. P. A. Bayesian, spatially-varying calibration model for the TEX86 proxy. Geochim. Cosmochim. Acta 127, 83–106 (2014).

20. Frieling, J. et al. Extreme warmth and heat-stressed plankton in the tropics during the Paleocene-Eocene Thermal Maximum. Sci. Adv. 3, e1600891 (2017).

21. Frieling, J. et al. Tropical Atlantic climate and ecosystem regime shifts during the Paleocene–Eocene Thermal Maximum. Clim. Past 14, 39–55 (2018).

22. Bohaty, S. M., Zachos, J. C., Florindo, F. & Delaney, M. L. Coupled greenhouse warming and deep-sea acidification in the middle Eocene. Paleoceanography 24, PA2207 (2009).

23. Sluijs, A., Pross, J. & Brinkhuis, H. From greenhouse to icehouse; organic-walled dinoflagellate cysts as paleoenvironmental indicators in the Paleogene. Earth Sci. Rev. 68, 281–315 (2005).

24. Liu, Z. et al. Global cooling during the Eocene-Oligocene climate transition. Science 323, 1187–1190 (2009).

25. Caballero, R. & Langen, P. L. The dynamic range of poleward energy transport in an atmospheric general circulation model. Geophys. Res. Lett. 32, L02705 (2005).

26. Goldner, A., Herold, N. & Huber, M. Antarctic glaciation caused ocean circulation changes at the Eocene-Oligocene transition. Nature 511, 574–577 (2014); erratum 519, 378 (2015).

27. Sluijs, A. et al. Warm and wet conditions in the Arctic region during Eocene Thermal Maximum 2. Nat. Geosci. 2, 777–780 (2009).

28. Kiehl, J. T. & Shields, C. A. Sensitivity of the Palaeocene–Eocene Thermal Maximum climate to cloud properties. Philos. Trans. R. Soc. A 371, 20130093 (2013).

29. Pierrehumbert, R. T. Thermostats, radiator fins, and the local runaway greenhouse. J. Atmos. Sci. 52, 1784–1806 (1995).

30. Matthews, K. J. et al. Global plate boundary evolution and kinematics since the late Paleozoic. Global Planet. Change 146, 226–250 (2016).

31. Hopmans, E. C., Schouten, S. & Sinninghe Damsté, J. S. The effect of improved chromatography on GDGT-based palaeoproxies. Org. Geochem. 93, 1–6 (2016).

32. Hopmans, E. C. et al. A novel proxy for terrestrial organic matter in sediments based on branched and isoprenoid tetraether lipids. Earth Planet. Sci. Lett. 224, 107–116 (2004).

33. Weijers, J. W. H., Lim, K. L. H., Aquilina, A., Sinninghe Damsté, J. S. & Pancost, R. D. Biogeochemical controls on glycerol dialkyl glycerol tetraether lipid distributions in sediments characterized by diffusive methane flux. Geochem. Geophys. Geosystems 12, Q10010 (2011).

34. Zhang, Y. G. et al. Methane index: a tetraether archaeal lipid biomarker indicator for detecting the instability of marine gas hydrates. Earth Planet. Sci. Lett. 307, 525–534 (2011).

35. Blaga, C. I., Reichart, G.-J., Heiri, O. & Damsté, J. S. S. Tetraether membrane lipid distributions in water-column particulate matter and sediments: a study of 47 European lakes along a north–south transect. J. Paleolimnol. 41, 523–540 (2009).

36. Taylor, K. W. R., Huber, M., Hollis, C. J., Hernandez-Sanchez, M. T. & Pancost, R. D. Re-evaluating modern and Palaeogene GDGT distributions: implications for SST reconstructions. Global Planet. Change 108, 158–174 (2013).

37. Schouten, S., Hopmans, E. C., Schefuß, E. & Sinninghe Damsté, J. S. Distributional variations in marine crenarchaeotal membrane lipids: a new tool for reconstructing ancient sea water temperatures? Earth Planet. Sci. Lett. 204, 265–274 (2002).

38. Trommer, G. et al. Distribution of Crenarchaeota tetraether membrane lipids in surface sediments from the Red Sea. Org. Geochem. 40, 724–731 (2009).

39. Ho, S. L. & Laepple, T. Flat meridional temperature gradient in the early Eocene in the subsurface rather than surface ocean. Nat. Geosci. 9, 606–610 (2016).

40. Tierney, J. E., Sinninghe Damsté, J. S., Pancost, R. D., Sluijs, A. & Zachos, J. C. Eocene temperature gradients. Nat. Geosci. 10, 538 (2017).

41. Tierney, J. E. & Tingley, M. P. A. TEX86 surface sediment database and extended Bayesian calibration. Sci. Data 2, 150029 (2015).

42. Kim, J.-H., Schouten, S., Hopmans, E. C., Donner, B. & Sinninghe Damsté, J. S. Global sediment core-top calibration of the TEX86 paleothermometer in the ocean. Geochim. Cosmochim. Acta 72, 1154–1173 (2008).

43. De Rosa, M., Gambacorta, A., Nicolaus, B. & Bu’Lock, J. D. Complex lipids of Caldariella acidophila, a thermoacidophile archaebacterium. Phytochemistry 19, 821–825 (1980).

44. Lai, D., Springstead, J. R. & Monbouquette, H. G. Effect of growth temperature on ether lipid biochemistry in Archaeoglobus fulgidus. Extremophiles 12, 271–278 (2008).

45. Boyd, E. S. et al. Temperature and pH controls on glycerol dibiphytanyl glycerol tetraether lipid composition in the hyperthermophilic crenarchaeon Acidilobus sulfurireducens. Extremophiles 15, 59–65 (2011).

46. Gliozzi, A., Paoli, G., De Rosa, M. & Gambacorta, A. Effect of isoprenoid cyclization on the transition temperature of lipids in thermophilic archaebacteria. Biochim. Biophys. Acta 735, 234–242 (1983).

47. Schouten, S. et al. Intact membrane lipids of “Candidatus Nitrosopumilus maritimus,” a cultivated representative of the cosmopolitan mesophilic group I crenarchaeota. Appl. Environ. Microbiol. 74, 2433–2440 (2008).

48. Pitcher, A. et al. Core and intact polar glycerol dibiphytanyl glycerol tetraether lipids of ammonia-oxidizing archaea enriched from marine and estuarine sediments. Appl. Environ. Microbiol. 77, 3468–3477 (2011).

49. Elling, F. J., Könneke, M., Mußmann, M., Greve, A. & Hinrichs, K.-U. Influence of temperature, pH, and salinity on membrane lipid composition and TEX86 of marine planktonic thaumarchaeal isolates. Geochim. Cosmochim. Acta 171, 238–255 (2015).

50. Zhang, Y. G., Pagani, M. & Wang, Z. Ring Index: a new strategy to evaluate the integrity of TEX86 paleothermometry. Paleoceanography 31, 220–232 (2016).

51. Schouten, S., Forster, A., Panoto, F. E. & Sinninghe Damsté, J. S. Towards calibration of the TEX86 palaeothermometer for tropical sea surface temperatures in ancient greenhouse worlds. Org. Geochem. 38, 1537–1546 (2007).

52. Wuchter, C., Schouten, S., Coolen, M. J. L. & Sinninghe Damsté, J. S. Temperature-dependent variation in the distribution of tetraether membrane lipids of marine Crenarchaeota: implications for TEX86 paleothermometry. Paleoceanography 19, PA4028 (2004).

53. Ho, S. L. et al. Appraisal of TEX86 and thermometries in subpolar and polar regions. Geochim. Cosmochim. Acta 131, 213–226 (2014).

54. Awad, W. K. & Oboh-Ikuenobe, F. E. Early Paleogene dinoflagellate cysts from ODP Hole 959D, Côte d’Ivoire-Ghana Transform Margin, West Africa: new species, biostratigraphy and paleoenvironmental implications. J. Afr. Earth Sci. 123, 123–144 (2016).

55. Shafik, S., Watkins, D. K. & Shin, I. C. Calcareous nannofossil paleogene biostratigraphy, Côte d’Ivoire-Ghana Marginal Ridge, Eastern Equatorial Atlantic. Proc. Ocean Drill. Program Sci. Results 159, 413–431 (1998).

56. Agnini, C. et al. Biozonation and biochronology of Paleogene calcareous nannofossils from low and middle latitudes. Newsl. Stratigr. 47, 131–181 (2014).

57. Gradstein, F. M., Ogg, J. G., Schmitz, M. D. & Ogg, G. M. The Geologic Time Scale 2012 (Elsevier, Amsterdam, 2012).

58. Ravizza, G. & Paquay, F. Os isotope chemostratigraphy applied to organic-rich marine sediments from the Eocene-Oligocene transition on the West African margin (ODP Site 959). Paleoceanography 23, PA2204 (2008).

59. Dalai, T. K., Ravizza, G. E. & Peucker-Ehrenbrink, B. The late Eocene 187Os/188Os excursion: chemostratigraphy, cosmic dust flux and the Early Oligocene glaciation. Earth Planet. Sci. Lett. 241, 477–492 (2006).

60. van der Ploeg, R. et al. Middle Eocene greenhouse warming facilitated by diminished weathering feedback. Nat. Commun. (in the press).

61. Bijl, P. K. et al. Transient middle Eocene atmospheric CO 2 and temperature variations. Science 330, 819–821 (2010).

62. Sluijs, A. et al. Southern ocean warming, sea level and hydrological change during the Paleocene-Eocene thermal maximum. Clim. Past 7, 47–61 (2011).

63. Bijl, P. K., Sluijs, A. & Brinkhuis, H. A magneto- and chemostratigraphically calibrated dinoflagellate cyst zonation of the early Palaeogene South Pacific Ocean. Earth Sci. Rev. 124, 1–31 (2013); erratum 134, 160–163 (2014).

64. Fuller, M. & Touchard, Y. in The Cenozoic Southern Ocean: Tectonics, Sedimentation, and Climate Change Between Australia and Antarctica (eds Exon, N. F. et al.) 63–78 (American Geophysical Union, Washington DC, 2004).

65. Dallanave, E. et al. Constraining early to middle Eocene climate evolution of the southwest Pacific and Southern Ocean. Earth Planet. Sci. Lett. 433, 380–392 (2016).

66. Aze, T. et al. Extreme warming of tropical waters during the Paleocene–Eocene Thermal Maximum. Geology 42, 739–742 (2014).

67. Pearson, P. N. et al. Extinction and environmental change across the Eocene-Oligocene boundary in Tanzania. Geology 36, 179–182 (2008).

68. Tripati, A. K. et al. Tropical sea-surface temperature reconstruction for the early Paleogene using Mg/Ca ratios of planktonic foraminifera. Paleoceanography 18, 1101 (2003).

69. Lear, C. H., Bailey, T. R., Pearson, P. N., Coxall, H. K. & Rosenthal, Y. Cooling and ice growth across the Eocene-Oligocene transition. Geology 36, 251–254 (2008).

70. Zhang, Y. G., Pagani, M., Liu, Z., Bohaty, S. M. & DeConto, R. A. 40-million-year history of atmospheric CO 2 . Philos. Trans. R. Soc. A 371, 20130096 (2013).

71. Boscolo Galazzo, F. et al. The middle Eocene climatic optimum (MECO): a multiproxy record of paleoceanographic changes in the southeast Atlantic (ODP Site 1263, Walvis Ridge). Paleoceanography 29, 1143–1161 (2014).

72. Anand, P., Elderfield, H. & Conte, M. H. Calibration of Mg/Ca thermometry in planktonic foraminifera from a sediment trap time series. Paleoceanography 18, 1050 (2003).

73. Hasiuk, F. J. & Lohmann, K. C. Application of calcite Mg partitioning functions to the reconstruction of paleocean Mg/Ca. Geochim. Cosmochim. Acta 74, 6751–6763 (2010).

74. Evans, D. & Müller, W. Deep time foraminifera Mg/Ca paleothermometry: nonlinear correction for secular change in seawater Mg/Ca. Paleoceanography 27, PA4205 (2012).

75. Erez, J. & Luz, B. Experimental paleotemperature equation for planktonic foraminifera. Geochim. Cosmochim. Acta 47, 1025–1031 (1983).

76. Shackleton, N. J. & Kennett, J. P. Paleotemperature history of the Cenozoic and the initiation of Antarctic glaciation: oxygen and carbon isotope analyses in DSDP Sites 277, 279 and 281. Initial Rep. Deep Sea Drill. Proj. 29, 743–755 (1975).

77. Zachos, J. C., Stott, L. D. & Lohmann, K. C. Evolution of Early Cenozoic marine temperatures. Paleoceanography 9, 353–387 (1994).

78. Kennett, J. P. & Stott, L. D. Abrupt deep-sea warming, palaeoceanographic changes and benthic extinctions at the end of the Palaeocene. Nature 353, 225–229 (1991).

79. Thomas, D. J., Zachos, J. C., Bralower, T. J., Thomas, E. & Bohaty, S. Warming the fuel for the fire: evidence for the thermal dissociation of methane hydrate during the Paleocene–Eocene thermal maximum. Geology 30, 1067–1070 (2002).

80. Coxall, H. K. & Wilson, P. A. Early Oligocene glaciation and productivity in the eastern equatorial Pacific: insights into global carbon cycling. Paleoceanography 26, PA2221 (2011).

81. Westerhold, T., Röhl, U., Donner, B., McCarren, H. K. & Zachos, J. C. A complete high-resolution Paleocene benthic stable isotope record for the central Pacific (ODP Site 1209). Paleoceanography 26, PA2216 (2011).

82. Sexton, P. F. et al. Eocene global warming events driven by ventilation of oceanic dissolved organic carbon. Nature 471, 349–352 (2011).

83. Littler, K., Röhl, U., Westerhold, T. & Zachos, J. C. A high-resolution benthic stable-isotope record for the South Atlantic: implications for orbital-scale changes in Late Paleocene–Early Eocene climate and carbon cycling. Earth Planet. Sci. Lett. 401, 18–30 (2014).

84. Lauretano, V., Hilgen, F. J., Zachos, J. C. & Lourens, L. J. Astronomically tuned age model for the early Eocene carbon isotope events: a new high-resolution δ13C benthic record of ODP Site 1263 between ~49 and ~54 Ma. Newsl. Stratigr. 49, 383–400 (2016).

85. Shackleton, N. J. & Hall, M. A. The late Miocene stable isotope record, Site 926. Proc. Ocean Drill. Program, Sci. Results 154, 367–373 (1997).

86. Pearson, P. N., Foster, G. L. & Wade, B. S. Atmospheric carbon dioxide through the Eocene–Oligocene climate transition. Nature 461, 1110–1113 (2009).

87. Foster, G. L., Royer, D. L. & Lunt, D. J. Future climate forcing potentially without precedent in the last 420 million years. Nat. Commun. 8, 14845 (2017).

88. Pagani, M., Zachos, J. C., Freeman, K. H., Tipple, B. & Bohaty, S. Marked decline in atmospheric carbon dioxide concentrations during the Paleogene. Science 309, 600–603 (2005).

89. Miller, K. G., Wright, J. D. & Browning, J. V. Visions of ice sheets in a greenhouse world. Mar. Geol. 217, 215–231 (2005).

90. Barker, P. F., Diekmann, B. & Escutia, C. Onset of Cenozoic Antarctic glaciation. Deep Sea Res. Part II Top. Stud. Oceanogr. 54, 2293–2307 (2007).

91. Gasson, E. et al. Exploring uncertainties in the relationship between temperature, ice volume, and sea level over the past 50 million years. Rev. Geophys. 50, RG1005 (2012).

92. Gulick, S. P. S. et al. Initiation and long-term instability of the East Antarctic Ice Sheet. Nature 552, 225–229 (2017).

93. Pross, J. et al. Persistent near-tropical warmth on the Antarctic continent during the early Eocene epoch. Nature 488, 73–77 (2012).

94. DeConto, R. M. et al. Thresholds for Cenozoic bipolar glaciation. Nature 455, 652–656 (2008).

95. Gasson, E. et al. Uncertainties in the modelled CO 2 threshold for Antarctic glaciation. Clim. Past 10, 451–466 (2014).

96. De Boer, B., van de Wal, R. S. W., Bintanja, R., Lourens, L. J. & Tuenter, E. Cenozoic global ice-volume and temperature simulations with 1-D ice-sheet models forced by benthic δ18O records. Ann. Glaciol. 51, 23–33 (2010).

97. Shields, C. A. et al. The low-resolution CCSM4. J. Clim. 25, 3993–4014 (2012).

98. Lunt, D. J. et al. Earth system sensitivity inferred from Pliocene modelling and data. Nat. Geosci. 3, 60–64 (2010).

99. Byrne, B. & Goldblatt, C. Radiative forcing at high concentrations of well-mixed greenhouse gases. Geophys. Res. Lett. 41, 152–160 (2014).