The 18O/16O ratios of biogenic carbonate and apatite are an essential proxy for paleotemperature and seawater δ18O. For decades, however, Earth scientists have debated the climate implications of the Phanerozoic 18O/16O record (reported as δ18O), which shows increasing values with decreasing age (e.g. Refs.1,2,3,4). The increase in biomineral δ18O toward the present has been interpreted three ways: (1) cooling of the Earth’s oceans through time (e.g. Ref.5), (2) evolving crustal cycling manifested in an increase in seawater δ18O (δ18Osw; e.g. Refs.2,3), and (3) progressive sample diagenesis with age (e.g. Ref.6). Correct interpretation of this record is fundamental to understanding climate drivers, the limits of Earth’s climate, and importantly, the evolution and thermal limits of metazoan life on geologic timescales.

To characterize and evaluate the Phanerozoic trend in biomineral δ18O and sea surface temperature (SST), we present a compilation of low-latitude (30° S–30° N) δ18O paleotemperatures for Phanerozoic carbonate and phosphate fossils and microfossils that, in contrast to earlier published records, corrects for the influence of ice volume and salinity (via paleolatitude relationships) on the δ18Osw of surface waters. Furthermore, for the first time we consider the impact of fractionation differences in belemnites7,8 to develop a 500-million-year paleotemperature curve that resolves the problem of anomalously cold paleotemperatures previously obtained for intervals in the Jurassic and Cretaceous. The compiled data reveal similar trends for carbonate and phosphate δ18O, providing evidence for signal preservation, and argue for extreme warmth in the early Paleozoic (30 to > 40 °C), comparable to that experienced at the end-Permian and earliest Triassic9,10.


Phanerozoic oxygen isotope records

The carbonate δ18O record combines data for well-preserved planktonic foraminifera, mollusks, and brachiopods (Fig. 1B). The data for well-preserved carbonates (N = 11,893 of 22,332 total) and phosphates (N = 4,427 of 4615 total) are available in Appendices 1 and 2 and the StabisoDB database ( Counts of δ18O analyses by stage, fossil group, and climate zone are in Appendix 3. The Locfit regressions (Locfit package in R version 3.6.2; smoothing factor α = 0.0511) combine data for the tropical (10° S–10° N) and tropical-subtropical (10–30° N and S latitude) climate zones. Distinctive features of the Phanerozoic record for carbonates include extremely low brachiopod δ18O values (~ −7.5‰ VPDB) for the Middle Ordovician, a latest Ordovician (Hirnantian) maximum (−3.6‰), an Early Devonian minimum (−5.9‰), a Middle Devonian maximum (−2.9‰), and a Late Devonian (Frasnian–Famennian) minimum (−5.2‰). Average brachiopod values increase to a Mississippian maximum of −1.1‰ and fluctuate between −3.3 and −1.2‰ in the Pennsylvanian and Early Permian before decreasing into the Triassic (< −3‰), a period for which carbonate δ18O data are scarce. For the Jurassic and Cretaceous, periods for which belemnite data dominate, the δ18O record features high values in the Late Jurassic (−1.5‰, Oxfordian-Kimmeridgian) and Early Cretaceous (−2.2‰, Aptian), when the foraminiferal record begins. Values then decrease to an early Late Cretaceous minimum (−5.6‰, Turonian), followed by an irregular increase in the Neogene to modern values (−1.9 ± 0.3‰).

Figure 1
figure 1

Oxygen isotope compositions of phosphate (A) and carbonate fossils and microfossils (B) from tropical-subtropical (0–30°) and temperate (30–50°) latitudes. Carbonate δ18O values less than −8‰ (N = 139) are not shown. These are almost exclusively Paleozoic brachiopod shells that fail quality control (QC) standards (i.e., not “select”). Locfit regression lines (α = 0.05) for tropical and subtropical samples are shown with ± 95% confidence limits (CL). ForamP = planktonic foraminifera, Biv-gast = bivalves and gastropods, Belem = belemnites, Brach = brachiopods, and select = data that have passed QC standards. Belemnite values were adjusted by −1.5‰ to correct for 18O enrichment. Letters in the bar between figures refers to geologic periods Cambrian, Ordovician, Silurian, Devonian, Mississippian, Pennsylvanian, Permian, Triassic, Jurassic, Cretaceous, Paleogene, and Neogene. Some symbols in key are enlarged for clarity.

Key features in the conodont δ18O record (Fig. 1A) mimic those of the carbonate record. Conodont δ18O values increase from very low values in the Early Ordovician (< 17‰ VSMOW) to higher values (19.0‰) in the Late Ordovician (Sandbian), followed by a minimum (17.5‰) in the earliest Silurian (Llandovery), a Wenlock maximum (18.5‰), and an Early Devonian minimum (17.1‰; Lochkovian). Values increase during the Early Devonian to a Middle Devonian maximum (~ 19.3‰) followed by a minimum (17.2‰) at the Frasnian-Famennian transition. After a Late Devonian high (18.3‰), values increase substantially during the Mississippian. Oxygen isotope compositions of Pennsylvanian conodonts from epicontinental (e.g., North America) and slope settings (South China) show considerable offset (~ 19.5‰ versus ~ 23‰ respectively) potentially due to lower salinities in shallow-water North American settings or deeper habitat depths of South China conodonts. The δ18O values decrease sharply from ~ 20.4 to ~ 17.7‰ across the Permian–Triassic boundary with low δ18O values persisting in the Early Triassic. In contrast to the Cambrian to Triassic conodont δ18O record, the Cenozoic fish δ18O record is of too low resolution to allow detailed interpretation. Direct comparison of stage averages (Fig. 2A) shows a strong correlation between carbonate and phosphate δ18O values (R2 = 0.667, p < 0.0001). The slope of 0.85 is nearly identical to the slope (0.82) of “equilibrium” carbonate δ18O (‰ VPDB) versus phosphate δ18O (‰ VSMOW) over the temperature range 10 to 45 °C for the paleotemperature equations used12,13, supporting the integrity of these records.

Figure 2
figure 2

Comparison of low-latitude (30° S to 30° N) δ18O values (A) and δ18O paleotemperatures (B) of phosphate and carbonate fossils and microfossils of Paleozoic and Triassic ages averaged by stage. The regression line was generated using a simple linear regression model because of the lower uncertainty in phosphate versus carbonate values (see Supplementary Information). Note that the slope for δ18OPO4 versus δ18OCaCO3 (0.85) is nearly identical to the slope of the phosphate-carbonate paleotemperature relations (0.82), and the slope for TPO4 versus TCaCO3 is 1.05. Both correlations are significant (p < 0.0001).

Phanerozoic low-latitude temperatures

Paleozoic paleotemperatures based on carbonates and phosphates (Figs. 3, 4) show similar trends such as very high late Cambrian and Early to Middle Ordovician temperatures (> 40 °C), high early Late Ordovician through Devonian temperatures (32–40 °C), a dramatic decline of as much as 15 °C at the Devonian to Mississippian transition, and cooler temperatures in the Carboniferous and Permian (19–35 °C; Fig. 4). The records show disagreement at intervals in which brachiopods were derived from paleo-arid regions, where high δ18Osw values, underestimated by our model, result in underestimated isotopic temperatures. Examples include Tournaisian-Viséan data from Indiana (USA) and Kungurian-Roadian data from the Ural Mountains (Russia)14,15. Paleotemperature differences also occur because of differences in the distribution of sample ages. Whereas brachiopods provide a robust record of the Hirnantian Cool Event, conodont data are essentially absent. In contrast, the hothouse at the end-Permian and Early Triassic is well represented in conodont data but not in brachiopod data9,10.

Figure 3
figure 3

δ18O paleotemperatures for phosphate and carbonate fossils and microfossils from low paleolatitudes (30° S to 30° N). Comparison of δ18O paleotemperature trends (Locfit regressions) for phosphate and carbonate fossils calculated using different corrections for seawater δ18O: (1) constant (ice-free, δ18Osw = −1.08‰ VSMOW), (2) ice volume corrected (IceV), and (3) ice volume and latitude corrected (IceV, lat). For greenhouse climates, the ice-free data (red dotted line) plot atop the ice volume corrected data (blue dotted lines). Aragonite fossils are corrected for aragonite-calcite fractionation (arag; −0.6‰) and belemnite data are corrected for 18O enrichment in belemnites (−1.5% where noted (bel). Locfit regression for data uncorrected for 18O enrichment in belemnites shown as pink line. Gaps in curves are intervals with little or no data. TEXH86 temperatures shown for comparison16,17. See Fig. 1 for key to period/subperiod bar at top.

Figure 4
figure 4

Comparison of oxygen isotope temperatures (E) with climate and tectonic proxy data. (A) Occurrence and latitudinal extent of glaciogenic sediments20; (B) estimated δ18Osw (this study); (C) atmospheric pCO221; (D) crustal accretion rate22 compared with combined phosphate and carbonate δ18O paleotemperature (low-latitude, Locfit regression and 5-myr averages); (E) Low-latitude phosphate and carbonate δ18O paleotemperatures calculated by correcting seawater δ18O for ice volume (iceV) and latitude (lat). Locfit regression (α = 0.05) with 95% Cl calculated for combined carbonate and phosphate δ18O paleotemperatures. Paleozoic clumped isotope paleotemperatures (clumped T) from Henkes et al.23 and Barney and Grossman24. Also shown are TEX86 paleotemperatures using the TEX86H-SST calibration16,17. Geologic time scale abbreviations same as in Fig. 1. Warm events: La Landovery, Lo Lochkovian, FF Frasnian–Famennian, PT end-Permian and early Triassic, To Toarcian, CT Cenomanian–Turonian, PETM Paleocene-Eocene Thermal Maximum, EECO Early Eocene Climatic Optimum.

Simple linear regression of carbonate and phosphate δ18O paleotemperatures averaged for Paleozoic and Triassic stages (Fig. 2B, Supplementary Tables 1 and S1) yields an equation:

$${\text{T}}_{{{\text{PO4}}}} = { 1}.0{5 }\left( { \pm 0.{14}} \right){\text{ T}}_{{{\text{CaCO3}}}} {-}{ 4}.{8 }\left( { \pm {4}.{3};{\text{ R}}^{{2}} = \, 0.{6615},p < 0.000{1}} \right).$$

The strong correlation (R2 = 0.6615) and slope near 1 are evidence that these materials retained their original isotopic signature. The ~ 4 °C average offset from the 1:1 line suggests higher paleotemperatures for the phosphate samples. This difference could reflect differences in aridity and the spatial and temporal distributions of specimens as mentioned above (e.g. Ref.18). Another contributing factor may be depth habitat. At some locations, nektonic conodonts may have lived shallower in the water column than benthic brachiopods. Lastly, differences in paleotemperature may indicate uncertainties in the paleotemperature equations. Applying the equation of Friedman and O’Neil19 for calcite decreases the temperature difference between Paleozoic stages from 3.6 to 2.0 °C. However, we use the Kim and O’Neil12 equation because it is more widely applied by the paleoclimate community. Combining the results for conodonts and brachiopods provides a continuous and comprehensive paleotemperature record for low latitudes (30° S–30° N; Fig. 4). Late Cambrian (Furongian) and Early to Middle Ordovician low-latitudes experienced the highest SSTs, 47 °C and between 35 and 47 °C, respectively. Late Ordovician to Devonian low-latitude SSTs were considerably cooler (32–40 °C). Cooler still were Carboniferous to modern low-latitude SSTs, which varied between 19 and 35 °C with relatively cool “icehouse” temperatures observed in the Carboniferous to Middle Permian (19–24 °C), Middle Jurassic to Early Cretaceous (18–27 °C), and late Eocene to modern times (23–25 °C). The late Permian to Middle Jurassic and Late Cretaceous to Eocene are recognized as warm climatic intervals (25–30 °C) with the Permian–Triassic transition, Early Triassic, and Cenomanian–Turonian standing out as hothouse intervals. The Paleocene-Eocene Thermal Maximum (PETM), another very warm period, is not well represented in our oxygen isotope dataset due to insufficient data for shallow-dwelling organisms.


The decrease in marine fossil δ18O with age, the trend expected with oxygen isotope exchange with meteoric water, has led some to question the preservation and efficacy of the original marine δ18O signal, especially with regard to the Paleozoic record. We address these concerns by restricting Paleozoic samples to the best-preserved material, brachiopod shell calcite and conodont apatite. Phosphate oxygen is more tightly bound in the crystal lattice than is calcite oxygen; in fact, apatite phosphate survives dissolution and reprecipitation as trisilverphosphate during sample preparation without altering its oxygen isotope composition. That both minerals yield similar δ18O trends through time (Figs. 2, 3) is evidence for preservation of primary signals. Additional evidence is comparable δ18O values for Pennsylvanian calcite versus aragonite25 and for Devonian conodont apatite experiencing minimal versus extensive heating26.

As with previous studies, our δ18O results show an increase from very low late Cambrian through Middle Ordovician values toward higher δ18O values in the modern (Fig. 5). Not surprisingly, our paleotemperatures show many of the same relative changes as in previous studies, an expectation considering the overlap in data sources; however, substantial differences occur in absolute temperature with higher Early Paleozoic temperatures in our study and much lower Phanerozoic temperatures in other studies. These offsets reflect differences in (1) sample material (carbonates versus combined carbonates and phosphates), (2) screening approaches, (3) methods of estimating seawater δ18O, and (4) paleotemperature equations1,4,27,28,29,30.

Figure 5
figure 5

Comparison of low-latitude Phanerozoic temperature curves from this study (30° S to 30° N), Song et al. (2019; 40° S to 40° N), Vérard and Veizer (2020; 35° S to 35° N), and Scotese et al.30 (“tropical”). Differences in curves reflect in part acceptance (this study; Song et al.30) or rejection22,30 of the buffered hydrosphere δ18O model31,32 which constrains global seawater δ18O between roughly −1 and 1‰ VSMOW. Geologic time scale abbreviations same as in Fig. 1. Dashed lines represent ± 95% confidence interval for this study’s results.

We start the discussion with Veizer and Prokoph’s4 seminal work because several studies adopt their data and interpretation (e.g., Refs.22,33). With regard to sample material, the Veizer and Prokoph4 δ18O curve is based on data only from brachiopods and planktonic foraminifera and excludes data from phosphates (e.g., conodonts), belemnites, bivalves, and gastropods. Importantly, planktonic foraminifera can be readily recrystallized on the cold sea floor; specimens not characterized as glassy or excellently preserved can yield δ18O values 1‰ higher than glassy foraminifera34. This in part accounts for very low paleotemperatures for the Cenozoic and Cretaceous. For example, Vérard and Veizer obtained average low-latitude paleo-SSTs of 10 °C for the Early Cretaceous (115–135 Ma), a time of greenhouse climate.

Another reason for unusually low paleotemperatures in Veizer and Prokoph4 and Vérard and Veizer22 is the assumption regarding seawater δ18O. Interpreting the δ18O trend as reflecting changes in seawater δ18O, they (1) fit a 2nd order regression to the trend, (2) adjust the equation to intersect δ18O = 0‰ VPDB at 0 Ma (i.e., set Y-intercept at 0‰), and (3) use the regression to “correct” carbonate δ18O values for changes in δ18Osw. The effect of this treatment is to set modern low-latitude SST for the dataset at ~ 18.0 °C, more than 7.4 °C lower that the modern average (25.4 °C; for that study’s paleolatitude window (35° S to 35° N) and 6.5 °C lower than average tropical proxy temperatures for the Late Pleistocene (~ 24.5 °C35). By comparison, for our study interval (30° S to 30° N) the temperature at 0 Ma is 23.5 °C, much closer to the modern and Late Pleistocene values. Veizer and Prokoph’s4 age correction of δ18Osw compensates for the low mineral δ18O values for the Ordovician through Devonian, shifting biomineral δ18O values + 5 to + 2‰ respectively, equivalent to 22 to 9 °C. A third consideration is the paleotemperature equation. Veizer and Prokoph4 and Mills et al.33 use a linear equation with a δ18O-temperature dependence of −4 °C per ‰, significantly lower than that of other studies (−4.3 to −4.8 °C per ‰; Grossman28), resulting in paleotemperature underestimation at temperatures above ~ 25 °C. These factors contribute to these studies’ findings of equable low-latitude paleotemperatures for Early Paleozoic oceans, and to the excessively cold temperatures of 10–12 °C for Pennsylvanian and early Permian oceans (325–295 Ma).

Another important Phanerozoic temperature curve is that of Song et al.29. This curve yields lower temperatures in the Paleozoic, early Mesozoic, and Cenozoic compared with ours (Fig. 5). These authors make use of phosphate δ18O data for the Paleozoic and carbonate δ18O data for the Mesozoic and Cenozoic, noting the better δ18O preservation of apatite compared with the calcite in Paleozoic fossils. These authors reject the hypothesis of increasing seawater δ18O in the Phanerozoic4 and instead assume a constant seawater δ18O of −1‰ VSMOW, representing ice-free conditions. The lower temperatures in Song et al.29 reflect (1) use of an ice-free seawater δ18O value during glacial conditions (an up to −6 °C effect; e.g., 10 °C temperatures for mid-Carboniferous), (2) lack of paleolatitude corrections for seawater δ18O (an effect of up to −5 °C for the subtropics), and (3) use of the phosphate-water paleothermometers of Lécuyer et al. (2013; an effect of up to −3.5 °C). We use the Pucéat et al.13 equation, which was produced in the same lab where the majority of Paleozoic phosphate samples were analyzed. Song et al.29 also includes samples for higher latitudes (up to ± 40°), which could lower paleotemperatures. However, in StabisoDB, phosphate samples from 30 to 40° paleolatitude only represent 7.5% of the samples between 0 and 40° paleolatitude, so this effect should be minor. Scotese et al.’s30 Phanerozoic temperature curve shows less extreme temperatures in the Early Paleozoic and late Cenozoic (Fig. 5). The curve uses a combination of isotopic data29 and paleotemperatures based on paleo-Köppen climate belts calibrated with modern Köppen belt temperature relations. While novel, this hybrid paleotemperature curve implicitly assumes modern temperature relations and thus may inject a uniformitarian bias into quantification of Earth’s temperature history. As discussed earlier, our Phanerozoic curve is the first to correct δ18Osw for paleolatitude and for 18O-enrichment in belemnites, which accounts for warmer proxy temperatures for the Jurassic compared with other isotopic studies.

Accepting that the Phanerozoic δ18O trend is not an artifact of diagenesis, the debate as to whether the trend reflects δ18Osw or temperature change distills to two endmember assumptions: (1) no long-term trend in seawater δ18O (e.g. Ref.36) and (2) no long-term trend in low-latitude SST3,4,27. In theory, the oxygen isotope history of seawater can be calculated from the rates and temperatures of oxygen exchange between the mantle, crustal reservoirs, and the ocean. Mass balance models have been used to argue for near-constant (e.g. Refs.36,37,38) or increasing (e.g. Refs.39,40) δ18Osw, depending on the proportion of crustal oxygen exchange at high-temperature (which increases δ18Osw) versus low-temperature (which decreases δ18Osw). Models that predict changes in δ18Osw through Earth history show trends that asymptotically approach modern values, consistent with minimal change in carbonate δ18O over the past ~ 350 myr (e.g. Ref.40). One limitation of crustal exchange models is the large uncertainty in hydrothermal fluid fluxes. These fluxes are estimated based on the difference between modeled and measured (conductive) ocean heat flux41. However, uncertainty in the temperature of off-ridge hydrothermal fluids can lead to greater than ± 50% uncertainty in hydrothermal flux and large uncertainty in the mineral–water 18O fractionation. A recent hypothesis is that Snowball-Earth sequestration of glacial ice might have resulted in 18O-enriched residual seawater that would re-equilibrate with ocean crust, lowering δ18Osw toward 0‰, followed by melting of 18O-depleted Snowball ice and lowering of global δ18Osw42. However, for this process to impact the δ18O of Cambrian and Ordovician oceans, large ice volumes with extremely low δ18O would be required in a slushball Earth42, an improbable scenario.

In summary, the different models for the temporal δ18Osw trend each lead to extreme climate scenarios. Assumption of a crustally-buffered hydrosphere near −1‰ (VSMOW) leads to high paleotemperatures in the Early to Middle Ordovician (> 45 °C). In contrast, the Phanerozoic δ18Osw trend of Veizer and Prokoph4 generates low-latitude δ18O temperatures of ~ 10 °C for the Late Ordovician, Pennsylvanian, and Early Cretaceous (Fig. 3 of Ref.22), temperatures incompatible with modern photozoan carbonate deposition mainly observed within the > 20 °C winter water temperature isotherm43.

Studies of the δ18O of non-carbonate phases, clumped isotopes in carbonates, and fluid inclusions support arguments for relatively high seawater δ18O and temperatures in the early Paleozoic. Hydrothermally-altered ophiolites31 and mudrocks32 yield constant δ18O values through time, suggesting constant seawater δ18O throughout the Phanerozoic. Moreover, magnetite veins in Moroccan ophiolites dated at 760 Ma indicate δ18Osw values of −1.3 ± 1.0‰44. Further, δ18O values of marine iron oxides from ooidal ironstones and other deposits spanning the last 2 billion years suggest lower δ18Osw in the Proterozoic but “largely stable δ18Osw in the Phanerozoic”45. Clumped isotopes indicate high temperatures for the Ordovician and Silurian23. For example, temperatures for Katian (~ 450 Ma) brachiopods and rugose corals from North America cluster around ~ 37 °C, while minimum Hirnantian (~ 444 Ma) values range from 29 to 35 °C46,47. These temperatures and associated δ18O values suggest δ18Osw values of −0.5 to 3.5‰. Reexamination of Katian brachiopods using microanalytical techniques yields clumped isotope temperatures with a mode of ~ 33 °C (mean = 35 ± 2.8 °C) for a subtropical upwelling setting24. These temperatures and carbonate δ18O values equate to a mean seawater δ18O of −0.3 ± 0.6‰ VSMOW. Tropical Silurian brachiopods yield similar clumped isotope temperatures and seawater δ18O values (33 ± 7 °C and −0.3 ± 1.3‰ respectively) for “the most pristine materials”48. Lastly, homogenization temperatures of fluid inclusions in Ediacaran halite (circa 546 Ma) also indicate high temperatures (39 °C49).

Another consideration in paleotemperature determination is paleoceanographic environment. The samples on which Paleozoic through Jurassic temperatures are based come from continental margins and epeiric seas, environments subjected to local runoff and restricted circulation. Local runoff can result in δ18Osw values lower than those estimated here, but typically such cases can be identified by the presence of euryhaline fauna50. Restricted circulation, on the other hand, can lead to temperatures that average 2 °C higher than open-ocean temperatures51; therefore, the Paleozoic and some Mesozoic temperatures reported in this study may be 2 °C higher than those of the contemporaneous open ocean.

Extreme warmth comparable to the Late Ordovician to Devonian has been recorded in younger times in Earth history. For example, δ18O measurements of end-Permian and Early Triassic conodonts yield temperatures of ≥ 36 °C9,10. TEX86 and δ18O data for planktonic foraminifera suggest late Cenomanian-to-Turonian equatorial SSTs of ≥ 35 °C16. Furthermore, multiple methods (TEX86H-SST calibration, Mg/Ca, Δ4717) indicate tropical SSTs throughout the Eocene of 30 to 36 °C for the Paleocene-Eocene Thermal Maximum (PETM), and ~ 35 to ~ 37 °C for the Early Eocene Climatic Optimum (EECO52; Fig. 4). Even higher TEX86 SSTs of 40 to 45 °C are reconstructed using the TEX86 BAYSPAR calibration16,53. Thus, low-latitude SSTs of 35 °C and warmer are not unique to the Early Paleozoic but occurred also during Mesozoic and Cenozoic warm intervals. Furthermore, these temperatures are close to tropical SST projected for the year 2100 if modern tropical seas (25–30 °C) warm by more than 4 °C54,55, as predicted by the RCP 8.5 scenario.

Comparing low-latitude temperature to seafloor accretion rate22 allows us to examine the link between plate tectonics and climate. Seafloor accretion rate correlates significantly with low latitude temperature (R2 = 0.47, p < 0.0001; Supplementary Fig. S1, Supplementary Table S2), with warmer temperatures associated with faster spreading rates. This linkage is attributed to high rates of volcanic CO2 degassing with higher rates of seafloor spreading and subduction30.

Isotopic temperatures of > 40 °C for the late Cambrian and Early Ordovician, which extend beyond the temperature tolerances of most modern multi-cellular Eukarya (e.g. Ref.56), present a conundrum. Is our understanding of the physiology and behavior of early animals incomplete? If Early Ordovician fauna were limited only to taxa able to tolerate unusually high temperatures, this would further strengthen Ordovician cooling as an explanation for the dramatic increase in Ordovician diversity, the Great Ordovician Diversification Event (GOBE)57. Furthermore, such cooling would raise the solubility of oxygen in seawater29 and, along with a posited increase in atmospheric oxygen levels, permit greater metabolic activity and predation58, leading to paleoecological reorganization59.

Our results can be used to examine the sensitivity of low-latitude temperatures to changes in pCO2 (low-latitude Earth system sensitivity or ESS) Overall, paleotemperature exhibits a significant correlation (R2 = 0.234, p = 0.0014) with pCO2 doubling based on the proxy record of Foster et al.21; Supplementary Table S3; based on 10-myr Locfit averages). This relationship indicates a role of pCO2 in controlling low-latitude Phanerozoic SST. For Phanerozoic climate, changes in solar radiation must be considered in addition to the radiative forcing controlled by pCO2. To examine the relationship between changes in low-latitude temperature (ΔTLL) and changes in radiative forcing of pCO2 and solar radiation (ΔS[CO2,SOL]), we convert pCO2 doubling to radiative forcing by multiplying by 3.7 W m−2, and correct for increasing solar radiation with time using the equation: ΔFsol = −238 W m−2 × 0.0000665 age (myr)60. ΔS[CO2,SOL] estimates yield significant correlations (p < 0.0001) with ΔTLL for the Paleozoic but not for the Mesozoic and Cenozoic (Fig. 6). Royer61 also found a poor relationship between surface temperature and combined CO2 and solar forcing for the Cenozoic and Mesozoic, noting that temperature data for the Mesozoic are sparse. Though not seen in our results based on limited planktonic foraminifera and macrofossil data, a strong relationship between Cenozoic temperatures and pCO2 is seen in studies based on benthic foraminiferal δ18O62.

Figure 6
figure 6

Change in pCO2 and solar radiative forcing (ΔS[CO2,SOL]) versus mean low-latitude (0–30°) paleotemperature (ΔTLL) for 10-myr intervals in the Cenozoic (orange), Mesozoic (green), and Paleozoic (blue-green). Filled symbols identify statistically significant relations (p < 0.05). Equations show Deming Model II regression (heavy dashed lines) and simple linear regression with associated uncertainty (gray dashed line with dotted uncertainty bands). Only Paleozoic data show a significant relationship.

Deming Model II (DMII) regression for the Paleozoic data generates the following relation:

$$\Delta {\text{T}}_{{{\text{LL}}}} \left( {^\circ {\text{C}}} \right) \, = { 2}.{91 }\left( { \pm 0.{76}} \right) \, \cdot \, \Delta {\text{S}}_{{[{\text{CO2}},{\text{ SOL}}]}} + { 7}.{5 }\left( { \pm {1}.{5}} \right) \, \left( {{\text{R}}^{{2}} = \, 0.{538}} \right).$$

DMII regression was chosen because of comparable uncertainty in both X and Y. This equation yields an Earth system sensitivity (ESS) value for Paleozoic low latitudes of 2.9 K W−1 m2 or 10.7 K per CO2 doubling. This value is high compared with the range for 35–150 Ma based on an ensemble of climate model simulations (3.5 and 5.5 K63), especially considering that (1) the 0°–30° latitude band accounts for only half of Earth’s surface and (2) SST change will underestimate change in global surface temperature, especially during icehouse climate61,64. On the other hand, the value is within those calculated for discrete time intervals in the Pliocene61. In comparing radiative forcing and temperature change, other studies of Earth system sensitivity have used simple linear regression (SLR), which considers only uncertainty in Y61,65. SLR of our results yields the following equation for the Paleozoic:

$$\Delta {\text{T}}_{{{\text{LL}}}} \left( {^\circ {\text{C}}} \right) \, = {1}.{7}0 \, \left( { \pm 0.{41}} \right) \, \cdot \, \Delta {\text{S}}_{{[{\text{CO2}},{\text{ SOL}}]}} + { 6}.{4 }\left( { \pm {1}.{2}} \right) \, \left( {{\text{R}}^{{2}} = \, 0.{538}} \right).$$

This equation provides an ESS value of 1.7 W−1 m2 or 6.3 K per CO2 doubling, similar to climate sensitivities determined for glaciated time64. Justification for using simple linear regression instead of Model II regression is discussed in Smith66 and centers on the objectives of the study. Since our objective is to “define some mutual, codependent “law” underlying the interaction between X [ΔpCO2 radiative forcing] and Y [ΔSST]”, and since the slope “will be used to interpret the pattern of change” (Smith66, p. 482), we favor Model II regression. On the other hand, Smith66 notes that “when an equation is used for prediction”, SLR is the “method of choice”. More detailed examination of choice of regression model is beyond the scope of this paper but clearly merits future consideration.

Note that this treatment does not account for changes in paleogeography, sea level, land ice area, vegetation, non-CO2 greenhouse gases, and aerosols, some of which also serve as feedback mechanisms; however, it does provide an estimate of ESS for the highest sustained CO2 levels in the past 420 myr (> 2000 ppm) and the worst-case scenario levels for a couple of centuries into the future55. Lastly, our finding that ESS was high in the Paleozoic compared with the Cenozoic supports studies suggesting higher ESS with higher CO2 levels (e.g. Ref.67).

Materials and methods

Details regarding samples and methods appear in Ref.1. The compilation builds upon previous efforts (e.g. Refs.4,27) and focuses on carbonate and phosphate fossils and microfossils that (1) are widely distributed in the sedimentary record, (2) are precipitated with quantitative δ18O fractionation relative to temperature, and (3) exhibit excellent preservation. Samples include mollusks, brachiopods, planktonic foraminifera, fish teeth, and conodonts.

The late Cambrian through Triassic record is based on brachiopod calcite and conodont phosphate. Thick brachiopods from cratons tend to show the best preservation and least scatter in their δ18O values (e.g. Refs.15,68,69). Targeting best preserved shells with petrographic and cathodoluminescence microscopy, combined with analyses of microsamples (< 100 µg), further reduces variability and allows for multiple analyses from a single shell. While our compilation includes all data, regressions for temporal trends and paleotemperature estimates only consider data from brachiopod shell that (1) is non-luminescent, (2) contains manganese contents < 250 ppm, or (3) thick-shelled and from areas known for excellent preservation (e.g., Moscow Basin; see Ref.1 for additional details). Biogenic apatite is less prone to diagenetic overprinting; however, the unknown habitat of conodonts may represent an uncertainty for interpretation of δ18O values. While brachiopods are benthic organisms, conodonts were active swimmers that could have lived in warm surface waters or deeper and thus colder parts of the water column. The comparison of oxygen isotope values of conodont taxa from sediments of different water depths gave equivocal results (e.g. Refs.70,71).

Belemnite rostra, calcite deposits in the cephalopod’s posterior, are the most common material analyzed from Jurassic and Cretaceous sediments. These fossils typically have δ18O values higher than those of co-occurring bivalves, confounding paleotemperature studies. However, recent clumped isotope studies have revealed that belemnites precipitated in warmer waters than their δ18O values indicate, prompting researchers to conclude that belemnite guards are precipitated in true equilibrium with seawater, and that δ18O paleotemperature relations for other biominerals and laboratory precipitates do not represent true equilibrium7,8. In our dataset, belemnites average 1.7 ± 0.5‰ (N = 19) and 1.1 ± 1.2‰ (N = 13) higher in δ18O compared with brachiopods and bivalves (Appendix 4). To account for this effect, we have applied a −1.5‰ correction to belemnite data as suggested by Vickers et al.8.

Planktonic foraminiferal data provide paleotemperatures for Cretaceous through Cenozoic climate. Because planktonic foraminiferal tests commonly recrystallize with burial on the sea floor34, we only use data for planktonic foraminifera that exhibit exceptional preservation (e.g., “glassy”, “excellent”16,34). The δ18O data for aragonite samples, mostly of Cenozoic age, are normalized to calcite δ18O by subtracting 0.6‰72.

Analytical techniques

Analytical techniques are summarized in Grossman and Joachimski1 and Joachimski et al.70 and presented in detail in the papers from which the data are derived. Briefly, carbonates of 0.05 to several milligrams are acidified with concentrated phosphoric acid and the CO2 evolved is analyzed on an isotope ratio mass spectrometer. Isotopic data are reported in delta (δ) notation and reported versus PDB (Peedee belemnite) or VPDB (Vienna PDB). The latter refers to calibration to PDB using the NBS-19 calcite standard (δ18O =  − 2.20‰ versus PDB73,74 or the new carbonate standard, IAEA-603 (δ18O =  − 2.37‰). The precision for oxygen isotope analyses of CaCO3 is typically ± 0.05 to 0.10‰, which equates to roughly ± 0.25 to ± 0.5 °C at 25 °C12. Oxygen isotope analyses of biogenic apatite are either measured by (1) TC-EA IRMS (thermally coupled elemental analyzer—isotope ratio mass spectrometry) on trisilverphosphate precipitated after dissolving calcium fluorapatite or (2) in situ by secondary ion mass spectrometry (SIMS). Whereas phosphate-bound oxygen is analyzed by TC-EA IRMS, total oxygen including phosphate-, carbonate- and hydroxyl-bound oxygen is measured by SIMS with the δ18O offset between these methodologies not well constrained. We applied a correction of −0.6‰ to all SIMS δ18O data based on the comparison of SIMS and TC-EA IRMS data75.

Paleotemperature and seawater δ18O determinations

We use the Kim and O’Neil12 and Pucéat et al.13 δ18O paleotemperature equations for calcite and phosphate, respectively. The δ18O of seawater (δ18Osw) for million-year intervals is based on estimates of the volume and δ18O of glacial ice (see Supplementary Materials, Supplementary Tables S4S6). Ice volumes through time are binned into simple categories of ice-free, low, moderate, and high based on studies of glacial sediments and sea level (e.g. Refs.76,77,78,79). For the δ18O of ice, we assume the δ18O values for the West Antarctica (−41‰) and Greenland ice sheets (−34‰) for “moderate” and “low” ice volumes respectively (Supplementary Table S4S6). The calculated values for mean δ18Osw range from −1.08‰ for the ice-free state to 0.45‰ for high ice volume (Pleistocene average; Supplementary Table S7). Lastly, δ18Osw was averaged for 1-myr steps using a 2-myr window to smooth the impact of assigned ice volume changes.

Paleolatitudinal correction

Paleolatitudes were reconstructed using the GPlates software80 with the Paleomap81 rotation model. For paleolatitudinal corrections of δ18Osw during icehouse climates, we use the modern latitude-δ18O relationship of Roberts et al.82; Supplementary Fig. S2, Supplementary Table S8) derived from gridded data modeled in LeGrande and Schmidt83. Using data for the Southern Hemisphere, which are less influenced by landmasses than Northern Hemisphere data, yields the relationship for 0–60° latitude:

$$\Delta^{18} {\text{O}}_{{\text{sw,lat,Mod}}} = \, - 6.650 \, \times \, 10^{ - 4} \lambda^{2} + \, 3.363 \times \, 10^{ - 2} \lambda + \, 0.174 \, \left( {{\text{R}}^{{2}} \, = \, 0.951} \right).$$

For hothouse climates, we generate the δ18Osw-latitude relation using the isotope-enabled ocean–atmosphere general circulation model (GCM) results of Ref.82 (Supplementary Table S8) for the early Paleogene. The modeled δ18Osw values for 0–60° latitude in the southern hemisphere (from Fig. 1 of Ref.82) give the equation:

$$\Delta^{18} {\text{O}}_{{{\text{sw}},{\text{lat}},{\text{Pg}}}} = \, - {4}.{944 } \times { 1}0^{{ - {4}}} \lambda^{{2}} + { 2}.{492} \times { 1}0^{{ - {2}}} \lambda + \, 0.{1}0{2 }\left( {{\text{R}}^{{2}} \, = \, 0.{932}} \right).$$

Latitudinal corrections for < 60° latitude (δ18Olat corr) were proportioned based on the estimated δ18Osw,iceV corr using the equation:

$${\Delta }^{18}{O}_\text{lat corr}={\Delta }^{18}{O}_{sw,lat,Mod} \frac{{\updelta }^{18}{O}_{sw,iceV} - -1.08}{(0.45 - -1.08)}+{\Delta }^{18}{O}_{sw,lat,Pg}\left(1-\frac{{\updelta }^{18}{O}_{sw,iceV} - -1.08}{(0.45 - -1.08)}\right)$$

where δ18Osw,iceV is the ice volume correction for global seawater and 0.45‰ is the icehouse endmember (average between glacial and interglacial states).

We bin our data into the following climate zones by paleolatitude: tropical (± 10°), tropical-subtropical (10°–30°), temperate (30°–50°), and subpolar–polar (50°–90°) using the maps from Scotese and Wright81. These bins were selected based on the temperature gradients for the latest Cretaceous through Recent reported in Zhang et al.84. Over the time interval studied, spanning greenhouse and icehouse climates, paleotemperatures within 10° N or S are invariant with paleolatitude. Inflections in latitudinal temperature gradients at 30° and 50° define boundaries for the next two bins. Lastly, stage-averaged paleotemperatures for the ± 10° and 10°–30° bins were found to be statistically similar (ΔT(10°–30° minus 0°–10°) (°C) = −1.0 ± 2.1(2SE) °C) (N = 25) for carbonates and −2.0 ± 2.2 (N = 25) for phosphates) and thus were combined. At latitudes higher than 30°, data become sparse. Further, the increased latitudinal temperature gradient at higher latitudes along with greater influence of 18O-depleted fresh water83 increases the uncertainty in paleotemperature determinations. Lastly, sample ages are based on the GTS2020 timescale85.