The barite record of the past seawater oxygen isotope composition

Domain: earth_science
Published: 2025-05-30
Editorial outcome: minor_revision

Abstract
The oxygen isotope composition of seawater (δ18O seawater) is shaped by high- and low-temperature rock-water interactions, reflecting Earth system’s dynamics and evolution. The history of δ18O seawater remains debated due partly to post-depositional imprints to all current mineral proxies. The oxygen atoms in sulfate minerals are among the most inaccessible to later exchange but often not in isotope equilibrium with ambient water. However, the δ18O sulfate may reach a plateau or approach equilibrium with the δ18O seawater as the corresponding δ34S increases during microbial sulfate reduction. Here we show 289 paired δ18O-δ34S values for sedimentary barite spanning six periods of the Phanerozoic Eon. The δ18O-δ34S trajectories point to variable equilibrium δ18O barite values for different periods. A ~4‰ lower δ18O barite value is evident before the Carboniferous than today if assuming the same formation temperature. Utilizing the barite δ18O-δ34S trajectory approach, we now have a robust proxy to advance the long-debated issue of seawater δ18O history.

Introduction
The oxygen isotope composition of seawater (δ18O seawater) is primarily determined by two competing geological processes: high-temperature rock-water interactions within the oceanic crust, which increase the δ18O seawater value, and low- or surface-temperature interactions on land and oceanic crust, which decrease the value1–3. Active plate tectonics may have maintained the δ18O seawater at its current value of 0‰ because the fluxes of these two processes may have reached steady state over much of Earth’s history based on the investigation of oxygen isotope compositions of ancient oceanic crusts (i.e., ophiolite data)3–8. However, this steady-state may be disrupted by changes in the thickness of the oceanic crust or seawater depth2,9,10. An increase of seawater δ18O value throughout the geological history is supported by δ18O proxies of various marine sedimentary minerals (e.g., carbonate minerals11,12, chert13, phosphate14, and iron oxides15,16) and ophiolites17–19. Unfortunately, most existing mineral proxies suffer from ambiguities in formation or lock-in temperature as well as post-depositional alteration. A potential solution to the temperature issue is to identify a mineral whose oxygen isotope fractionation is insensitive to the surface formation temperature range. While iron oxides are promising candidates15, their fine-grained nature and intergrowth with other silicates in sediments may introduce significant analytical uncertainties in their δ18O measurements. Additionally, the age of sedimentary iron oxides can be in question, as many are secondary minerals formed via the oxidation of Fe(II) carbonates or Fe(II) silicates in later geological ages20,21. Meanwhile, quantifying post-depositional alteration on δ18O remains largely an intractable problem. Recently, a promising approach has been proposed by combining δ18O and clumped isotope composition (Δ47) of carbonate minerals to identify the extent of alteration based on different water/rock ratios during diagenesis12. However, this approach requires the assumption that the carbonate minerals experienced only a single episode of post-depositional fluid interaction, which contradicts the fact that multiple fluid-rock interaction events and fluid sources often occurred during late diagenesis22,23. Sulfate, an oxygen-bearing mineral group, is non-labile and chemically stable in its oxygen isotope composition, with no exchange occurring between sulfate and water under most surface temperature conditions24. Moreover, the original δ18O signal of sulfate can be preserved for over a billion years, as evident from the retention of non-mass-dependent 17O signatures in Proterozoic sulfate25. However, the remarkable stability of the δ18O sulfate comes at a “cost”: it is rarely in equilibrium with the δ18O of ambient water. Here, we proposed a new proxy for the δ18O seawater, namely, the plateau δ18O sulfate value in the δ18O-δ34S trajectory of a set of 34S-variable sulfates, commonly found in sedimentary barite deposits.

During microbial sulfate reduction (MSR), sulfate can effectively exchange its oxygen isotopes with that of ambient water through reversable enzyme-catalyzed steps26–32 (Fig. 1). These steps include the uptake of extracellular sulfate by cell, its activation to adenosine 5’phosphosulfate (APS) via adenosine-triphosphate (ATP) enzymes, the reduction of APS to intermediate valence state sulfur species (e.g., sulfite), and the eventual reduction to hydrogen sulfide (HS)27,32–36. In particular, the rapid oxygen exchange between intermediate S(IV) species, e.g., sulfite, and water is a key step in establishing the oxygen isotope equilibrium between sulfate and water, however, it alone does not account for either theoretical or observed fractionation factors (α sulfate-water). Theoretical calculation predicted an α sulfate-water value at approximately 1.023 to 1.026 at temperatures between 10 °C and 25 °C37, whereas an α sulfite-water value ranging from 1.008 to around 1.015 at room temperature within a wide pH range from 2 to 1038–40. The enzyme-mediated rate of the backward MSR reaction becomes increasingly significant as sulfate concentration decreases or H2S/HS- concentration increases36,41. This backward rate eventually approaches the forward sulfate reduction rate, thereby achieving oxygen isotope equilibrium between sulfate and water. Although the detailed kinetics warrants further exploration, it is anticipated that an oxygen is added to sulfite via an enzyme to become sulfate and that oxygen must have equilibrated with water. Otherwise, we would not observe a plateauing δ18O sulfate value as the corresponding δ34S value increases. Non-equilibrium scenarios would exhibit variable δ18O/δ34S slopes on the δ18O–δ34S trajectories32. Importantly, data from laboratory experiments26,31 and modern sediment porewater sulfate29,32,42–47 are consistent with theoretical prediction of the α sulfate-water values.

Sedimentary barite deposits, both bedded and nodular types, are well-documented in geological records for their association with MSR activities48–54. These deposits display a wider range of δ34S values, often exceeding 50‰ within individual nodules or beds. If we measure the δ18O-δ34S paired data for a set of barite samples collected for a specific geological time, the plateau δ18O sulfate value in a δ18O-δ34S trajectory should reflect the δ18O seawater value of that time. Here, we collected six sets of sedimentary bedded and nodular barite deposits from different geological periods of the Phanerozoic Eon. Samples from South China cover the Early Cambrian (Guizhou and Anhui Provinces), Late Ordovician (Yunnan Province), Early Silurian (Chongqing Municipality), and Late Devonian (Guizhou Province and Guangxi Zhuang Autonomous Region), while Late Carboniferous samples were obtained from northwest Mexico (Sonora) and Mid-Cretaceous ones from southeast France (Nyons) (Supplementary Text 1–3, Table S1). Petrographic examinations of the sedimentary barite deposits by scanning electron microscope were conducted to characterize their mineral assemblage and paragenesis (Figures S1–S6).

Results
Sedimentary bedded barite deposits often occur in organic-rich siliceous clastic rocks, with a significant temporal clustering in the Paleozoic Era. A recent study has integrated the oceanic redox history and seawater sulfate concentrations, proposing that sulfate-limited euxinic conditions in seawater facilitate the scavenging of hydrothermally derived metal ions (Zn2+, Pb2+) and promote the accumulation of Ba2+ ions in the sulfate-free water body55. Subsequently, the Ba2+-rich water mass encountered a sulfate-rich one in the ocean, leading to the formation of massive bedded barite ore deposits, referred to as the Sulfate-limited Euxinic Seawater (SLES) model55. All sedimentary bedded barite deposits exhibit a wider δ34S range and higher δ34S values compared to those of the contemporaneous seawater, consistent with sulfate-limited seawater conditions. Sedimentary nodular barite deposits, however, do not exhibit clear temporal clustering and are found throughout the Phanerozoic Eon. Barite nodules formed during early diagenesis, in association with the oxidization of organic matter and microbial sulfate reduction within pore water centimeters to meters below the sediment-water interface48,56,57 and occasionally found in association with bedded barite deposits49,50,58. Evidence supporting their syngenetic origin includes the distortion of external lamination around the barite nodules48,56,57. Similarly high δ34S values are observed in nodular barite deposits48,56,57.

The petrographic results reveal that both bedded and nodular barite types exhibit primary crystal morphologies, with barite grains dispersed within a silica and/or calcium matrix (Figs. 2 and S1–S6). For instance, the Early Cambrian and Late Carboniferous barite deposits contain both bedded and nodular types. The Early Cambrian deposits are characterized by disseminated barite within quartz and calcite, while the Late Carboniferous deposits occur as columnar or globular barite in quartz (Figs. 2 and S1, S5). The Late Ordovician and Late Devonian deposits are predominantly bedded type with massive barite and minor quartz (Figs. 2 and S2, S4). The Early Silurian deposit is of nodular type, with columnar barite grains, similar to those found in the Mid-Cretaceous barite nodules (Figs. 2 and S3, S6). Petrographic examination was conducted to exclude apparent late diagenetic barite, e.g., barite veins. As we emphasized, petrographic examination cannot guarantee that we selected only the unaltered original barite. It is the δ18O-δ34S trajectory that filters out the post-depositional alternated signatures if any.

Each of the six barite deposits displays a wide range of δ18O and δ34S values. Importantly, the δ18O values approach a plateau as its corresponding δ34S values increases from ~35‰ to 80‰ for individual periods (Fig. 3). Approximately, the plateau δ18O barite is at 18‰ during much of the early Paleozoic Era (Fig. 3), but rise to 22‰ during the early Carboniferous and mid-Cretaceous periods (Fig. 3a, 3b). In the early Silurian, barite’s plateau δ18O values approach 20‰ but declines to 18‰ in the late Devonian (Fig. 3c, 3d). In general, the plateau δ18O value of the sedimentary barite increased ~4‰ from the Cambrian to the Cretaceous periods.

The δ18O and δ34S plateauing trajectory for the six sets of barite samples largely resemble the typical pattern seen in culture experiments26,31 and field observations29,32,42–47. Under different MSR rates, the corresponding δ34S values can vary while the plateau δ18O barite value is set by the same seawater or pore water. This is seen in the Devonian barite sample set, in which two distinct clusters of the same plateau δ18O barite region in δ18O-δ34S space have the δ34S barite at approximately 36–38‰ or greater than 55‰, respectively (Fig. 3c). A similar spread of plateau δ18O barite region is also observed at the δ34S barite of 51‰ and 58‰, respectively, in the Silurian data (Fig. 3d). Mixing with any sulfate source of non-equilibrium δ18O sulfate value, being it a pulse of riverine sulfate or sulfate from deep water or an adjacent basin during the barite precipitation should have pulled down the δ18O barite values, so would any post-depositional alteration. We observed a decrease in the δ18O barite at the highest δ34S barite in the Cretaceous and Cambrian data (Figs. 3a and f), which may or may not be attributed to the mixing of a small amount of seawater sulfates not in equilibrium with seawater or other unknown factors. Further statistical treatment in a plateau region would have to assume certain relationship between the δ18O and δ34S of the barite samples, which is not necessarily true in our sample set. Therefore, for now we selected the maximum δ18O barite value in a plateau region to represent the equilibrium δ18O barite with seawater during a particular time period, allowing the trajectory to be enhanced with new data addition in the future. Based on this criterium, the equilibrium δ18O barite values are 18.2‰ for the Early Cambrian, 17.8‰ for the Late Ordovician, 20.4‰ for the Early Silurian, 18.4‰ for the Late Devonian, 21.5‰ for the Late Carboniferous and 21.2‰ for the Mid-Cretaceous (Fig. 3).

These δ18O-δ34S trajectories allow for independent evaluation of both oxygen isotope equilibrium and diagenetic imprints. This is what sets barite apart from other mineral proxies, such as calcite, quartz, apatite, and iron oxide, that rely on empirical and statistical assessments of optical, textural, and trace element criteria15,59–61.

While our barite δ18O-δ34S trajectory approach can offer a δ18O sulfate value that were in equilibrium with the δ18O seawater of a particular geological time, translating the δ18O barite to δ18O seawater requires an independent constraint on the barite formation temperature, as the equilibrium fractionation factor (α sulfate-water) is notably temperature-sensitive. However, the below-wave continental shelf depositional settings, constrained by thin beddings and an organic-rich siliceous clastic sequence, and their all low paleolatitude settings support a similar formation temperature for all the six time periods (Supplementary Text 4). If indeed the barite formation temperature for all the six periods are more or less similar, the ~4‰ late Paleozoic rise in the plateau δ18O barite values indicate a similar degree of δ18O seawater values change. This 4‰ shift may be taken seriously because similar record was also observed in a group of Devonian-Carboniferous carbonate minerals59,62 and confirmed by a reactive transport model consisting of hydrothermal alteration and continental weathering fluxes18 (Figure S7). A late Paleozoic rise of the δ18O seawater would require a dramatic increase in the flux of high-temperature relative to surface-temperature rock-water alteration. We can speculate potential causes for the rise: 1) a deepening of ocean depth, which enhanced seawater penetration and hydrothermal fluid circulation2,10, 2) sediment “blanketing” on land and ocean crust, which decreased low-temperature alteration flux2,10, 3) a decrease in the rate of authigenic clay formation16, and 4) the oxidation of the deep ocean as mentioned for the Neoproterozoic oxygenation event15.

The δ18O difference between mineral and water is temperature sensitive for all non-iron-oxide mineral proxies and mineral samples of the same time period could come from different paleolatitudes thus their δ18O were affected by different temperatures. Thus, a secular δ18O trend could be mis-represented by samples’ uneven paleolatitude distribution. Although we argue for an attenuated variation for the formation temperature for all six sets of sedimentary barite deposits, it does not guarantee that all the six sets of barite samples formed under the same temperature. However, unlike other mineral proxies, because our barite δ18O-δ34S trajectory approach guarantees the most likely δ18O barite value that was in equilibrium with the co-eval seawater δ18O, we now have established a robust methodology so that we can sample barite from different paleolatitudes of a particular time to quantify the paleotemperature difference. What we provide here is not the final result, but a platform for incorporating additional data, thereby enhancing both the temporal and spatial resolution of the current pattern of the plateau δ18O sulfate. This platform holds significant promise for ultimately resolving the longstanding debate surrounding one of the most important issues in Earth’s history: the δ18O and temperature history of Earth’s ocean.

Methods
Petrographic observation
Representative barite samples of each period were first sectioned, polished, and carbon-coated. Petrographic observations were then conducted using a FEI Scios Dual beam field emission scanning electron microscope equipped with an EDAX spectrometer at the Institute of Geochemistry, Chinese Academy of Sciences (IGCAS). Backscattered electron imaging and energy-dispersive spectrometer analysis was employed for texture analysis and mineral identification.

The δ18O and δ34S measurement on barite
Barite samples were obtained using a micro-drill device and pulverized to a fine powder (<200 mesh) using an agate mortar. The resulting powders were initially treated with 10 wt% hydrochloric acid to remove possible carbonate minerals. The residual material underwent a diethylenetriaminepentaacetic-acid dissolution and re-precipitation (DDARP) procedure to extract and purify BaSO463. The oxygen (δ18O) and sulfur isotope (δ34S) compositions of purified barite were analyzed using an EA-HT-Delta V plus and an EA-Isolink-Delta V plus, respectively, at the International Center for Isotope Effects Research, Nanjing University. The δ18O value for each barite sample was measured in duplicate, with the average value reported, while δ34S value was measured once (Source Data). Sulfur isotope measurements were calibrated against Vienna Canyon Diablo Troilite (VCDT) using two in-house barium sulfate standards: ICIER-SO-1 (15.05‰) and ICIER-SO-2 (4.05‰), both of which were calibrated against two international barite standards NBS127 (20.3‰) and IAEA-SO-5 (0.49‰). Oxygen isotope measurements were calibrated against Vienna Standard Mean Ocean Water (VSMOW) using one in-house barium sulfate standard (ICIER-SO-3, 11.81‰), itself calibrated against two international barium standards NBS127 (8.6‰) and IAEA-SO-6 (−11.35‰). The standard deviation for both δ18O and δ34S measurements was better than 0.3‰ based on the performance of the in-house standards.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In the manuscript, Yan et al. presented paired δ18O-δ34S data of sedimentary barite deposits from the Cambrian, Ordovician, Devonian, Silurian, Carboniferous, and Cretaceous periods. They suggested that the plateau δ18Osulfate values within the δ18O-δ34S trajectory can serve as a new proxy of the coeval δ18Oseawater. The proposed idea is novel and interesting - I do like it. However, the data interpretation is oversimplified and not convincing enough in the current version. The data presented here does not warrant publication in Nature Communications but fits better for a specialized journal like Geology. I will explain in more detail in the following, which I hope will strengthen the manuscript.\nThe main concern is that several assumptions in data interpretation require further justification.\n1. The authors calculated the δ18Oseawater value using a theoretical O-isotope fractionation equilibrium coefficient (αsulfate-H2O) of 1.024 at 20℃ to represent the average low-latitude seawater temperature at a water depth of 200-400 m. Although the six barite deposits formed within a similar low-latitude range, their climatic conditions (e.g., pCO2, greenhouse vs. icehouse) vary significantly across the Phanerozoic Eon (e.g., Scotese et al., 2021 Earth-Science Reviews). As αsulfate-H2O associated with MSR is very sensitive to temperature, using the same temperature (it is also unclear why they assumed a water depth of 200-400 m for the locus of sedimentary barite deposits, as modern marine barite often preserves in deep ocean basins) will introduce uncertainties (overestimate or underestimate) of the δ18Oseawater predictions.\n2. How the authors identified the plateau δ18Osulfate values is a bit rough and subjective. In Fig. 2, some dashed lines are slightly lower than the maximum δ18Osulfate values in that period, whereas some are somewhat higher. As the plateau δ18Osulfate values are important for the following discussion, they need to be done more statistically (although the change in the number is small).\n3. It is also noticeable that the maximum δ18Osulfate values do not always correspond to the maximum δ34S values (e.g., Fig. 2a & 2d), but this is not discussed in the manuscript. Assuming MSR is responsible for the plateau δ18Osulfate values, the maximum δ18Osulfate and maximum δ34S should be paired unless other processes further raise δ34S or lower δ18Osulfate. Here are some possibilities I would consider.\ni. Diagenetic imprints. For example, MSR in deep sediments after barite deposition could further increase δ34S, and its effects differ depending on the sedimentary systems' openness (Halevy et al., 2023 Science).\nii. Microbial disproportionation. Microbial disproportionation produces δ18Osulfate 8-21‰ higher than ambient δ18Oseawater (e.g., Böttcher and Thamdrup, 2001 GCA; Böttcher et al., 2005 Geochem. J.), while further enriching sulfate δ34S. The presented δ18O- δ34S data trajectory could be a combined effect of MSR and microbial disproportionation.\niii. Temperature variabilities. The temperature could have been different for various samples within the same period. The temperature of diagenesis is likely different from that of barite formation.\nAlthough the authors explained syngenetic sedimentary barite, it is still unclear to me how petrographic observations screen samples.\n4. Another IMPORTANT assumption yet to be clarified is whether the sedimentary barite δ18Obarite records the contemporaneous seawater sulfate δ18Osulfate. This is not true if the barite samples have been altered by diagenesis - I am not entirely convinced by δ34S and petrographic examinations. Even if these barites precipitate directly in the ocean, they may be fractionated from seawater sulfate. For example, the coretop marine barite δ18Obarite has a 2-5‰ offset from the modern seawater sulfate δ18Osulfate, which was suggested to be associated with barite precipitation rates (Turchyn & Schrag, 2004). Since the magnitude of this offset is similar to that of the δ18Oseawater variation suggested from their barite samples, it may affect the interpretation of δ18Oseawater and should be considered in data discussion.\nLastly, the manuscript presents short arguments about the mechanism of the Phanerozoic δ18Oseawater change. Other supporting evidence must be provided, and more details must be discussed to draw a robust conclusion.\nMinor comments:\nL102： spell out “SLES”", "reviewer_2": "Dear authours,\nPlease find the attached pdf file.", "reviewer_3": "Review: The barite record of the past seawater oxygen isotope composition\nHan et al\nIn this paper the authors address the problem of the evolution of the oxygen isotopic composition of the ocean through the measurement of the oxygen and sulfur isotopic composition of nodular and bedded barite deposits from six time periods in the Phanerozoic. Whether or not the oxygen isotopic composition of the ocean has changed over time is a question that has frustrated the research community for decades, with different mineral reconstructions coming to different and conflicting answers. The holy grail of this would be if we could resolve how the oxygen isotopic composition of the ocean has changed we would be able to directly reconstruct how temperature has changed.\nThe authors approach this fundamental question by using oxygen isotope ratios in sulfate, combined with the sulfur isotope ratios in sulfate. The premise of this is that during microbial sulfate reduction, the oxygen isotope composition of sulfate approaches a value where all oxygen atoms have exchanged with water through intermediate valence state sulfur species (likely mostly sulfite), but the sulfur isotopic composition of sulfate can continue to increase. This plateau in the oxygen isotopic composition of sulfate during microbial sulfate reduction has been seen in a plethora of modern marine environments and laboratory cultures. In theory, if the oxygen isotopic composition of the water changed (in this case ancient ocean seawater) then the oxygen isotopic composition of the sulfate preserved in diagenetic barite nodules and beds would also change. This is, indeed, what the authors find.\nI strongly recommend this paper for publication. I will be honest, I have wanted to do something like this for a long time, and am pleased that someone has done it. I think it adds information to our growing understanding of this topic and I think it is an important contribution. It is also provocative and I think Nature Communications is the right journal for this.\nHowever, there are places where this manuscript needs some work and I’d like this to be addressed before publication. The paper seems to have been written for a much shorter format journal and could use clarification and expansion in places.\nThere are editorial comments throughout. I will highlight these below. There are a mix of small comments and larger comments here.\nLine 17 – “Sulfate’s oxygen resists alteration under most burial conditions…” – this is awkwardly phrased. The oxygen atoms in the sulfate molecule do not exchange with water easily in most environmental settings, and rarely achieve isotopic equilibrium with ambient water”\nLine 21 – I’d be clearer here. This plateau d18Oso4 value reflects the isotopic equilibrium between intermediate valence state sulfur species and water and thus records changes in the d18O of the water.\nLine 35 and 36 – rather than ‘elevates’ and ‘depletes’ (which can be confused for increasing or decreasing the isotope content of one or the other isotope) I’d say ‘increases’ and ‘decreases’ the d18Osw.\nLine 42- You could also include Turchyn et al., 2013 (GCA) which showed that hydrothermal vein minerals also suggest a 4‰ increase in the d18O of the ocean.\nTurchyn, A. V., Alt, J. C., Brown, S. T., DePaolo, D. J., Coggon, R. M., Chi, G., ... & Skulski, T. (2013). Reconstructing the oxygen isotope composition of late Cambrian and Cretaceous hydrothermal vent fluid. Geochimica et cosmochimica acta, 123, 440-458.\nLine 42 – I’d avoid the colloquial ‘carbonates’ ‘cherts’ – in favor of carbonate minerals, chert, etc.\nLine 44 – alteration should be singular\nLine 46 – to fit the bill is a bit colloquial, might choose another phrasing\nLine 47 – silicates – change to silicate minerals\nLine 50 – again ‘silicates’ and ‘carbonates’ should be silicate minerals and carbonate minerals\nLine 56 – this sentence should have a reference\nLine 57-59 – Rennie and Turchyn 2014 (L&O methods) did experiments on the timescale of exchange and would be a good reference to include here.\nRennie, V. C., & Turchyn, A. V. (2014). Controls on the abiotic exchange between aqueous sulfate and water under laboratory conditions. Limnology and Oceanography: methods, 12(4), 166-173.\nLine 64 – why at low concentrations? I’d start the sentence with Sulfate… the exchange starts right away, you just see the plateau when enough of the sulfate has cycled through the cell.\nLine 66 – This comes up throughout the text and I would just urge caution. It is not equilibrium between sulfate and water – it is equilibrium between intermediate valence state sulfur species and water that is reflected in a constant value of d18O of sulfate outside the cell. Ben Brunner wrote the best paper on this that really explained it well.\nBrunner, B., Einsiedl, F., Arnold, G. L., Müller, I., Templer, S., & Bernasconi, S. M. (2012). The reversibility of dissimilatory sulphate reduction and the cell-internal multi-step reduction of sulphite to sulphide: insights from the oxygen isotope composition of sulphate. Isotopes in environmental and health studies, 48(1), 33-54.\nIn this paper and other work by Brunner they suggest that we call it an apparent isotope fractionation between sulfate and water. In modern sedimentary pore fluids it can range from 24-30permil, and it is NOT the value that sulfate would achieve if it were to exchange its isotopes with water. I think you should explain this better because it is not something that people would understand intuitively. The fact that the value changes could be temperature (as you discuss later) but could also be that the equilibrium changes with rates as suggested by a few papers. I would strongly encourage you NOT to term this isotope fractionation between sulfate and water as this is not what this is.\nLine 68 – might rather than intermediate sulfite say ‘intermediate valence state sulfur species sulfite’\nLine 74 – 76 – I’d be sure to include the Brunner reference (and look around, he has had several papers on this – they are very important papers for this idea).\nLine 78-80 – Again, same comment as above (‘Line 66’). This is not the fractionation between sulfate and water. That is part of the reason why it varies. It is important that you clarify this.\nLine 86 – I’d use ‘reflect’ rather than ‘record’. It doesn’t record the d18O of the water. It does reflect any large changes in the d18O of the water.\nLine 86-87 – Might remove this mention of temperature – as it intrigued me how you would determine this, and then as it turns out later you just assume that they are all at similar temperatures (which I agree, I doubt the temperature changed dramatically except the fact that the Mesozoic deepsea temperatures might have been 15 degrees warmer than the Paleozoic or the Cenozoic).\nBut you should acknowledge that the d18O of pore fluids is not the same always as the d18O of the ocean. This also explains some of the variability in the d18O of sulfate in modern pore fluids. The d18O of pore fluid water tends to decrease by 4-5permil due to reaction with underlying basalt.\nLine 100 – this needs a reference\nLine 109-110 – you mean organoclastic microbial sulfate reduction (I think you mean remineralisation of organic matter) – I might just be clearer and say oxidation rather than mineralisation.\nLine 142-147 – Again you should be careful using alpha in this way as it is NOT a true exchange of oxygen atoms in sulfate and water. I can’t remember offhand how Brunner thought it best to do this but alpha-apparent might work.\nLine 147-155 – See my comment above about temperature. Yes the temperature is low but for the samples from the Mesozoic it could be warmer although we don’t have a particularly good sense of deep ocean temperature changes pre Mesozoic. But you must include a discussion of how pore fluid d18O changes. Dan Schrag studied this all the way back in the 1990’s.\nSchrag, D. P., DePaolo, D. J., & Richter, F. M. (1995). Reconstructing past sea surface temperatures: Correcting for diagenesis of bulk marine carbonate. Geochimica et Cosmochimica Acta, 59(11), 2265-2278.\nLine 163-165 – Figure 2 is good but a Figure 3 could be good which shows a temporal plot of changes in the d18O of the ocean suggested by your data. I also don’t think the data from the Silurian is different to the data from the Ordovician and Devonian – given we see variability of 4-5permil across modern sedimentary pore fluids, we can explain a 2 permil difference between these two time periods pretty easily. It could be good to add onto here other proposed seawater curves for the Phanerozoic (add onto a hypothetical Figure 3).\nLine 169 – comment on carbonates similar to above\nLine 173 – I think you have the words to expand this a bit.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to reviewers,\nOverall, we see three issues being raised and all can be addressed. Below, we\nprovide a general response to them. At the subsequent point-by-point responses, we’ll\nrefer to “general response #_” at appropriate places.\n1. Does the plateau δ18O values represent an equilibrium fractionation\nbarite\nbetween sulfate and water or between sulfite and water?\nReply: It is between sulfate and water, and this is the foundation of our study.\nYes, indeed, as reviewer 2 and 3 suggested, the rapid oxygen exchange between\nintermediate-valence state sulfur species (e.g., sulfite) and water is a key step in\nestablishing oxygen isotope equilibrium between sulfate and water. However, there\nare additional key steps, i.e., reversible reactions between sulfate and adenosine\n5’phosphosulfate (APS), between APS and intermediate-valence state sulfur species\n(e.g., sulfite), during microbial sulfate reduction (MSR) (Fritz et al., 1989; Brunner et\nal., 2005, 2012; Wortmann et al., 2007; Mangalo et al., 2007; Farquar et al., 2008;\nAntler et al., 2013). Sulfite-water exchange equilibrium alone does not account for\neither theoretical or observed oxygen isotope fractionation factors (α ).\nsulfate-water\nTheoretical calculation predicted an α value at approximately 1.023 to 1.026\nsulfate-water\nat temperatures between 10 ℃ and 25 ℃ (Zeebe et al., 2010), whereas an α\nsulfite-water\nvalue ranging from 1.008 to around 1.015 at room temperature within a wide pH\nrange from 2 to 10 (Müller et al., 2013; Wankel et al., 2014; Hemingway et al., 2022).\nThe theoretically predicted α values are consistent with those determined in\nsulfate-water\nlaboratory experiments (Fritz et al., 1989; Farquar et al., 2008) as well as those\nobserved in modern sediment porewater sulfate (Böttcher et al., 1999; Aharon and Fu,\n2000; Wortman et al., 2007; Turchyn et al., 2006, 2016; Wehrmann et al., 2011;\nFeng and Roberts, 2011; Antler et al., 2013).\nAlthough the exact molecular mechanism for sulfate-water oxygen isotope\nequilibrium exchange may be vague in detail, we can predict that enzyme-catalyzed,\nreversable redox reaction between sulfite and APS is a key step in incorporating oxygen\nfrom water into sulfate, allowing the establishment of oxygen isotope equilibrium\nbetween sulfate and water. Therefore, when the oxygen isotope composition of seawater\nchanged over time, the plateau δ18O value would also change over time.\nbarite\nWe have added the explanation in the legend of Figure 1 and in the revised version\nand, now it reads (at line 70-90) “During microbial sulfate reduction (MSR), sulfate can\neffectively exchange its oxygen isotopes with that of ambient water through reversable enzyme-\ncatalyzed steps26-32 (Fig.1). These steps include the uptake of extracellular sulfate by the cell, its\nactivation to adenosine 5’phosphosulfate (APS) via adenosine-triphosphate (ATP) enzymes, the\nreduction of APS to intermediate valence state sulfur species (e.g., sulfite), and the eventual reduction\nto hydrogen sulfide (H S)27,32-36. In particular, the rapid oxygen exchange between intermediate S(IV)\n2\nspecies, e.g., sulfite, and water is a key step in establishing the oxygen isotope equilibrium between\nsulfate and water, however, it alone does not account for either theoretical or observed fractionation\nfactors (α ). Theoretical calculation predicted an α value at approximately 1.023 to\nsulfate-water sulfate-water\n1.026 at temperatures between 10 ℃ and 25 ℃37, whereas an α value ranging from 1.008 to\nsulfite-water\n1\naround 1.015 at room temperature within a wide pH range from 2 to 1038-40. The enzyme-mediated\nrate of the backward MSR reaction becomes increasingly significant as sulfate concentration decreases\nor H S/HS- concentration increases36,41. This rate eventually approaches the forward sulfate reduction\n2\nrate, thereby achieving oxygen isotope equilibrium between sulfate and water. Although the detail\nwarrants further exploration, it is anticipated that an oxygen is added to sulfite via an enzyme to\nbecome sulfate and that oxygen must have equilibrated with water. Importantly, laboratory\nexperiments26,31 and modern sediment porewater sulfate29,32,42-47 all confirmed the theoretical\nprediction of the α value.”\nsulfate-water\n2. Post-depositional alteration on the δ18O and statistical treatment on the\nbarite\nplateau δ18O values and the corresponding uncertainties.\nbarite\nReply: Barite offers a distinct advantage due not only to sulfate’s known stability\nin holding its original oxygen isotope composition (i.e., non-labile) but also to the set\nof barite’s δ18O-δ34S trajectory in which the δ18O approaches a plateau as the\ncorresponding δ34S value increases. Due to different MSR rates and therefore\nreversibility within intracellular steps, the δ34S values can vary while the\nbarite\nequilibrium δ18O is buffered by the same seawater or pore water (see two distinct\nbarite\nclusters of the same plateaued δ18O region in δ18O-δ34S space where the\nbarite barite\nδ34S is at approximately 36-38‰ and greater than 55‰ in our Devonian barite\nbarite\nsamples).\nHowever, any additional fluid introduction can disrupt an otherwise smooth\ntrajectory of δ18O plateauing as the corresponding δ34S value increase in a closed-\nbarite\nsystem during microbial sulfate reduction, usually displaying a drop in the δ18O value\nin the trajectory. For instance, such disruption may occur due to mixing with a pulse\nof terrestrial sulfate near the coastline or a pool of sulfate that had not reached a\nplateau δ18O value during barite precipitation, or to alteration on the barite’s δ18O\nsulfate\nvalues by post-depositional processes. Overall, the δ18O-δ34S trajectory observed in\neach barite set is largely consistent with the results from laboratory experiments and\nsediment pore water sulfate, despite slight variations in δ18O values at a given\nbarite\nδ34S value, reflecting seawater sulfate that has undergone MSR processes without\nbarite\nsignificant mixing of riverine or other source of sulfate (including carried in via late\ndiagenetic fluids).\nIn this revised version, we have explicitly added that we selected the maximum\nδ18O value at each plateaued δ18O region even though the highest δ34S value\nbarite barite\nmay be associated with a slightly lower δ18O value (line 159-165). The uncertainty\nbarite\nin the assigned plateau δ18O value is our external measurement uncertainty for\nbarite\nδ18O , i.e., ±0.3‰ (line 239). This is what sets barite apart from other mineral\nbarite\nproxies that rely on empirical and statistical assessments of optical, textural, and trace\nelement criteria.\nThat said, apparent later diagenetic imprints on barite should be readily identified\nand excluded for isotope analysis in the first place by petrographic screening. That\nwas what we did in this study. In the revised manuscript, we have included photos of\nthe typical textures of early (not late) diagenetic barite (i.e., a new Fig. 2 in the main\ntext and new Figs. S1-S6 in Supplementary Information).\n2\n3. The temperature assumption used to determine the δ18O .\nseawater\nReply: Our barite samples were shallow shelf deposits, not the modern deep-water\n(often >3000 m) barite equivalents. Some of our barite sulfates contain early diagenetic\nporewater sulfate. In fact, those that are approaching δ18O equilibrium value with\nsulfate\nseawater are mostly likely porewater sulfate during early diagenesis. Their formation\ntemperature is probably most representative of the average shallow ocean temperature\nat that time.\nHowever, despite the below-wave depositional settings (supported by thin bedding\nevidence) and low paleolatitude ranges of all six sets of samples, we cannot be sure all\nthe barite samples of the six periods were formed in the same temperature. Here in the\nrevised one, we have deleted the mention of 200-400m (which is certainly debatable).\nWhile all other mineral proxies suffer from the same uncertainty in paleo-\ntemperature representation of a geological time because samples of different ages could\ncome from different paleolatitudes, our barite δ18O-δ34S trajectory proxy sets itself apart\nfrom the others in that it is 1) resistant to later alteration and 2) easy to identify altered\nsignatures. This barite proxy offers us a hopeful approach to reconstructing the δ18O of\npaleo-seawater because we now could intentionally collect barite samples from\ndifferent paleolatitudes of the same period to examine their plateau δ18O value\ndifference. We finally have a proxy that can move forward rather than march in place\nwith the seawater δ18O problem.\nThe following are point by point responses to the four reviewers’ comments and\nour corresponding revision.\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nIn the manuscript, Han et al. presented paired δ18O-δ34S data of sedimentary\nbarite deposits from the Cambrian, Ordovician, Devonian, Silurian, Carboniferous,\nand Cretaceous periods. They suggested that the plateau δ18O values within the\nsulfate\nδ18O-δ34S trajectory can serve as a new proxy of the coeval δ18O .\nseawater\nThe proposed\nidea is novel and interesting - I do like it. However, the data interpretation is\noversimplified and not convincing enough in the current version. The data presented\nhere does not warrant publication in Nature Communications but fits better for a\nspecialized journal like Geology. I will explain in more detail in the following, which\nI hope will strengthen the manuscript.\nThe main concern is that several assumptions in data interpretation require\nfurther justification.\n1. The authors calculated the δ18O value using a theoretical O-isotope\nseawater\nfractionation equilibrium coefficient (α ) of 1.024 at 20℃ to represent the\nsulfate-H2O\naverage low-latitude seawater temperature at a water depth of 200-400 m. Although\nthe six barite deposits formed within a similar low-latitude range, their climatic\n3\nconditions (e.g., pCO , greenhouse vs. icehouse) vary significantly across the\nsulfate-H2O\nassociated with MSR is very sensitive to temperature, using the same temperature (it\nis also unclear why they assumed a water depth of 200-400 m for the locus of\nsedimentary barite deposits, as modern marine barite often preserves in deep ocean\nbasins) will introduce uncertainties (overestimate or underestimate) of the δ18O\nseawater\npredictions.\nReply: Thank you for raising the paleo-depositional temperature issue. Please see\nour general response #3.\nIn light of the comment, we have made the following revision in the revised\nmanuscript, in line 177-184 and line 197-208 now it reads “While our barite δ18O-δ34S\ntrajectory approach can offer aδ18O value that were in equilibrium with the δ18O of a\nsulfate seawater\nparticular geological time, translating the δ18O to δ18O requires an independent constraint\nsulfate seawater\non the barite formation temperature, as the equilibrium fractionation factor (α )is notably\nsulfate-water\ntemperature-sensitive. However, the below-wave continental shelf depositional settings, constrained\nby thin beddings and an organic-rich siliceous clastic sequence, and their all low paleolatitude settings\nsupport a similar formation temperature for all the six time periods (Supplementary Text 4).” and\n“The δ18O difference between mineral and water is temperature sensitive for all non-iron-oxide\nmineral proxies and mineral samples of the same time period could come from different\npaleolatitudes thus their δ18O were affected by different temperatures. Thus, a secular δ18O trend\ncould be mis-represented by samples’ uneven paleolatitude distribution. Although we argue for an\nattenuated variation for the formation temperature for all six sets of sedimentary barite deposits, it\ndoes not guarantee that all the six sets of barite samples formed under the same temperature.\nHowever, unlike other mineral proxies, because our barite δ18O-δ34S trajectory approach guarantees\nthe most likely δ18O value that was in equilibrium with the co-eval seawater δ18O, we now have\nbarite\nestablished a solid methodology so that we could sample barite from different paleolatitudes of a\nparticular time to quantify the paleotemperature difference.”\n2. How the authors identified the plateau δ18O values is a bit rough and\nsulfate\nsubjective. In Fig. 2, some dashed lines are slightly lower than the maximum\nδ18O values in that period, whereas some are somewhat higher. As the plateau\nsulfate\nδ18O values are important for the following discussion, they need to be done more\nsulfate\nstatistically (although the change in the number is small).\nReply: Thank you for pointing this out. See our general response #2.\nIn the revised manuscript, we have added the discussion in line 151-170 as: “The\nδ18O and δ34S plateauing trajectory for the six sets of barite samples largely resemble the typical\npattern seen in culture experiments26,31 and field observations29,32,42-47, reflecting seawater sulfate that\nhas undergone different degrees of MSR without significant mixing of riverine or other source of\nsulfate (including carried in by late diagenetic fluids). In addition, due to different MSR rates, the\ncorresponding δ34S values can vary while the plateau δ18O value is set by the same seawater or\nbarite barite\npore water. This is seen in the Devonian barite samples, in which two distinct clusters of the same\nplateau δ18O region in δ18O-δ34S space has the δ34S at approximately 36-38‰ or greater\nbarite barite barite\nthan 55‰ (Fig. 3c). A similar spread of plateau δ18O region is also observed at 51‰ and 58‰\nbarite\nδ34S in the Silurian data (Fig. 3d). Mixing with any sulfate source of non-equilibrium δ18O\nbarite sulfate\n4\nvalue, being it a pulse of riverine sulfate or sulfate from deep water or an adjacent basin during the\nbarite precipitation should have pulled down the δ18O values, so would any post-depositional\nbarite\nalteration. We observed a decrease in the δ18O at the highest δ34S in the Cretaceous and\nbarite barite\nCambrian data (Fig. 3a and 3f). Therefore, we selected the maximum δ18O value in a plateau\nbarite\nregion to represent the equilibrium δ18O with seawater during a particular time period. Based on\nbarite\nthis criterium, the equilibrium δ18O values are 18.2‰ for the Early Cambrian, 17.8‰ for the Late\nbarite\nOrdovician, 20.4‰ for the Early Silurian, 18.4‰ for the Late Devonian, 21.5‰ for the Late\nCarboniferous and 21.2‰ for the Mid-Cretaceous (Fig. 3).”\n3. It is also noticeable that the maximum δ18O values do not always\nsulfate\ncorrespond to the maximum δ34S values (e.g., Fig. 2a & 2d), but this is not discussed\nin the manuscript. Assuming MSR is responsible for the plateau δ18O values,\nsulfate\nthe\nmaximum δ18O and maximum δ34S should be paired unless other processes\nsulfate\nfurther raise δ34S or lower δ18O . Here are some possibilities I would consider.\nsulfate\ni. Diagenetic imprints. For example, MSR in deep sediments after barite\ndeposition could further increase δ34S, and its effects differ depending on the\nsedimentary systems' openness (Halevy et al., 2023 Science).\nReply: See our general response #2 and response to your main concern #2 above.\nYes, depositional condition and reduction rate will affect the δ34S of pyrite as\nillustrated by many (e.g., Lang et al., 2020; Bryant et al., 2023; Halevy et al., 2023).\nHowever, the oxygen in the remaining SO 2- should be buffered by the porewater\n4\noxygen, leading to the observed δ18O plateauing.\nsulfate\nii. Microbial disproportionation. Microbial disproportionation produces δ18O\nsulfate\n8-21‰ higher than ambient δ18O (e.g., Böttcher and Thamdrup, 2001 GCA;\nseawater\nBöttcher et al., 2005 Geochem. J.), while further enriching sulfate δ34S. The presented\nδ18O-δ34S data trajectory could be a combined effect of MSR and microbial\ndisproportionation.\nReply: Sulfate in barite beds and nodules came from water column or porewater.\nSome of the bumps in the δ¹⁸O-δ34S trajectory may well be due to transient changes in\nsulfur redox chemistry including possible microbial S disproportionation. The “8-\n21‰ higher than ambient δ18O ” is a good example, but the oxygen isotope\nseawater\nexchange between the intermediates and water and associated with reversible\nenzymatic reactions are also affecting the δ18O value. That’s why we argue that\nsulfate\nthe δ¹⁸O-δ34S plateauing trajectory is a more robust approach to constrain equilibrium\nδ¹⁸O value.\nsulfate\niii. Temperature variabilities. The temperature could have been different for\nvarious samples within the same period. The temperature of diagenesis is likely\ndifferent from that of barite formation.\nReply: Please see our general response #3 and response to your main concern #1\nabove.\nAlthough the authors explained syngenetic sedimentary barite, it is still unclear to\nme how petrographic observations screen samples.\nReply: The petrographic screening is employed here to tell apart the late diagenetic\nbarite if any, which should be easy to identify. We used the δ18O-δ34S trajectory\n5\napproach to eliminate much of the complexity introduced by late diagenetic or post-\ndepositional alteration.\nIn the revised manuscript, we have refined it and now reads at line 137-140:\n“Petrographic examination was conducted to exclude apparent late diagenetic barite, e.g., barite veins.\nAs we emphasized, petrographic examination cannot promise that we selected only unaltered original\nbarite. It is the δ¹⁸O-δ³⁴S trajectory that filters out post-depositional alteration if any.”\n4. Another IMPORTANT assumption yet to be clarified is whether the\nsedimentary barite δ18O records the contemporaneous seawater sulfate δ18O .\nbarite sulfate\nThis is not true if the barite samples have been altered by diagenesis - I am not\nentirely convinced by δ34S and petrographic examinations. Even if these barites\nprecipitate directly in the ocean, they may be fractionated from seawater sulfate. For\nexample, the coretop marine barite δ18O has a 2-5‰ offset from the modern\nbarite\nseawater sulfate δ18O , which was suggested to be associated with barite\nsulfate\nprecipitation rates (Turchyn & Schrag, 2004). Since the magnitude of this offset is\nsimilar to that of the δ18O variation suggested from their barite samples, it may\nseawater\naffect the interpretation of δ18O and should be considered in data discussion.\nseawater\nReply: Yes, we agree that δ34S and petrographic examinations cannot exclude\npotential late diagenetic barite. That’s why we emphasize the δ18O-δ34S trajectory\napproach, i.e., the δ18O plateau value reflects the equilibrium δ18O of\nbarite\ncontemporaneous seawater. Please see our general response #2 and response to your\nmain concern #3 above.\nWe agree with Turchyn & Schrag (2004) on their interpretation of the 2-5‰\noffset in δ18O values of core-top marine barite relative to modern seawater sulfate\n(δ18O ). But these deep-sea barite samples are not our shallow shelf barite beds or\nsulfate\nconcretions and therefore not comparable. Most importantly, individual δ18O data\nbarite\npoints can be out of equilibrium with seawater like most of our data that did not reach\na plateau. Only the δ18O-δ34S trajectory approach can determine the potential δ18O\nbarite\nvaluethat is likely in equilibrium with δ18O .\nseawater\nLastly, the manuscript presents short arguments about the mechanism of the\nPhanerozoic δ18O change. Other supporting evidence must be provided, and more\nseawater\ndetails must be discussed to draw a robust conclusion.\nReply: Thanks for your suggestions. Due to the temperature issue shared by both\nbarite and other mineral proxies (see our general response #3), we intended not to\nemphasize the potential rise of δ18O during the late Paleozoic and therefore\nseawater\nprovided only concise discussion on the possible causes.\nIn line 189-196 of the revised version now it reads: “A late Paleozoic rise of δ18O\nseawater\nwould require a dramatic increase in the flux of high-temperature relative to surface-temperature\nrock-water alteration. We can speculate potential causes for the rise: 1) a deepening of ocean depth,\nwhich enhanced seawater penetration and hydrothermal fluid circulation2,10, 2) sediment “blanketing”\non land and ocean crust, which decreased low-temperature alteration flux2,10, 3) a decrease in the rate\nof authigenic clay formation16, and 4) the oxidation of the deep ocean as mentioned for the\nNeoproterozoic oxygenation event15.”\nL102: spell out “SLES”\nReply: We have spelled out “SLES” as “Sulfate-limited Euxinic Seawater”.\nReviewer #2 (Remarks to the Author):\nDear authours,\nPlease find the attached pdf file.\nReferee Report: The Barite Record of the Past Seawater Oxygen Isotope\nComposition, January 29, 2025\nSummary of the Paper\nThis manuscript, titled “The Barite Record of the Past Seawater Oxygen Isotope\nComposition” aims to explore the oxygen isotope composition of seawater\n(δ18O ) through the analysis of sedimentary barite deposits from various periods\nseawater\nof the Phanerozoic Eon. The authors suggest that the plateau δ18O values in barite\nsulfate\ncan serve as a proxy for historical seawater δ18O values, providing insights into the\nglobal ocean’s temperature and chemical history.\nStrengths of the Paper\nThe manuscript presents a significant approach to studying the history of\nseawater oxygen isotopes using barite deposits. The proposed proxy for seawater δ18O\nusing plateau δ18O is an interesting and promising method, particularly given the\nsulfate\nstability of sulfate under most burial conditions. The data presented, including paired\nδ18O and δ34S measurements, offer valuable insights into the past variations in\nseawater composition.\n• The data collection is extensive, covering six periods of the Phanerozoic Eon,\nwhich adds temporal depth to the analysis.\n• The use of well-preserved syngenetic barite samples with petrographic\nscreening is a strength of the study, reducing potential biases from post-depositional\nalterations (which we urge the authors to share more details about and not just with\nthe (one) supplementary figure currently included).\n• The methodology is sound, and the measurements were carefully calibrated\nusing international standards.\nMajor Concerns and Suggestions for Improvement\nDespite the strengths, there are several areas where the manuscript can be\nimproved:\n1. Lack of Discussion on Post-Depositional Alteration\nAlthough the authors claim that the barite samples are well-preserved and the\nδ18O − δ34S trajectory is independent of post-depositional alteration (maintext; lines\n131-134), the manuscript could benefit from a more detailed discussion on potential\npost-depositional effects, especially in relation to microbial sulfate reduction (MSR).\nWhile the study mentions the stability of sulfate oxygen, it is important to better\naddress how potential alteration mechanisms in the sediments may influence the\n7\nδ18O values.\nsulfate\nRecommendation: A more in-depth exploration of post-depositional processes\nand their potential impact on the δ18O values should be incorporated.\nsulfate\nFurthermore, a sensitivity analysis on the effect of post-depositional alteration would\nstrengthen the conclusions.\nReply: Thank you for your valuable suggestion.\nPlease see our general response #2.\n2. Clarity and Precision of the Results\nSome parts of the manuscript, especially in the “The δ18O and δ34S of barite”\nsection, could benefit from clearer presentation. For example, the figures showing the\nδ18O − δ34S data (Figures 2A, 2B, etc.) are referenced in the text, but a more detailed\nexplanation of the trajectory and the specific significance of the plateau δ18O\nsulfate\nvalues could help readers understand the implications of the data more effectively. In\naddition, Figure 1 schematic explanation must be grounded by citing actual references\nthat support this simplified cycle as presented.\nRecommendation: The authors should clarify the interpretation of the plateau\nvalues in the figures and ensure that the text provides a detailed explanation of how\nthese values are derived and their significance for understanding the history of\nseawater oxygen isotopes. In addition, none of the markers are presented with\nuncertainty bars, which is really “screaming” to be addressed. Finally, the value of the\nplateau seems to be determined arbitrarily, and at certain points is just seemed to be\nwrong (e.g., Figure 2A). It is strongly suggested that the authors use a proper\nmathematical framework to determine the plateau value and elaborate more on\ncaptions of all figures.\nReply: These are very useful suggestions and we have redrawn Figures 1 and 2\n(i.e., new Figure 3) and added additional details to the legends. In this revised version,\nwe have explicitly added that we selected the maximum δ18O on the plateau as the\nbarite\ncorresponding δ34S rise. The uncertainty in the assigned plateau δ18O value is\nbarite barite\nour external measurement uncertainty for δ18O , i.e., ±0.3‰.\nbarite\nSee our general response #2.\nWe have added the “Data uncertainty is the external measurement uncertainty,\nwith ±0.3‰ for both δ18O and δ34S , all smaller than the size of the symbols.”\nbarite barite\nto the legends.\n3. Temperature Sensitivity of the Fractionation Factor\n3a Variability of Ocean Temperature Through Time\nThe study assumes a constant fractionation factor (αSO 2− −H O) of 1.024 at\n4 2\n20°C for the entire study period following reference 24 of the maintext1. Given the\npotential variability of ocean temperatures throughout Earth’s history, as to the\ntemperature gradient in the modern ocean, this assumption could introduce significant\nerrors, especially when extrapolating the data to earlier geological periods. The\ninfluence of temperature on the oxygen isotope fractionation between sulfate and\nwater is acknowledged, but the manuscript does not fully explore how this assumption\n8\nmight affect the derived seawater δ18O values.\nRecommendation: A discussion on the uncertainty introduced by assuming a\nconstant fractionation factor over geological timescales should be included.\nAdditionally, further validation of the temperature assumption could improve the\nrobustness of the findings (see point 3b below).\nReply: See our general response #3.\n3b The Effect of Barite Deposit Type and Depositional Depth on δ18O\nsulfate\nIn Figure 2 of the maintext, we observe a trend that is not discussed in the study:\nthe lower δ18O values, around 18‰ of the Cambrian, Ordovician, and Devonian\nsulfate\n(maintext; Figure 2C, 2E, 2F, lines 122-126) are associated with bedded barites, while\nthe higher values, around 20‰, of the Silurian, Carboniferous, and Cretaceous are\nassociated with barite nodules (maintext; Figure 2A, 2B, 2D, lines 122-126). Given\nthat a 2‰ difference can be caused by a 10°C temperature difference in a sulfate-\nwater system, based on the fractionation factor estimates of reference 24 of the\nmaintext1, it is important to consider the depth of the water in which the barites\nformed, not just the latitude. This is because barite often forms in the thermocline\nzone, where the temperature drops rapidly, and a 10°C temperature difference can\neasily occur within this zone2. Although the study provides paleolatitude estimates\nand detailed general lithological descriptions of the formations in the supplementary\ninformation, it does not fully address the potential water depth differences between\nthe samples from different formations. For example, if the bedded barites have formed\nin deeper water compared to barite nodules in this exact case, this could potentially\nexplain why the bedded barite samples show lower δ18O values. If this is the case for\nthe barites in the study, the δ18O values may be partially influenced by differences\nsulfate\nin the depth of seawater they formed in, making it difficult to disentangle this factor\nfrom the influence of δ18O . Currently, the manuscript does not fully address this\nseawater\npotential uncertainty.\nRecommendation: The manuscript could benefit from a more detailed\ndescription of the layers hosting the barites, especially with respect to the water\ndepth and depositional environment. A sensitivity analysis quantifying the effect of water\ndepth uncertainty on the δ18O would strengthen the manuscript. The authors are\nsulfate\nsuggested to address and discuss the different oxygen isotopes values yielded by the\ntwo barite types and reason why (or why not) the sedimentary bedded and\nsedimentary nodular barites could exhibit different oxygen isotope signals despite\nbeing deposited from seawater with the same δ18O.\nReply: Thanks for alerting us the apparent correlation between the δ18O and\nbarite\nbarite types. Determining the specific water depth for both bedded and nodular barite\ntypes is challenging. We can only constrain their formation to continental shelf\nsettings, characterized by rich organic matter, terrestrial input and quiet sedimentary\nconditions. In fact, both bedded and nodular barites occur in both Carboniferous and\nCambrian barite deposits, forming in the same depositional settings. In this study, we\ngrouped all barite types from each period, as their sulfate source is derived from\nseawater sulfate subjected to MSR, ultimately reaching oxygen isotope equilibrium\n9\nwith water. In the revised version, we have illustrated the bedded and nodular barites\nwith different symbols for a clear presentation in a new Figure 3.\nPlease refer to our general response #3.\n4. The Influence of Terrestrial Input on δ18O\nsulfate\nLines 131-134 of the maintext briefly discuss the potential influence of meteoric\nwater on δ18O after the deposition, but the manuscript could benefit from a more\nsulfate\ndetailed discussion on potential terrestrial effects during deposition. For example, a\nnew study3 showed that the oxygen isotopes of sulfates deposited in shallow marine\nenvironments or restricted basins reflect the influence of meteoric water with more\nnegative δ18O. One can raise the question; could the different values of the plateaus be\nthe result of mixed sourced parent solution sulfate (meteoric, marine, etc)? In this\ncase, the plateau δ18O value differ between sections solely due to varying rates of\nterrestrial sulfate influx, potentially related to factors such as distance from the\ncoastline?\nRecommendation: We suggest the authors to include a discussion on the\npotential effect of terrestrial sulfate influx on the plateau δ18O and explicitly add the\nneeded information to the existing supplementary tables. This would enhance the\nclarity of the manuscript and strengthen the case for the proxy.\nReply: See our general response #2.\nAt line 151-170, we inserted sentences “The δ18O and δ34S plateauing trajectory for the\nsix sets of barite samples largely resemble the typical pattern seen in culture experiments26,31 and field\nobservations29,32,42-47, reflecting seawater sulfate that has undergone different degrees of MSR without\nsignificant mixing of riverine or other source of sulfate (including carried in by late diagenetic fluids).\nIn addition, due to different MSR rates, the corresponding δ34S values can vary while the plateau\nbarite\nδ18O value is set by the same seawater or pore water. This is seen in the Devonian barite samples,\nbarite\nin which two distinct clusters of the same plateau δ18O region in δ18O-δ34S space has the\nbarite barite\nδ34S at approximately 36-38‰ or greater than 55‰ (Fig. 3c). A similar spread of plateau δ18O\nbarite barite\nregion is also observed at 51‰ and 58‰ δ34S in the Silurian data (Fig. 3d). Mixing with any sulfate\nbarite\nsource of non-equilibrium δ18O value, being it a pulse of riverine sulfate or sulfate from deep\nsulfate\nwater or an adjacent basin during the barite precipitation should have pulled down the δ18O\nbarite\nvalues, so would any post-depositional alteration. We observed a decrease in the δ18O at the\nbarite\nhighest δ34S in the Cretaceous and Cambrian data (Fig. 3a and 3f). Therefore, we selected the\nbarite\nmaximum δ18O value in a plateau region to represent the equilibrium δ18O with seawater\nbarite barite\nduring a particular time period. Based on this criterium, the equilibrium δ18O values are 18.2‰ for\nbarite\nthe Early Cambrian, 17.8‰ for the Late Ordovician, 20.4‰ for the Early Silurian, 18.4‰ for the Late\nDevonian, 21.5‰ for the Late Carboniferous and 21.2‰ for the Mid-Cretaceous (Fig. 3).”\n5. Discussion on Sulfite-Water Fractionation Factor\nThe study uses the sulfate-water fractionation factor from reference1 for\nbackcalculating δ18O (maintext; lines 161-162). Several studies emphasized that\nseawater\nδ18O values rely heavily on the oxygen isotope fractionation between\nsulfate\nintermediates like sulfite and water4–7, and Figure 1 of the maintext also highlights the\nimportance of this exchange reaction. Currently, the study does not address the effect\n10\nof αSO 2-−H O on δ18O .\n3 2 sulfate\nRecommendation: We suggest that the authors include a discussion explaining\nwhy they believe αSO 2-−H O has no effect on δ18O , as this interpretation may\n3 2 sulfate\nnot be intuitive to all readers.\nReply: See our general response #1.\nMinor Comments\n• The abstract could be shortened to make it more concise and directly highlight\nthe most important findings.\nReply: We have revised the abstract to be within 150 words to meet the\nrequirements of Nature Communications.\n• Figure 1 is helpful, but a more detailed caption would be beneficial to explain\nthe sulfur and oxygen isotope fractionation pathway in microbial sulfate reduction\nmore clearly.\nReply: Detailed information of a variety of steps involved in MSR processes has\nbeen added in the revised manuscript and in the legend of a new Figure 1.\nFigure 1 Enzyme-catalyzed reversible intracellular steps of sulfur and oxygen isotope fractionation\nduring microbial sulfate reduction processes. These steps mainly include the activation of adenosine\n5’phosphosulfate (APS) from sulfate, the reduction of APS to intermediate-valence state sulfur species\n(e.g., sulfite), and reduction of sulfite to hydrogen sulfide (H S)27, 32-36. Sulfur isotope fractionation is\n2\ncontrolled by the reduction of APS to sulfite and sulfite to sulfide, and their reversibility36,41, while\noxygen isotope fractionation of sulfate occurs during the reversible redox reactions between sulfate\nand APS, APS and intermediate-valence state sulfur species (e.g., sulfite) as well as sulfite-water\nexchange26-32.\n• In Figure 2, the axis values and spaces are not uniform between the different\npanels and it would be very helpful for the readers if it would be.\nReply: We have redrawn Figure 2 (now the new Figure 3) to unify axis values of\nall panels. The maximum δ18O value of each period is chosen as the plateau δ18O\nbarite barite\nvalue for that period.\nmaximum δ18O values in the plateau region is chosen as plateau δ18O value that was in\nbarite barite\nequilibrium with ambient water (see explanation in the main text). Data uncertainty is the external\nmeasurement uncertainty, with ±0.3‰ for both δ18O and δ34S , all smaller than the size of the\nbarite barite\nsymbols.\n• In several instances, the authors reference previous work to support claims that\nare not consistent with the findings or conclusions of the original articles. We strongly\nrecommend reviewing all citations to ensure that the references are accurately\nrepresented and aligned with the original studies.\nReply: Thanks for the alert. We have re-checked and corrected citations. For\nexample, although the δ¹⁸O records from both phosphate and chert show an increasing\ntrend over time, studies by Shemesh et al. (1983) and Robert et al. (2006) did not\nsupport a continuous rise in the δ¹⁸O . We have corrected these mis-cited\nseawater\nreferences and replaced them with Hearing et al. (2018) for phosphate and Hren et al.\n(2009) for chert.\nWe have also examined and rearranged the references used in the oxygen isotope\nfractionation of sulfate during MSR processes. They are the intracellular steps of\nsulfate reduction from Fritz et al. (1989); Brunner et al. (2005, 2012); Wortmann et al.\n(2007); Mangalo et al. (2007); Farquar et al. (2008) and Antler et al. (2013) and the\noxygen isotope exchange between the sulfite and water from Müller et al. (2013);\nWankel et al. (2014) and Hemingway et al. (2022).\n• The manuscript would be strengthened by including an additional\nsupplementary figure that compares the current findings with existing oxygen isotope\nrecords. This enhancement would provide readers with a clearer context and facilitate\na more comprehensive understanding of the study’s contributions.\nReply: We have now added a new Figure S7 in the Supplementary Information.\nFigure S7 compares our barite record (assuming the increase in the plateaued δ18O\nbarite\nvalues since the Cambrian reflects the rise of δ18O in seawater) with other existing\nmineral records of the δ18O history. Because the barite depositional temperature\nseawater\nissue remains as we illustrated in our general response #3, we prefer not to emphasize\n12\nthis result and therefore displaying the result in a supplemental figure is appropriate at\nthis time (Supplementary Text 4). We are currently actively gathering data from\ndifferent paleolatitudes to determine the latitudinal temperature gradients based on the\nbarite δ18O-δ34S trajectory approach. Stay tuned for our upcoming contributions.\nTo reiterate, our barite δ18O-δ34S trajectory approach sets itself apart from other\nmineral proxies in its confidence in obtaining a reliable paleo δ18O value. Now,\nseawater\nwe finally have a way to resolve the more than half-century-old seawater δ18O\nproblem. Our database provides a platform for incorporating additional data in the\nfuture, thereby enhancing both the temporal and spatial resolution of the current\npattern of plateau δ18O trend.\nsulfate\nPlease see our general response #3 for more discussion.\nFigure S7 Compilation of δ18O history inferred from barite, carbonate, iron-oxides proxies and\nseawater\ngeochemical modeling. Theoretical equilibrium oxygen isotope fractionation factor (i.e., α ) of\nsulfate-water\n1.024 at 20℃ to 1.022 at 28℃ were used to calculate the δ18O value based on the maximum\nseawater\nδ18O value for each period (see explanation in the main text). The temperature assumptions are\nbarite\ndiscussed in detail in Supplementary Text 4. The late Paleozoic rise in δ18O value as is apparent in\nseawater\nour barite record closely resembles the trend in the carbonate proxy21,22, but differs from those\ninferred by geochemical modeling23 or Fe oxide records24,25 which indicate an early Paleozoic\nδ18O rise (e.g., ~6‰).\nseawater\nConclusion\nIn conclusion, this manuscript has the potential to serve as a valuable\ncontribution to our understanding of the history of seawater oxygen isotopes. The\nnovel approach using barite deposits as a proxy for δ18O is promising and the\nseawater\ndata presented are compelling. However, some key aspects of the analysis require\nfurther clarification and discussion, especially regarding the assumptions about post-\ndepositional alteration and temperature sensitivity, and proper mathematical\nframework. With these revisions, the manuscript could become a significant\ncontribution to the field.\n[1] Richard E Zeebe. A new value for the stable oxygen isotope fractionation\nbetween dissolved sulfate ion and water. Geochimica et Cosmochimica Acta,\n74(3):818–828, 2010.\n[2] Lynne D Talley. Descriptive physical oceanography: an introduction.\nAcademic press, 2011.\n[3] Peter W Crockford, Anna Rose Waldeck, Andrey Bekker, Marcus Kunzmann,\nRachita Ghosh, Prosenjit Ghosh, Nina Sergeeva, Sergey Michurin, Itay Halevy, and\nDavid Johnston. Depositional controls on the preservation of f ∆’17O signatures in\nsedimentary sulfate. Authorea Preprints, 2025.\n[4] Peter W Crockford, Marcus Kunzmann, Andrey Bekker, Justin Hayles,\nHuiming Bao, Galen P Halverson, Yongbo Peng, Thi H Bui, Grant M Cox, Timothy\nM Gibson, et al. Claypool continued: Extending the isotopic record of sedimentary\nsulfate. Chemical Geology, 513:200–225, 2019.\n[5] Alexandra V Turchyn, Volker Brüchert, Timothy W Lyons, Gregory S Engel,\nNurgul Balci, Daniel P Schrag, and Benjamin Brunner. Kinetic oxygen isotope effects\nduring dissimilatory sulfate reduction: a combined theoretical and experimental\napproach. Geochimica et Cosmochimica Acta, 74(7):2011–2024, 2010.\n[6] Inigo A Müller, Benjamin Brunner, Christian Breuer, Max Coleman, and\nWolfgang Bach. The oxygen isotope equilibrium fractionation between sulfite species\nand water. Geochimica et Cosmochimica Acta, 120:562–581, 2013.\n[7] Scott D Wankel, Alexander S Bradley, Daniel L Eldridge, and David T\nJohnston. Determination and application of the equilibrium oxygen isotope effect\nbetween water and sulfite. Geochimica et Cosmochimica Acta, 125: 694–711, 2014.\nReviewer #3 (Remarks to the Author):\nReview: The barite record of the past seawater oxygen isotope composition\nHan et al\nIn this paper the authors address the problem of the evolution of the oxygen\nisotopic composition of the ocean through the measurement of the oxygen and sulfur\nisotopic composition of nodular and bedded barite deposits from six time periods in\nthe Phanerozoic. Whether or not the oxygen isotopic composition of the ocean has\nchanged over time is a question that has frustrated the research community for\ndecades, with different mineral reconstructions coming to different and conflicting\nanswers. The holy grail of this would be if we could resolve how the oxygen isotopic\ncomposition of the ocean has changed we would be able to directly reconstruct how\ntemperature has changed.\nThe authors approach this fundamental question by using oxygen isotope ratios\nin sulfate, combined with the sulfur isotope ratios in sulfate. The premise of this is\nthat during microbial sulfate reduction, the oxygen isotope composition of sulfate\napproaches a value where all oxygen atoms have exchanged with water through\nintermediate valence state sulfur species (likely mostly sulfite), but the sulfur isotopic\ncomposition of sulfate can continue to increase. This plateau in the oxygen isotopic\ncomposition of sulfate during microbial sulfate reduction has been seen in a plethora\n14\nof modern marine environments and laboratory cultures. In theory, if the oxygen\nisotopic composition of the water changed (in this case ancient ocean seawater) then\nthe oxygen isotopic composition of the sulfate preserved in diagenetic barite nodules\nand beds would also change. This is, indeed, what the authors find.\nI strongly recommend this paper for publication. I will be honest, I have wanted\nto do something like this for a long time, and am pleased that someone has done it. I\nthink it adds information to our growing understanding of this topic and I think it is an\nimportant contribution. It is also provocative and I think Nature Communications is\nthe right journal for this.\nHowever, there are places where this manuscript needs some work and I’d like\nthis to be addressed before publication. The paper seems to have been written for a\nmuch shorter format journal and could use clarification and expansion in places.\nThere are editorial comments throughout. I will highlight these below. There are a mix\nof small comments and larger comments here.\n1. Line 17 – “Sulfate’s oxygen resists alteration under most burial conditions…”\n– this is awkwardly phrased. The oxygen atoms in the sulfate molecule do not\nexchange with water easily in most environmental settings, and rarely achieve\nisotopic equilibrium with ambient water”.\nReply: Thank you. We have replaced the sentence with your suggested one.\n2. Line 21 – I’d be clearer here. This plateau d18O value reflects the isotopic\nSO4\nequilibrium between intermediate valence state sulfur species and water and thus\nrecords changes in the d18O of the water.\nReply: See our general response #1.\n3. Line 35 and 36 – rather than ‘elevates’ and ‘depletes’ (which can be confused\nfor increasing or decreasing the isotope content of one or the other isotope) I’d say\n‘increases’ and ‘decreases’ the d18Osw.\nReply: Good suggestions. Revised.\n4. Line 42- You could also include Turchyn et al., 2013 (GCA) which showed\nthat hydrothermal vein minerals also suggest a 4‰ increase in the d18O of the ocean.\nTurchyn, A. V., Alt, J. C., Brown, S. T., DePaolo, D. J., Coggon, R. M., Chi,\nG., ... & Skulski, T. (2013). Reconstructing the oxygen isotope composition of late\nCambrian and Cretaceous hydrothermal vent fluid. Geochimica et cosmochimica acta,\n123, 440-458.\nReply: Yes, thanks. The work is now added at line 44 where we introduced the\n“frustrating” δ18O issue.\nseawater\n5. Line 42 – I’d avoid the colloquial ‘carbonates’ ‘cherts’ – in favor of carbonate\nminerals, chert, etc.\nReply: Revised.\n6. Line 44 – alteration should be singular\n7. Line 46 – to fit the bill is a bit colloquial, might choose another phrasing\nReply: We have changed the “While iron oxides appear to fit the bill” to “While\niron oxides are promising candidates”.\n8. Line 47 – silicates – change to silicate minerals\nReply: Changed.\n9. Line 50 – again ‘silicates’ and ‘carbonates’ should be silicate minerals and\ncarbonate minerals\nReply: Changed.\n10. Line 56 – this sentence should have a reference\nReply: A new reference, Banner and Hanson (1990) was added at line 60.\nBanner, J. L., & Hanson, G. N. (1990). Calculation of simultaneous isotopic and\ntrace element variations during water-rock interaction with applications to carbonate\ndiagenesis. Geochim. Cosmochim. Acta 54, 3123-3137.\n11. Line 57-59 – Rennie and Turchyn 2014 (L&O methods) did experiments on\nthe timescale of exchange and would be a good reference to include here.\nRennie, V. C., & Turchyn, A. V. (2014). Controls on the abiotic exchange\nbetween aqueous sulfate and water under laboratory conditions. Limnology and\nOceanography: methods, 12(4), 166-173.\nReply: A great suggestion. Added at line 63.\n12. Line 64 – why at low concentrations? I’d start the sentence with Sulfate…\nthe exchange starts right away, you just see the plateau when enough of the sulfate has\ncycled through the cell.\nReply: Agree. We were trying to say that at a lower sulfate concentration the\nreversibility may increase more effectively than at a higher sulfate concentration\nduring microbial sulfate reduction. To avoid distracting the reader, we have removed\nthese words.\n13. Line 66 – This comes up throughout the text and I would just urge caution. It\nis not equilibrium between sulfate and water – it is equilibrium between intermediate\nvalence state sulfur species and water that is reflected in a constant value of d18O of\nsulfate outside the cell. Ben Brunner wrote the best paper on this that really explained\nit well.\nBrunner, B., Einsiedl, F., Arnold, G. L., Müller, I., Templer, S., & Bernasconi, S.\nM. (2012). The reversibility of dissimilatory sulphate reduction and the cell-internal\nmulti-step reduction of sulphite to sulphide: insights from the oxygen isotope\ncomposition of sulphate. Isotopes in environmental and health studies, 48(1), 33-54.\nIn this paper and other work by Brunner they suggest that we call it an apparent\nisotope fractionation between sulfate and water. In modern sedimentary pore fluids it\n16\ncan range from 24-30permil, and it is NOT the value that sulfate would achieve if it\nwere to exchange its isotopes with water. I think you should explain this better\nbecause it is not something that people would understand intuitively. The fact that the\nvalue changes could be temperature (as you discuss later) but could also be that the\nequilibrium changes with rates as suggested by a few papers. I would strongly\nencourage you NOT to term this isotope fractionation between sulfate and water as\nthis is not what this is.\nReply: Please refer to our general response #1.\n14. Line 68 – might rather than intermediate sulfite say ‘intermediate valence\nstate sulfur species sulfite’\nReply: Agreed and revised.\n15. Line 74 – 76 – I’d be sure to include the Brunner reference (and look around,\nhe has had several papers on this – they are very important papers for this idea).\nReply: Yes, Brunner and his colleagues have provided important insights to the\nreversibility issue during microbial sulfate reduction (Ben calls himself “the\nreversibility guy”). There is no conflict between ours and their view. We cited their\npapers at line 72 and 75. Please also refer to our general response #1.\n16. Line 78-80 – Again, same comment as above (‘Line 66’). This is not the\nfractionation between sulfate and water. That is part of the reason why it varies. It is\nimportant that you clarify this.\nReply: Please refer to our general response #1.\n17. Line 86 – I’d use ‘reflect’ rather than ‘record’. It doesn’t record the d18O of\nthe water. It does reflect any large changes in the d18O of the water.\nReply: Revised.\n18. Line 86-87 – Might remove this mention of temperature – as it intrigued me\nhow you would determine this, and then as it turns out later you just assume that they\nare all at similar temperatures (which I agree, I doubt the temperature changed\ndramatically except the fact that the Mesozoic deepsea temperatures might have been\n15 degrees warmer than the Paleozoic or the Cenozoic).\nBut you should acknowledge that the d18O of pore fluids is not the same always\nas the d18O of the ocean. This also explains some of the variability in the d18O of\nsulfate in modern pore fluids. The d18O of pore fluid water tends to decrease by 4-\n5permil due to reaction with underlying basalt.\nReply: The statement about temperature assumptions has been removed from the\nIntroduction section. See our general response #3.\nSince all barite samples were deposited in shallow water or shallow pore-water,\nthe fluid water is essentially the contemporaneous seawater. Yes, when it gets >1000\nm or much deeper in sediments, the pore-water δ18O may decrease by 4-5‰ due to\nreaction with underlying basalt, but our barite beds or concretions did not form at that\n17\ndepth.\n19. Line 100 – this needs a reference\nReply: Added.\nHan, T., Peng, Y. & Bao, H. Sulfate-limited euxinic seawater facilitated\nPaleozoic massively bedded barite deposition. Earth Planet. Sci. Lett. 582, 117419\n(2022).\n20. Line 109-110 – you mean organoclastic microbial sulfate reduction (I think\nyou mean remineralisation of organic matter) – I might just be clearer and say\noxidation rather than mineralisation.\nReply: Accepted and Revised.\n21. Line 142-147 – Again you should be careful using alpha in this way as it is\nNOT a true exchange of oxygen atoms in sulfate and water. I can’t remember offhand\nhow Brunner thought it best to do this but alpha-apparent might work.\nReply: Please refer to our general response #1.\n22. Line 147-155 – See my comment above about temperature. Yes the\ntemperature is low but for the samples from the Mesozoic it could be warmer\nalthough we don’t have a particularly good sense of deep ocean temperature changes\npre Mesozoic. But you must include a discussion of how pore fluid d18O changes. Dan\nSchrag studied this all the way back in the 1990’s.\nSchrag, D. P., DePaolo, D. J., & Richter, F. M. (1995). Reconstructing past sea\nsurface temperatures: Correcting for diagenesis of bulk marine carbonate. Geochimica\net Cosmochimica Acta, 59(11), 2265-2278.\nReply: Schrag et al. (1995) probably dealt with a much higher frequency event or\nshorter-term change (Quaternary glacial-interglacial seawater δ18O change) than what\nour barite beds or nodules reflected. Please refer to our general response #3.\n23. Line 163-165 – Figure 2 is good but a Figure 3 could be good which shows a\ntemporal plot of changes in the d18O of the ocean suggested by your data. I also don’t\nthink the data from the Silurian is different to the data from the Ordovician and\nDevonian – given we see variability of 4-5permil across modern sedimentary pore\nfluids, we can explain a 2 permil difference between these two time periods pretty\neasily. It could be good to add onto here other proposed seawater curves for the\nPhanerozoic (add onto a hypothetical Figure 3).\nReply: See our specific response #18 to your concern above our barite data being\ndifferent from the 4-5‰ variability across modern sedimentary pore fluids.\nBecause the barite depositional temperature issue remains as we illustrated in our\ngeneral response #3, we intend not to emphasize this result and therefore displaying\nthe result in a supplemental figure is appropriate at this time. The new Figure S7\n(copied and pasted below) in Supplementary Information is our response to your\nsuggestion. Please see our general response #3 above.\nseawater\ngeochemical modeling. Theoretical equilibrium oxygen isotope fractionation factor (i.e., α ) of\nsulfate-water\n1.024 at 20℃ to 1.022 at 28℃ were used to calculate the δ18O value based on the maximum\nseawater\nδ18O value for each period (see explanation in the main text). The temperature assumptions are\nbarite\ndiscussed in detail in Supplementary Text 4. The late Paleozoic rise in δ18O value as is apparent in\nseawater\nour barite record closely resembles the trend in the carbonate proxy21,22, but differs from those\ninferred by geochemical modeling23 or Fe oxide records24,25 which indicate an early Paleozoic\nδ18O rise (e.g., ~6‰).\nseawater\n24. Line 169 – comment on carbonates similar to above\nReply: Revised.\n25. Line 173 – I think you have the words to expand this a bit.\nReply: Because of the temperature issue suffered by the barite and other mineral\nproxies (see our general response #3), we are not sure about the late Paleozoic rise of\nδ18O and we prefer not to emphasize this finding and therefore provided only\nseawater\nconcise discussion on the possible causes.\nIn line 189-196 of the revised version now it reads: “A late Paleozoic rise of δ18O\nseawater\nwould require a dramatic increase in the flux of high-temperature relative to surface-temperature\nrock-water alteration. We can speculate potential causes for the rise: 1) a deepening of ocean depth,\nwhich enhanced seawater penetration and hydrothermal fluid circulation2,10, 2) sediment “blanketing”\non land and ocean crust, which decreased low-temperature alteration flux2,10, 3) a decrease in the rate\nof authigenic clay formation16, and 4) the oxidation of the deep ocean as mentioned for the\nNeoproterozoic oxygenation event15.”\nReviewer #4 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed\nreports. This is part of the Nature Communications initiative to facilitate training in\npeer review and to provide appropriate recognition for Early Career Researchers who\nco-review manuscripts.\nReply: We sincerely appreciate your constructive comments. Senior author\ndoing peer reviewing for many years. That’s one of the nice things of the Nature\nGroup.\n(Our responses are in blue)\nReviewer #1 (Remarks to the Author):\nThe authors have adequately addressed all my concerns and improved the quality of the\nmanuscript. I would like to recommend it for publication in Nature Communications.\nReply: Thanks.\nReviewer #2 (Remarks to the Author):\nIntroduction\nThe authors have provided extensive responses to the reviewers’ comments and have\nrevised their manuscript accordingly. While we appreciate the effort made to address\nthe points raised, several responses remain unconvincing or insufficiently justified. In\nthe following document, we outline our responses to each major issue raised, focusing\non both content and clarity. Our aim is to ensure that the final version of the manuscript\nrobustly addresses concerns regarding post-depositional alteration, temperature\nassumptions, and the detailed treatment of data.\n1.1 Equilibrium Fractionation and the Role of Intermediate Species\n• Response Overview: The authors state that the plateau δ18O value reflects\nequilibrium between sulfate and water, mediated through enzyme-catalyzed reversible\nreactions involving APS and sulfite. They refer to both theoretical predictions and\nlaboratory results. The authors have added a thorough explanation (main text, lines 75–\n90) clarifying why αSO 2- −H O does not affect δ18O , addressing our suggestion\n3 2 sulfate\nthat such clarification would improve the manuscript’s clarity.\n• Critical Comment: Although this additional explanation enhances the discussion,\nit remains largely qualitative. The manuscript would benefit from a quantitative\nassessment of the role of intermediate species. In particular, providing additional data\nor model-based comparisons that substantiate the assumption of independence for\nαSO 2- −H O would greatly strengthen the mechanistic argument.\n3 2\nReply: The logic flow of our story starts with a premise or a standing ground. That is,\nas the corresponding δ34S increases, the plateauing of the δ¹⁸O values is a\nsulfate sulfate\nmanifestation of the δ¹⁸O value approaching equilibrium with the δ¹⁸O of the\nsulfate\noverwhelming ambient water.\nWith that premise, the question how the equilibrium was achieved is a separate\nresearch subject. It is a relevant subject when we are to explore the kinetics of oxygen\nisotope exchange during the microbial mediated sulfate-water oxygen isotope\nequilibrium. When it comes to the non-equilibrium scenarios, the 18α does\nSO3 2--H2O\nmatter and it matters in two specific ways: 1) the α value is temperature sensitive;\nand\n2) the rate of SO 2-−H O oxygen isotope exchange is competing with the rate of SO 2-\n3 2 3\nbackward oxidation to sulfate as well as the rate of SO 2- forward reduction to sulfide,\n3\n1\nall mediated by enzymes.\nYour suggestion of a “quantitative assessment of the role of intermediate species”\ntherefore inspired us to add the following sentences at Line 88-90: “Otherwise, we\nwould not observe a plateauing δ18O value as the corresponding δ34S value\nsulfate sulfate\nincreases.Non-equilibrium scenarios would exhibit variable δ18O/δ34S slopes on the\nδ18O–δ34S trajectories32.”\nWe maintain, however, that 18α is not 18α .\nSO3 2--H2O SO4 2--H2O\n1.2 Post-Depositional Alteration and Data Selection Criteria\n• Response Overview: The authors assert that their petrographic screening and\nthe δ18O–δ34S trajectory approach effectively eliminate post-depositional alteration\nissues. They argue that the plateau in the δ18O data is robust against\nbarite\nperturbations and that the maximum value in the plateau region represents equilibrium\nwith ambient water.\n• Critical Comment: We respectfully disagree with the notion that the maximum\nvalue adequately represents equilibrium with ambient water. Our concern is that\nthe maximum value might be influenced by outlier behavior or experimental noise\nrather than reflecting the true equilibrium state. Instead of simply taking the\nhighest measured value, a more rigorous statistical treatment of the plateau is\nrecommended. Methods such as curve-fitting or segmented regression techniques,\nalong with an explicit consideration of measurement uncertainty, would allow for\nan objective definition of the plateau. Additionally, the caption in Figure 3 stating\n“The maximum δ18O values in the plateau region is chosen as plateau δ18O value”\nbarite barite\nis misleading—a maximum is not equivalent to a plateau. A more careful\nmathematical treatment of the data is required.\nFinally, the claim that SEM backscattered electron (BSE) images can unequivocally\ndetermine whether a barite sample—or any other sample, for that matter—\nhas undergone diagenesis appears to be overambitious. We recommend tempering\nthis assertion and presenting the SEM BSE results as supportive evidence\nrather than definitive proof of diagenetic alteration. Please discuss the alternatives.\nReply: We agree with the reviewer that petrographic screening cannot eliminate the\npost-depositional altered barite when picking samples. In fact, our δ18O–δ34S trajectory\napproach is insensitive to barite samples that may have been later altered because those\nlater altered data points would deviate from the plateauing δ18O–δ34S trajectory. The\nonly reason we did petrographic screening is to avoid sampling the apparent later\nrecrystallized or vein barite.\nTo ensure clarity, we have revised the sentences on SEM observation at Line 105-\n107 to read “Petrographic examinations of the sedimentary barite deposits by scanning\nelectron microscope were conducted to characterize their mineral assemblage and\nparagenesis (Figs. S1-S6).” and at Line 139-142 “Petrographic examination was\nconducted to exclude apparent late diagenetic barite, e.g., barite veins. As we\nemphasized, petrographic examination cannot guarantee that we selected only the\nunaltered original barite. It is the δ¹⁸O-δ³⁴S trajectory that filters out post-depositional\nalteration if any.”\nexperimental noise rather than reflecting the true equilibrium state”, we fully agree\nwith the reviewer’s point. Then, why didn’t we use some statistical scheme to determine\na plateauing δ¹⁸O ? This is because the barite samples were deposited in a time-\nsulfate\nspace heterogeneous oceanic environment where seawater sulfate underwent varying\ndegrees of sulfate reduction and mixing, resulting in a broad range of δ18O and δ34S\nvalues. The measured δ18O and δ34S pair values in the many barite samples thus are\nindependent and lack a clear physical relationship among them. For example, the\noccasionally observed dips in the δ¹⁸O at the highest corresponding δ34S values may\nsulfate\nor may not be due to a mixed-in of a small amount of normal sulfate or due to other\nunknown factors.\nFor now, selecting the maximum δ¹⁸O value within the plateau region is a simple\nbarite\nmeasure that allows a trajectory to be improved and revised with new data addition in\nthe future. This is also the reason we refrained from speculating in the manuscript too\nmuch on the possible rising of the δ18O of seawater since the late Paleozoic, as our data\napparently indicated.\nWe have revised the sentences at Line 168-173 to clarify. They now read “Further\nstatistical treatment in a plateau region would have to assume certain relationship\nbetween the δ18O and δ34S of the barite samples, which is not necessarily true in our\nsample set. Therefore, for now we selected the maximum δ18O value in a plateau\nbarite\nregion to represent the equilibrium δ18O with seawater during a particular time\nbarite\nperiod, allowing the trajectory to be enhanced with new data addition in the future.”\nThe most important message of this study is that now we have a sulfate δ18O-δ34S\ntrajectory approach that allows us to build a proxy for seawater δ18O history, a proxy\nthat is diagenesis-proof, unlike any other mineral proxies.\n1.3 Temperature Sensitivity and the Use of a Constant Fractionation Factor\n• Response Overview: The authors maintain the use of a constant fractionation\nfactor (α of 1.024 at 20°C) based on previous literature. They argue\nsulfate-water\nthat the shallow shelf depositional settings and low paleolatitude range support a\nsimilar formation temperature for all sample sets.\n• Critical Comment: The authors state that “low paleolatitude settings support a\nsimilar formation temperature for all six time periods” (main text, line 183). However,\nsince a thermocline is often present over continental shelves, these settings could\nencompass a range of formation temperatures. This introduces an additional\nsource of uncertainty which should be acknowledged. The manuscript would be\nimproved by discussing this potential variability and, if possible, assessing its impact\non the calculated fractionation factors.\nReply: We emphasized in the previous version that this assumption does not guarantee\nthat all the six sets of barite samples formed under the same temperature. For example,\nwe had sentences at Line 190-193 like “If indeed the barite formation temperature for\nall the six periods are more or less similar, the ~4‰ late Paleozoic rise in plateau\nδ18O values indicate a similar degree of δ18O values change in seawater …”. In\nbarite\naddition, we proposed that samples from different paleolatitudes can help to determine\n3\nif temperature effect on the plateau δ18O is consistent.\nsulfate\nNo further revisions have been made to the text on this issue.\nIn summary, the revised manuscript demonstrates significant progress in addressing\nearlier concerns; however, several issues remain that warrant further attention. The\ncurrent approach to defining the plateau in δ18O data is insufficiently rigorous and\nbarite\nmay be susceptible to outliers and noise, calling for a more systematic statistical\ntreatment. Finally, the assumption of a constant fractionation factor across variable\ndepositional temperatures should be revisited in light of potential temperature gradients\nover continental shelves.\nOverall, we support publication of this manuscript provided that the authors adequately\naddress these issues. The lack of an apparent plateau for most of the geological\nperiods shown in Figure 3 (e.g., Late Devonian) requires the strengthening of the quantitative\nframework and explicitly acknowledging the limitations of this work. It will enhance\nthe scientific robustness and overall impact of it.\nReply: See our response to your comments above.\nReviewer #3 (Remarks to the Author):\nI am generally happy with the response to the reviewers comments and to my comments.\nI would quibble a bit with Response 1. The implication that it is a fractionation between\nsulfate and water implies that there is a chemical reaction like:\nS16O + H 18O <--> S18O16O + H 16O\n4 2 3 2\nThat is in sulfate you cleave a S-O bond and allow the oxygen atoms to exchange with\nwater. That doesn't happen. As you say in response 1, it is because of reversibility of\nenzyme catalyzed reactions inside and on the cell membrane that you can cleave the S-\nO bond in extracellular sulfate and see a signal of a change in the d18O of the water. I\nmight consider calling this an 'apparent isotope fractionation between sulfate and water'.\nOtherwise I think this is good to go.\nReply: Please see the beginning part of our response to Reviewer #2.\nYes, you are correct in that if the above equation is an elementary step, that doesn’t\nhappen. The actual oxygen isotope exchange between sulfate and water involves many\nlinked steps and even branched steps (e.g., sulfite-water exchange). Going from sulfite\nto sulfate (i.e., the backward oxidation) may occur via enzyme-mediated electron\ntransfer inside the cell, not necessarily exclusively extracellular.\nOur understanding or terminology is that for a given compound involved in a reaction,\nif the forward and backward reactions go through the same sets of transition states,\nwhen the two rates are the same, we call it “in equilibrium”. If the two rates are not the\nsame, we call it “in non-equilibrium”, not “in apparent equilibrium”. Calling it\n“apparent isotope fractionation” is ok. However, if the forward and backward reactions\ngo through their own pathways with two different sets of transition states, when the two\n4\nrates are the same, we call it “in steady-state”. If the two rates are not the same, we call\nit “in non-steady state”. The use of these terms has been quite loose in the community\nand often different communities have different and often opposite meanings. Thank you\nfor bringing up this discussion.\nNo further revisions have been made to the text on this issue.\nReviewer #4 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nReply: Thank you for your constructive input.\nSeawater Oxygen Isotope Composition\nJanuary 29, 2025\nSummary of the Paper\nThis manuscript, titled ”The Barite Record of the Past Seawater Oxygen\nIsotope Composition,” aims to explore the oxygen isotope composition of\nseawater (δ18O ) through the analysis of sedimentary barite deposits\nseawater\nfrom various periods of the Phanerozoic Eon. The authors suggest that\nthe plateau δ18O values in barite can serve as a proxy for historical\nsulfate\nseawater δ18O values, providing insights into the global ocean’s temperature\nand chemical history.\nStrengths of the Paper\nThe manuscript presents a significant approach to studying the history of\nseawater oxygen isotopes using barite deposits. The proposed proxy for sea-\nwater δ18O using plateau δ18O is an interesting and promising method,\nsulfate\nparticularly given the stability of sulfate under most burial conditions. The\ndata presented, including paired δ18O and δ34S measurements, offer valuable\ninsights into the past variations in seawater composition.\n• Thedatacollectionisextensive, coveringsixperiodsofthePhanerozoic\nEon, which adds temporal depth to the analysis.\n• The use of well-preserved syngenetic barite samples with petrographic\nscreening is a strength of the study, reducing potential biases from\npost-depositional alterations (which we urge the authors to share more\ndetailsaboutandnotjustwiththe(one)supplementaryfigurecurrently\nincluded).\n1\n• The methodology is sound, and the measurements were carefully cali-\nbrated using international standards.\nMajor Concerns and Suggestions for Improve-\nment\nDespite the strengths, there are several areas where the manuscript can be\nimproved:\n1. Lack of Discussion on Post-Depositional Alteration\nAlthough the authors claim that the barite samples are well-preserved and\nthe δ18O − δ34S trajectory is independent of post-depositional alteration\n(maintext; lines 131-134), the manuscript could benefit from a more de-\ntailed discussion on potential post-depositional effects, especially in relation\nto microbial sulfate reduction (MSR). While the study mentions the stability\nof sulfate oxygen, it is important to better address how potential alteration\nmechanisms in the sediments may influence the δ18O values.\nsulfate\nRecommendation: A more in-depth exploration of post-depositional\nprocesses and their potential impact on the δ18O values should be incor-\nsulfate\nporated. Furthermore, asensitivityanalysisontheeffectofpost-depositional\nalteration would strengthen the conclusions.\n2. Clarity and Precision of the Results\nSomepartsofthemanuscript, especiallyinthe”Theδ18O andδ34S ofbarite”\nsection, could benefit from clearer presentation. For example, the figures\nshowing the δ18O − δ34S data (Figures 2A, 2B, etc.) are referenced in the\ntext, but a more detailed explanation of the trajectory and the specific sig-\nnificance of the plateau δ18O values could help readers understand the\nsulfate\nimplications of the data more effectively. In addition, Figure 1 schematic\nexplanation must be grounded by citing actual references that support this\nsimplified cycle as presented.\nRecommendation: The authors should clarify the interpretation of the\nplateau values in the figures and ensure that the text provides a detailed\nexplanation of how these values are derived and their significance for under-\nstanding the history of seawater oxygen isotopes. In addition, none of the\nmarkers are presented with uncertainty bars, which is really ”screaming” to\nbe addressed. Finally, the value of the plateau seems to be determined arbi-\ntrarily, and at certain points is just seemed to be wrong (e.g., Figure 2A). It\n2\nis strongly suggested that the authors use a proper mathematical framework\nto determine the plateau value and elaborate more on captions of all figures.\n3. Temperature Sensitivity of the Fractionation Factor\n3a Variability of Ocean Temperature Through Time\nThe study assumes a constant fractionation factor (α ) of 1.024 at\nSO2\n4\n−−H2O\n20°C for the entire study period following reference 24 of the maintext1.\nGiven the potential variability of ocean temperatures throughout Earth’s\nhistory, as to the temperature gradient in the modern ocean, this assumption\ncould introduce significant errors, especially when extrapolating the data to\nearliergeologicalperiods. Theinfluenceoftemperatureontheoxygenisotope\nfractionation between sulfate and water is acknowledged, but the manuscript\ndoes not fully explore how this assumption might affect the derived seawater\nδ18O values.\nRecommendation: A discussion on the uncertainty introduced by as-\nsuming a constant fractionation factor over geological timescales should be\nincluded. Additionally, further validation of the temperature assumption\ncould improve the robustness of the findings (see point 3b below).\n3b The Effect of Barite Deposit Type and Depositional\nDepth on δ18O\nsulfate\nIn Figure 2 of the maintext, we observe a trend that is not discussed in\nthe study: the lower δ18O values, around 18‰ of the Cambrian, Or-\nsulfate\ndovician, and Devonian (maintext; Figure 2C, 2E, 2F, lines 122-126) are\nassociated with bedded barites, while the higher values, around 20‰, of the\nSilurian, Carboniferous, and Cretaceous are associated with barite nodules\n(maintext; Figure2A,2B,2D,lines122-126). Giventhata2‰differencecan\nbe caused by a 10◦C temperature difference in a sulfate-water system, based\non the fractionation factor estimates of reference 24 of the maintext1, it is\nimportant to consider the depth of the water in which the barites formed, not\njust the latitude. This is because barite often forms in the thermocline zone,\nwhere the temperature drops rapidly, and a 10◦C temperature difference can\neasily occur within this zone2. Although the study provides paleolatitude\nestimates and detailed general lithological descriptions of the formations in\nthe supplementary information, it does not fully address the potential water\ndepth differences between the samples from different formations. For exam-\nple, if the bedded barites have formed in deeper water compared to barite\nnodules in this exact case, this could potentially explain why the bedded\n3\nbarite samples show lower δ18O values. If this is the case for the barites in\nthe study, the δ18O values may be partially influenced by differences in\nsulfate\nthe depth of seawater they formed in, making it difficult to disentangle this\nfactor from the influence of δ18O . Currently, the manuscript does not\nseawater\nfully address this potential uncertainty.\nRecommendation: The manuscript could benefit from a more detailed\ndescription of the layers hosting the barites, especially with respect to the\nwaterdepthanddepositionalenvironment. Asensitivityanalysisquantifying\nthe effect of water depth uncertainty on the δ18O would strengthen the\nsulfate\nmanuscript. The authors are suggested to address and discuss the different\noxygen isotopes values yielded by the two barite types and reason why (or\nwhy not) the sedimentary bedded and sedimentary nodular barites could\nexhibitdifferentoxygenisotopesignalsdespitebeingdepositedfromseawater\nwith the same δ18O.\n4. The Influence of Terrestrial Input on δ18O\nsulfate\nLines 131-134 of the maintext briefly discuss the potential influence of me-\nteoric water on δ18O after the deposition, but the manuscript could\nsulfate\nbenefit from a more detailed discussion on potential terrestrial effects during\ndeposition. For example, a new study3 showed that the oxygen isotopes of\nsulfates deposited in shallow marine environments or restricted basins reflect\nthe influence of meteoric water with more negative δ18O. One can raise the\nquestion; could the different values of the plateaus be the result of mixed\nsourced parent solution sulfate (meteoric, marine, etc)? In this case, the\nplateau δ18O value differ between sections solely due to varying rates of ter-\nrestrial sulfate influx, potentially related to factors such as distance from the\ncoastline?\nRecommendation: We suggest the authors to include a discussion on\nthe potential effect of terrestrial sulfate influx on the plateau δ18O and ex-\nplicitly add the needed information to the exisiting supplementary tables.\nThis would enhance the clarity of the manuscript and strengthen the case\nfor the proxy.\n5. Discussion on Sulfite-Water Fractionation Factor\nThestudyusesthesulfate-waterfractionationfactorfromreference1 forback-\ncalculating δ18O (maintext; lines 161-162). Several studies emphasized\nseawater\nthat δ18O values rely heavily on the oxygen isotope fractionation be-\nsulfate\ntween intermediates like sulfite and water4–7, and Figure 1 of the maintext\n4\nalsohighlightstheimportanceofthisexchangereaction. Currently, thestudy\ndoes not address the effect of α on δ18O .\nSO2\n3\n−−H2O sulfate\nRecommendation: We suggest that the authors include a discussion\nexplaining why they believe α has no effect on δ18O , as this\nSO2−−H2O sulfate\n3\ninterpretation may not be intuitive to all readers.\nMinor Comments\n• The abstract could be shortened to make it more concise and directly\nhighlight the most important findings.\n• Figure 1 is helpful, but a more detailed caption would be beneficial to\nexplain the sulfur and oxygen isotope fractionation pathway in micro-\nbial sulfate reduction more clearly.\n• In Figure 2, the axis values and spaces are not uniform between the\ndifferent panels and it would be very helpful for the readers if it would\nbe.\n• In several instances, the authors reference previous work to support\nclaims that are not consistent with the findings or conclusions of the\noriginal articles. We strongly recommend reviewing all citations to\nensure that the references are accurately represented and aligned with\nthe original studies.\n• The manuscript would be strengthened by including an additional sup-\nplementary figure that compares the current findings with existing oxy-\ngen isotope records. This enhancement would provide readers with a\nclearer context and facilitate a more comprehensive understanding of\nthe study’s contributions.\nConclusion\nIn conclusion, this manuscript has the potential to serve as a valuable contri-\nbution to our understanding of the history of seawater oxygen isotopes. The\nnovel approach using barite deposits as a proxy for δ18O is promising\nseawater\nand the data presented are compelling. However, some key aspects of the\nanalysis require further clarification and discussion, especially regarding the\nassumptions about post-depositional alteration and temperature sensitivity,\nand proper mathematical framework. With these revisions, the manuscript\ncould become a significant contribution to the field.\n[1] Richard E Zeebe. A new value for the stable oxygen isotope fractionation\nbetween dissolved sulfate ion and water. Geochimica et Cosmochimica\nActa, 74(3):818–828, 2010.\n[2] Lynne D Talley. Descriptive physical oceanography: an introduction. Aca-\ndemic press, 2011.\n[3] Peter W Crockford, Anna Rose Waldeck, Andrey Bekker, Marcus Kunz-\nmann, Rachita Ghosh, Prosenjit Ghosh, Nina Sergeeva, Sergey Michurin,\nItay Halevy, and David Johnston. Depositional controls on the preserva-\ntion of’17o signatures in sedimentary sulfate. Authorea Preprints, 2025.\n[4] Peter W Crockford, Marcus Kunzmann, Andrey Bekker, Justin Hayles,\nHuiming Bao, Galen P Halverson, Yongbo Peng, Thi H Bui, Grant M\nCox, Timothy M Gibson, et al. Claypool continued: Extending the iso-\ntopicrecordofsedimentarysulfate. Chemical Geology, 513:200–225, 2019.\n[5] Alexandra V Turchyn, Volker Bru¨chert, Timothy W Lyons, Gregory S\nEngel, Nurgul Balci, Daniel P Schrag, and Benjamin Brunner. Kinetic\noxygen isotope effects during dissimilatory sulfate reduction: a combined\ntheoretical and experimental approach. Geochimica et Cosmochimica\nActa, 74(7):2011–2024, 2010.\n[6] Inigo A Mu¨ller, Benjamin Brunner, Christian Breuer, Max Coleman, and\nWolfgang Bach. The oxygen isotope equilibrium fractionation between\nsulfite species and water. Geochimica et Cosmochimica Acta, 120:562–\n581, 2013.\n[7] Scott D Wankel, Alexander S Bradley, Daniel L Eldridge, and David T\nJohnston. Determination and application of the equilibrium oxygen iso-\ntope effect between water and sulfite. Geochimica et Cosmochimica Acta,\n125:694–711, 2014.\n(“The Barite Record of the Past Seawater Oxygen\nIsotope Composition”)\nReviewer 2\nApril 11, 2025\nIntroduction\nThe authors have provided extensive responses to the reviewers’ comments and have\nrevised their manuscript accordingly. While we appreciate the effort made to address\nthe points raised, several responses remain unconvincing or insufficiently justified. In the\nfollowing document, we outline our responses to each major issue raised, focusing on both\ncontent and clarity. Our aim is to ensure that the final version of the manuscript robustly\naddresses concerns regarding post-depositional alteration, temperature assumptions, and\nthe detailed treatment of data.\n1.1 Equilibrium Fractionation and the Role of Intermediate Species\n• Response Overview: The authors state that the plateau δ18O value reflects equi-\nlibrium between sulfate and water, mediated through enzyme-catalyzed reversible\nreactions involving APS and sulfite. They refer to both theoretical predictions and\nlaboratory results. The authors have added a thorough explanation (main text,\nlines 75–90) clarifying why α does not affect δ18O , addressing our\nSO2\n3\n−−H2O sulfate\nsuggestion that such clarification would improve the manuscript’s clarity.\n• Critical Comment: Although this additional explanation enhances the discus-\nsion, it remains largely qualitative. The manuscript would benefit from a quan-\ntitative assessment of the role of intermediate species. In particular, providing\nadditional data or model-based comparisons that substantiate the assumption of\nindependence for α would greatly strengthen the mechanistic argument.\nSO2\n3\n−−H2O\n1.2 Post-Depositional Alteration and Data Selection Criteria\n• Response Overview: The authors assert that their petrographic screening and\nthe δ18O–δ34S trajectory approach effectively eliminate post-depositional alter-\nation issues. They argue that the plateau in the δ18O data is robust against\nbarite\nperturbations and that the maximum value in the plateau region represents equi-\nlibrium with ambient water.\n1\n• Critical Comment: We respectfully disagree with the notion that the maximum\nvalue adequately represents equilibrium with ambient water. Our concern is that\nthe maximum value might be influenced by outlier behavior or experimental noise\nrather than reflecting the true equilibrium state. Instead of simply taking the\nhighest measured value, a more rigorous statistical treatment of the plateau is\nrecommended. Methods such as curve-fitting or segmented regression techniques,\nalong with an explicit consideration of measurement uncertainty, would allow for\nan objective definition of the plateau. Additionally, the caption in Figure 3 stating\n”Themaximumδ18O valuesintheplateauregionischosenasplateauδ18O\nbarite barite\nvalue” is misleading—a maximum is not equivalent to a plateau. A more careful\nmathematical treatment of the data is required.\nFinally, the claim that SEM backscattered electron (BSE) images can unequiv-\nocally determine whether a barite sample—or any other sample, for that mat-\nter—has undergone diagenesis appears to be overambitious. We recommend tem-\npering this assertion and presenting the SEM BSE results as supportive evidence\nratherthandefinitiveproofofdiageneticalteration. Pleasediscussthealternatives.\n1.3 Temperature Sensitivity and the Use of a Constant Frac-\ntionation Factor\n• Response Overview: The authors maintain the use of a constant fractionation\nfactor (α of 1.024 at 20°C) based on previous literature. They argue\nsulfate-water\nthat the shallow shelf depositional settings and low paleolatitude range support a\nsimilar formation temperature for all sample sets.\n• Critical Comment: The authors state that ”low paleolatitude settings support a\nsimilar formation temperature for all six time periods” (main text, line 183). How-\never, since a thermocline is often present over continental shelves, these settings\ncould encompass a range of formation temperatures. This introduces an additional\nsourceofuncertaintywhichshouldbeacknowledged. Themanuscriptwouldbeim-\nproved by discussing this potential variability and, if possible, assessing its impact\non the calculated fractionation factors.\nIn summary, the revised manuscript demonstrates significant progress in addressing ear-\nlier concerns; however, several issues remain that warrant further attention. The current\napproach to defining the plateau in δ18O data is insufficiently rigorous and may be\nbarite\nsusceptible to outliers and noise, calling for a more systematic statistical treatment. Fi-\nnally, the assumption of a constant fractionation factor across variable depositional tem-\nperatures should be revisited in light of potential temperature gradients over continental\nshelves.\nOverall, we support publication of this manuscript provided that the authors ade-\nquately address these issues. The lack of an apparent plateau for most of the geological\nperiods shown in Figure 3 (e.g., Late Devonian) requires the strengthening of the quan-\ntitative framework and explicitly acknowledging the limitations of this work. It will\nenhance the scientific robustness and overall impact of it.\n2"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have adequately addressed all my concerns and improved the quality of the manuscript. I would like to recommend it for publication in Nature Communications.", "reviewer_2": "Please find the attached pdf file.", "reviewer_3": "I am generally happy with the response to the reviewers comments and to my comments. I would quibble a bit with Response 1. The implication that it is a fractionation between sulfate and water implies that there is a chemical reaction like:\nS16O4 + H218O <--> S18O16O3 + H216O\nThat is in sulfate you cleave a S-O bond and allow the oxygen atoms to exchange with water. That doesn't happen. As you say in response 1, it is because of reversibility of enzyme catalyzed reactions inside and on the cell membrane that you can cleave the S-O bond in extracellular sulfate and see a signal of a change in the d18O of the water. I might consider calling this an 'apparent isotope fractionation between sulfate and water'.\nOtherwise I think this is good to go.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to reviewer comments\n(Our responses are in blue)\nReviewer #1 (Remarks to the Author):\nThe authors have adequately addressed all my concerns and improved the quality of the\nmanuscript. I would like to recommend it for publication in Nature Communications.\nReply: Thanks.\nReviewer #2 (Remarks to the Author):\nIntroduction\nThe authors have provided extensive responses to the reviewers’ comments and have\nrevised their manuscript accordingly. While we appreciate the effort made to address\nthe points raised, several responses remain unconvincing or insufficiently justified. In\nthe following document, we outline our responses to each major issue raised, focusing\non both content and clarity. Our aim is to ensure that the final version of the manuscript\nrobustly addresses concerns regarding post-depositional alteration, temperature\nassumptions, and the detailed treatment of data.\n1.1 Equilibrium Fractionation and the Role of Intermediate Species\n• Response Overview: The authors state that the plateau δ18O value reflects\nequilibrium between sulfate and water, mediated through enzyme-catalyzed reversible\nreactions involving APS and sulfite. They refer to both theoretical predictions and\nlaboratory results. The authors have added a thorough explanation (main text, lines 75–\n90) clarifying why αSO 2- −H O does not affect δ18O , addressing our suggestion\n3 2 sulfate\nthat such clarification would improve the manuscript’s clarity.\n• Critical Comment: Although this additional explanation enhances the discussion,\nit remains largely qualitative. The manuscript would benefit from a quantitative\nassessment of the role of intermediate species. In particular, providing additional data\nor model-based comparisons that substantiate the assumption of independence for\nαSO 2- −H O would greatly strengthen the mechanistic argument.\n3 2\nReply: The logic flow of our story starts with a premise or a standing ground. That is,\nas the corresponding δ34S increases, the plateauing of the δ¹⁸O values is a\nsulfate sulfate\nmanifestation of the δ¹⁸O value approaching equilibrium with the δ¹⁸O of the\nsulfate\noverwhelming ambient water.\nWith that premise, the question how the equilibrium was achieved is a separate\nresearch subject. It is a relevant subject when we are to explore the kinetics of oxygen\nisotope exchange during the microbial mediated sulfate-water oxygen isotope\nequilibrium. When it comes to the non-equilibrium scenarios, the 18α does\nSO3 2--H2O\nmatter and it matters in two specific ways: 1) the α value is temperature sensitive;\nand\n2) the rate of SO 2-−H O oxygen isotope exchange is competing with the rate of SO 2-\n3 2 3\nbackward oxidation to sulfate as well as the rate of SO 2- forward reduction to sulfide,\n3\n1\nall mediated by enzymes.\nYour suggestion of a “quantitative assessment of the role of intermediate species”\ntherefore inspired us to add the following sentences at Line 88-90: “Otherwise, we\nwould not observe a plateauing δ18O value as the corresponding δ34S value\nsulfate sulfate\nincreases.Non-equilibrium scenarios would exhibit variable δ18O/δ34S slopes on the\nδ18O–δ34S trajectories32.”\nWe maintain, however, that 18α is not 18α .\nSO3 2--H2O SO4 2--H2O\n1.2 Post-Depositional Alteration and Data Selection Criteria\n• Response Overview: The authors assert that their petrographic screening and\nthe δ18O–δ34S trajectory approach effectively eliminate post-depositional alteration\nissues. They argue that the plateau in the δ18O data is robust against\nbarite\nperturbations and that the maximum value in the plateau region represents equilibrium\nwith ambient water.\n• Critical Comment: We respectfully disagree with the notion that the maximum\nvalue adequately represents equilibrium with ambient water. Our concern is that\nthe maximum value might be influenced by outlier behavior or experimental noise\nrather than reflecting the true equilibrium state. Instead of simply taking the\nhighest measured value, a more rigorous statistical treatment of the plateau is\nrecommended. Methods such as curve-fitting or segmented regression techniques,\nalong with an explicit consideration of measurement uncertainty, would allow for\nan objective definition of the plateau. Additionally, the caption in Figure 3 stating\n“The maximum δ18O values in the plateau region is chosen as plateau δ18O value”\nbarite barite\nis misleading—a maximum is not equivalent to a plateau. A more careful\nmathematical treatment of the data is required.\nFinally, the claim that SEM backscattered electron (BSE) images can unequivocally\ndetermine whether a barite sample—or any other sample, for that matter—\nhas undergone diagenesis appears to be overambitious. We recommend tempering\nthis assertion and presenting the SEM BSE results as supportive evidence\nrather than definitive proof of diagenetic alteration. Please discuss the alternatives.\nReply: We agree with the reviewer that petrographic screening cannot eliminate the\npost-depositional altered barite when picking samples. In fact, our δ18O–δ34S trajectory\napproach is insensitive to barite samples that may have been later altered because those\nlater altered data points would deviate from the plateauing δ18O–δ34S trajectory. The\nonly reason we did petrographic screening is to avoid sampling the apparent later\nrecrystallized or vein barite.\nTo ensure clarity, we have revised the sentences on SEM observation at Line 105-\n107 to read “Petrographic examinations of the sedimentary barite deposits by scanning\nelectron microscope were conducted to characterize their mineral assemblage and\nparagenesis (Figs. S1-S6).” and at Line 139-142 “Petrographic examination was\nconducted to exclude apparent late diagenetic barite, e.g., barite veins. As we\nemphasized, petrographic examination cannot guarantee that we selected only the\nunaltered original barite. It is the δ¹⁸O-δ³⁴S trajectory that filters out post-depositional\nalteration if any.”\nexperimental noise rather than reflecting the true equilibrium state”, we fully agree\nwith the reviewer’s point. Then, why didn’t we use some statistical scheme to determine\na plateauing δ¹⁸O ? This is because the barite samples were deposited in a time-\nsulfate\nspace heterogeneous oceanic environment where seawater sulfate underwent varying\ndegrees of sulfate reduction and mixing, resulting in a broad range of δ18O and δ34S\nvalues. The measured δ18O and δ34S pair values in the many barite samples thus are\nindependent and lack a clear physical relationship among them. For example, the\noccasionally observed dips in the δ¹⁸O at the highest corresponding δ34S values may\nsulfate\nor may not be due to a mixed-in of a small amount of normal sulfate or due to other\nunknown factors.\nFor now, selecting the maximum δ¹⁸O value within the plateau region is a simple\nbarite\nmeasure that allows a trajectory to be improved and revised with new data addition in\nthe future. This is also the reason we refrained from speculating in the manuscript too\nmuch on the possible rising of the δ18O of seawater since the late Paleozoic, as our data\napparently indicated.\nWe have revised the sentences at Line 168-173 to clarify. They now read “Further\nstatistical treatment in a plateau region would have to assume certain relationship\nbetween the δ18O and δ34S of the barite samples, which is not necessarily true in our\nsample set. Therefore, for now we selected the maximum δ18O value in a plateau\nbarite\nregion to represent the equilibrium δ18O with seawater during a particular time\nbarite\nperiod, allowing the trajectory to be enhanced with new data addition in the future.”\nThe most important message of this study is that now we have a sulfate δ18O-δ34S\ntrajectory approach that allows us to build a proxy for seawater δ18O history, a proxy\nthat is diagenesis-proof, unlike any other mineral proxies.\n1.3 Temperature Sensitivity and the Use of a Constant Fractionation Factor\n• Response Overview: The authors maintain the use of a constant fractionation\nfactor (α of 1.024 at 20°C) based on previous literature. They argue\nsulfate-water\nthat the shallow shelf depositional settings and low paleolatitude range support a\nsimilar formation temperature for all sample sets.\n• Critical Comment: The authors state that “low paleolatitude settings support a\nsimilar formation temperature for all six time periods” (main text, line 183). However,\nsince a thermocline is often present over continental shelves, these settings could\nencompass a range of formation temperatures. This introduces an additional\nsource of uncertainty which should be acknowledged. The manuscript would be\nimproved by discussing this potential variability and, if possible, assessing its impact\non the calculated fractionation factors.\nReply: We emphasized in the previous version that this assumption does not guarantee\nthat all the six sets of barite samples formed under the same temperature. For example,\nwe had sentences at Line 190-193 like “If indeed the barite formation temperature for\nall the six periods are more or less similar, the ~4‰ late Paleozoic rise in plateau\nδ18O values indicate a similar degree of δ18O values change in seawater …”. In\nbarite\naddition, we proposed that samples from different paleolatitudes can help to determine\n3\nif temperature effect on the plateau δ18O is consistent.\nsulfate\nNo further revisions have been made to the text on this issue.\nIn summary, the revised manuscript demonstrates significant progress in addressing\nearlier concerns; however, several issues remain that warrant further attention. The\ncurrent approach to defining the plateau in δ18O data is insufficiently rigorous and\nbarite\nmay be susceptible to outliers and noise, calling for a more systematic statistical\ntreatment. Finally, the assumption of a constant fractionation factor across variable\ndepositional temperatures should be revisited in light of potential temperature gradients\nover continental shelves.\nOverall, we support publication of this manuscript provided that the authors adequately\naddress these issues. The lack of an apparent plateau for most of the geological\nperiods shown in Figure 3 (e.g., Late Devonian) requires the strengthening of the quantitative\nframework and explicitly acknowledging the limitations of this work. It will enhance\nthe scientific robustness and overall impact of it.\nReply: See our response to your comments above.\nReviewer #3 (Remarks to the Author):\nI am generally happy with the response to the reviewers comments and to my comments.\nI would quibble a bit with Response 1. The implication that it is a fractionation between\nsulfate and water implies that there is a chemical reaction like:\nS16O + H 18O <--> S18O16O + H 16O\n4 2 3 2\nThat is in sulfate you cleave a S-O bond and allow the oxygen atoms to exchange with\nwater. That doesn't happen. As you say in response 1, it is because of reversibility of\nenzyme catalyzed reactions inside and on the cell membrane that you can cleave the S-\nO bond in extracellular sulfate and see a signal of a change in the d18O of the water. I\nmight consider calling this an 'apparent isotope fractionation between sulfate and water'.\nOtherwise I think this is good to go.\nReply: Please see the beginning part of our response to Reviewer #2.\nYes, you are correct in that if the above equation is an elementary step, that doesn’t\nhappen. The actual oxygen isotope exchange between sulfate and water involves many\nlinked steps and even branched steps (e.g., sulfite-water exchange). Going from sulfite\nto sulfate (i.e., the backward oxidation) may occur via enzyme-mediated electron\ntransfer inside the cell, not necessarily exclusively extracellular.\nOur understanding or terminology is that for a given compound involved in a reaction,\nif the forward and backward reactions go through the same sets of transition states,\nwhen the two rates are the same, we call it “in equilibrium”. If the two rates are not the\nsame, we call it “in non-equilibrium”, not “in apparent equilibrium”. Calling it\n“apparent isotope fractionation” is ok. However, if the forward and backward reactions\ngo through their own pathways with two different sets of transition states, when the two\n4\nrates are the same, we call it “in steady-state”. If the two rates are not the same, we call\nit “in non-steady state”. The use of these terms has been quite loose in the community\nand often different communities have different and often opposite meanings. Thank you\nfor bringing up this discussion.\nNo further revisions have been made to the text on this issue.\nReviewer #4 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nReply: Thank you for your constructive input.\n5"}]

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