The sub-arc mantle has remained oxidized since the Neoproterozoic oxygenation event

Domain: earth_science
Published: 2025-08-18
Editorial outcome: major_revision

Abstract
The redox state of the sub-arc mantle impacts magma degassing at arc volcanoes and arc-related ore deposits. However, the evolution of the oxygen fugacity (fO2) of the sub-arc mantle during the Neoproterozoic Oxygenation Event (NOE) remains poorly understood. Here, we applied machine learning to identify arc basalts, then calculated V/Sc ratios of primitive arc basalts since ~0.8 billion years ago (Ga). Our results show that average V/Sc remained nearly constant at ~7.16, suggesting an oxidized sub-arc mantle since ~0.8 Ga. This implies that increased surficial oxygen levels during the NOE may not directly oxidize the sub-arc mantle. Instead, its oxidation likely stems from the influx of oxidized fluids and melts via subducted serpentinized oceanic crust. The persistently oxidized sub-arc mantle may have controlled the long-term oxidation of arc magmas and thus influenced the oxidation of Earth’s surficial environments since ~0.8 Ga, though it was not the NOE’s primary driver.

Introduction
The redox state of Earth’s upper mantle, which is quantified by oxygen fugacity (fO2), governs the behavior of redox-sensitive elements in magmas, the formation of ore deposits, and has profoundly impacted Earth’s long-term climate1–7. The elevated fO2 of the upper mantle and mantle-derived melts may have facilitated the Archean–Proterozoic Great Oxidation Event (GOE)8–10. However, intriguingly and oppositely, increased oxygen concentrations in the atmosphere and oceans during the Neoproterozoic Oxygenation Event (NOE) ~0.8–0.4 billion years ago (Ga)11–17 are suspected to have controlled the oxidation of the sub-arc mantle through the increased input of marine sulfate via subducted slabs18. Today, the sub-arc mantle is more oxidized than the mid-ocean ridge basalt (MORB) mantle, primarily due to the influx of oxidized materials from subducted slabs19–24. Accordingly, arc magmas are more oxidized than MORBs1,25,26. However, it remains unclear whether the fO2 of the sub-arc mantle has changed over time, particularly across the Proterozoic–Phanerozoic boundary, despite the pivotal importance of this information for unraveling the relationships between mantle fO2, the evolution of Earth’s surface environments, and animal diversification11,12,14,27.

Two critical steps are needed to address these gaps in our understanding: (1) establishing a reliable redox proxy and (2) identifying suitable samples that faithfully record sub-arc mantle fO2 over time. Fe3+/ΣFe measurements in mineral inclusions and glasses are ideal, but are limited by sample availability and high analytical costs28. As an alternative, the multivalent element vanadium (2+, 3+, 4+, 5+) demonstrates increasing incompatibility under increasingly oxidizing conditions, and the trivalent element scandium behaves incompatibly during mantle partial melting29–31. Accordingly, petrological modeling of non-modal partial melting indicates that the V/Sc ratio in basalts is a reliable proxy for mantle fO2 because V and Sc exhibit analogous partitioning behaviors during mantle melting processes and are relatively insensitive to mantle lithologies and chemical compositions32.

To overcome the inaccuracies of traditional methods used to distinguish arc basalts from non-arc basalts, we used a high-dimensional machine learning (ML) approach to classify basalts accurately and identify ancient arc-type basalts (hereafter, simply “arc basalts”)33. As a widely used ML technique, eXtreme Gradient Boosting (XGBoost) is a supervised ML model; it is trained by applying decision trees to a known and labeled dataset, then makes predictions when applied to an unknown application dataset. Therefore, we trained an XGBoost ML model on geochemical data from modern arc and non-arc basalts (Supplementary Figs. S1–S4; see “Methods”). To constrain the redox state of the sub-arc mantle, we excluded back-arc and fore-arc basalts from the training dataset. We applied the trained model to identify global arc basalts erupted since ~0.8 Ga (Supplementary Figs. S5–S8; see “Methods”). Then, we calculated the global mean V/Sc values of primitive arc basalts since ~0.8 Ga and translated them using petrological modeling to estimate changes in the sub-arc mantle fO2 through time (see “Methods”).

Results
ML modeling results
Based on the input features (Nb/La, Ti, U/Nb, La, Nb, Rb/Nb, Pb/Nd, Ba, Nb/Yb, U, Sr/Nd, Ba/La, Ba/Nb, Th, P, Pb/Nb, Nb/Th, La/Yb, Zr/Y, Sr, Y, Ce, Zr, Pb, Rb, Ti/Y, Ta)32, our arc vs. non-arc classification model achieved an average accuracy and F1 score of 0.95±0.01 (1 standard deviation; s.d.) and 0.94±0.01 (1 s.d.), respectively, when applied to the training subset (70% of the training dataset). The F1 score is widely used to evaluate the performance of a classification model (see “Methods”), and the confusion matrix visualizes model performance by comparing known and predicted data labels. As shown in the confusion matrix (Fig. 1b), the model similarly achieved an accuracy and F1 score of 0.95 and 0.94, respectively, when applied to the testing subset (30% of the parental training dataset). These high accuracies and F1 scores illustrate that our ML model can reliably distinguish between arc and non-arc basalts.

XGBoost incorporates algorithms to calculate the relative importance of each feature to the overall ML model. Feature importance scores are widely used to improve model interpretability and better understand the high-dimensional geological processes modeled33–40. Here, our results show that Nb/La, Ti, U/Nb, La, and Nb are the five most important features in our classification model (Fig. 1a), consistent with the observations of Liu et al.33. Furthermore, all feature importances are <0.09, implying that all input features were important when building the classification model. Therefore, unlike traditional binary discrimination diagrams, the high-dimensional model with multiple parameters is less affected by individual elements33,40.

Temporal variations of the mean V/Sc ratios of primitive arc basalts
Here, we applied our classification model to predict the probability that each sample in our basaltic application dataset is an arc basalt (Supplementary Fig. S8; see “Methods”). We then determined the mean V/Sc ratios of primitive arc basalts (8–17 wt% MgO, 60–72 Mg#, where molar Mg#=100×MgO/(MgO+FeOtot); Supplementary Fig. S7)20 at 100-million-year (Myr) intervals using a weighted bootstrap resampling technique41,42 (Supplementary Fig. S9). The secular evolution of mean V/Sc values in primitive arc basalts is consistent regardless of the time interval chosen (100 Myr in Fig. 2a; 50 and 25 Myr in Supplementary Fig. S10), indicating that the observed trend is not biased by the choice of interval. Furthermore, the weighted bootstrap resampling method incorporates a weight that is inverse to a sample’s age and location to minimize spatiotemporal bias (see “Methods”). Our results reveal that the mean V/Sc ratios of primitive arc basalts have remained consistent around a value of 7.16±0.91 (2 s.d.) since ~0.8 Ga (Fig. 2a). Within uncertainties, this mean V/Sc ratio aligns with the contemporary global average in primitive arc basalts (7.50±1.67, 1 s.d.) (Fig. 2a).

Validation of the ML classification model
Some non-arc basalts are influenced by slab-derived fluids and sediments, resulting in arc-like geochemical signatures. These signatures include enrichment in large-ion lithophile elements and depletion in high-field-strength elements43,44. Therefore, it is essential to compile independent datasets to test whether our ML model can accurately discriminate between arc basalts and non-arc basalts with arc-like signatures33. One such case is Cenozoic intraplate basalts in Northeast China, which exhibit high H2O/Ce and Ba/Th ratios and low Ce/Pb ratios, suggesting the influence of subducted fluids and sediments from the flat slab in the mantle transition zone beneath the region45–47. Previous ML models, including random forest and deep neural networks, predicted that most of these Cenozoic intraplate basalts were affected by stagnant-slab-derived fluids48. Our ML model classified these Cenozoic intraplate basalts (n=331) from Northeast China48 as non-arc basalts with ~99% accuracy.

Furthermore, some island arc basalts, such as those from the Mota arc (Vanuatu), exhibit atypical arc geochemical signatures, such as Nb enrichment44,49. Importantly, we incorporated typical Nb-enriched arc basalts, such as those from Panama, Costa Rica, and Kamchatka, into our training model50,51. Our ML model accurately recognized all of the atypical Mota arc basalts (n=6)44. Consequently, the results of our independent model validation indicate that our ML model robustly distinguishes between arc and non-arc basalts. We stress, though, that our ML model is primarily designed to classify arc vs. non-arc tectonic settings only for basalts and basaltic andesites (45–54 wt% SiO2), i.e., the SiO2 range included in our training dataset.

Furthermore, the identified island arc igneous rocks may have been compromised by traditional tectonic-magmatic discrimination methods, which are less accurate32. Additionally, their compiled dataset of island arc igneous rocks exhibits significant compositional variability, including mafic, intermediate, and felsic compositions (~40–80 wt% SiO2). However, it is only plausible to constrain the sub-arc mantle fO2 using medium- to high-silica magmatic rocks if the degrees of partial melting, fractional crystallization, and assimilation are well understood. Otherwise, these processes may obscure the fO2 information inherited from the mantle source. In comparison, primitive basalts effectively reflect the composition and redox state of the mantle source.

Moreover, some compiled whole-rock Fe3+/ΣFe data were obtained using wet chemical methods18, including colorimetry and titration. Colorimetric measurements are known to overestimate Fe3+/ΣFe ratios in basaltic samples, whereas titration methods are more reliable52. Furthermore, Mariana back-arc basalts are systematically more reduced than the sub-arc mantle there19. Considering that the back-arc rocks were included in the analysis18, the temporal evolution of Fe3+/ΣFe and V/Sc ratios they reported may be biased by the preservation and sampling of both arc and back-arc rocks. In summary, the secular evolution of Fe3+/ΣFe and V/Sc ratios previously reported in island arc igneous rocks is undermined by issues of sample representativeness and data reliability (Supplementary Figs. S11–S14). Notably, variations in these ratios may not fully reflect changes in sub-arc mantle fO2 because they are also influenced by melting pressure (P), temperature (T), mantle source composition, and the degree of partial melting. Therefore, it is necessary to more quantitatively constrain the secular evolution of the sub-arc mantle fO2.

We meticulously curated a high-quality dataset by manually reviewing the geochronological data and geochemical compositions of Precambrian samples (Supplementary Fig. S6; see “Methods”), significantly improving the quality of data obtained from current geochemical databases such as EarthChem33,40,53. Additionally, our ML model incorporates some fluid-mobile elements (e.g., U and Pb) as input features, which may be modified during metamorphism and post-alteration processes. That said, if our model were highly biased by fluid-mobile elements, it would have incorrectly classified highly altered samples. However, the relative importances of U and Pb were <0.04 in our classification model (Fig. 1a). To further confirm that our model is not biased by fluid-mobile elements, we applied it to weathered Cretaceous arc basalts from the Benbow Inlier in eastern Jamaica (n=8)54 and Neogene non-arc basalts from Hainan Island, South China (n=21)55; most Cretaceous arc (n=7) and Neogene non-arc basalts (n=20) were correctly identified. These validation results further indicate that our ML model can accurately discriminate arc from non-arc basalts and minimize misclassifications. Consequently, our refined dataset and ML classification model provide a more reliable record of the temporal evolution of V/Sc ratios in global primitive arc basalts.

Elevated mean V/Sc ratios of primitive arc basalts could be attributed to subaerial oxidation (weathering). If this were the case, though, we would expect a decrease in the mean V/Sc ratio since the NOE, because V5+ is increasingly fluid-mobile (as H2VO4−) under increasingly oxidizing conditions56. The consistent V/Sc ratio over time instead suggests that weathering processes had a limited impact (Fig. 2a). Additionally, the temporal evolution of the mean V/Sc ratio might be influenced by differences in the preservation of continental vs. oceanic arc basalts because our classification model does not differentiate between them. However, the mean V/Sc ratio of modern global primitive continental arc basalts (8.02±1.70, 1 s.d.) largely overlaps with that of modern oceanic arc basalts (7.23±1.59, 1 s.d.), indicating similar oxidation states over a given period (continental and oceanic arc basalts extracted from the GEOROC database). This suggests that the preservation bias between continental and oceanic arc basalts also has a minimal effect on the temporal evolution of the mean V/Sc ratio. Our estimated mean V/Sc ratio of primitive arc basalts thus provides a first-order constraint on the evolution of the sub-arc mantle fO2.

Furthermore, V/Sc ratios in primary melts are not solely governed by mantle fO2, but are also significantly affected by the P-T conditions during melting and by the degree of partial melting30. By considering the evolution of melting P-T conditions during arc magma genesis, we calculated the average P-T conditions during mantle melting that produced the primitive arc basalts since ~0.8 Ga57,58 (Supplementary Fig. S15; see “Methods”). The average melting P and T conditions have remained relatively stable through time, fluctuating within respective narrow ranges of 1.3±0.2 GPa (2 s.d.), largely within the spinel stability field30, and 1255±35°C (2 s.d.) (Fig. 2b, c). Under relatively oxidized conditions (e.g., ΔFMQ+1; ΔFMQ representing the deviation of a system’s fO2 from the fayalite-magnetite-quartz buffer, FMQ), V/Sc in primary melts slightly increases with decreasing degree of partial melting30. Because La is more incompatible than Nd during mantle melting, the constant mean La/Nd ratio through time suggests that the degree of partial melting has had a minimal effect on the mean V/Sc ratio of primitive arc basalts (Supplementary Fig. S16).

Accordingly, we converted the mean V/Sc values of primitive arc basalts into estimates of sub-arc mantle fO2 by assuming a mantle lithology of spinel lherzolite with a depleted MORB mantle (DMM) chemical composition59 (see “Methods”). Our results indicate that the average sub-arc mantle fO2 has remained relatively oxidized at ΔFMQ+1.36±0.89 (2 standard errors of the mean, s.e.m.) since the late Neoproterozoic (Fig. 3a). Such mean fO2 conditions are consistent with the modern sub-arc mantle value (ΔFMQ+1.0–ΔFMQ+1.6) inferred from Fe3+/ΣFe ratios in olivine-hosted primary melt inclusions from Mariana arc magmas19. Intriguingly, our estimate suggests that the sub-arc mantle has been consistently more oxidized than the ambient upper mantle (ΔFMQ−1–ΔFMQ+1)10 since ~0.8 Ga (Fig. 3a).

Secular changes of the sub-arc mantle fO2 since the late Neoproterozoic
A previous study suggested that the sub-arc mantle fO2 increased during ~0.8–0.4 Ga, based on the higher mean Fe3+/ΣFe and V/Sc ratios of Phanerozoic island arc igneous rocks compared to those of their Precambrian counterparts18. However, directly calculating mean values for individual island arc segments may be susceptible to preservation and sampling biases due to the uneven spatiotemporal sample distribution41,42, which could lead to highly variable observed mean Fe3+/ΣFe and V/Sc ratios in Precambrian rocks18. To mitigate this, we employed the weighted bootstrap resampling technique to minimize spatiotemporal preservation bias when estimating mean V/Sc ratios through time. Our analysis of V/Sc ratios in primitive arc basalts suggests a relatively stable value since the late Neoproterozoic (Fig. 2a).

The long-term oxidation of the sub-arc mantle
Prior research has indicated that latitude-dependent variations of Cenozoic sub-arc mantle fO2 have been influenced by the presence of less oxidized sediments in subducted slabs at lower latitudes60. Nonetheless, latitude-dependent redox effects cannot be the sole cause of the consistently oxidized sub-arc mantle since the late Neoproterozoic for two reasons. First, despite similar V/Sc ratios in low-latitude arc samples and MORBs, low-latitude sub-arc mantle fO2 values remain more oxidized than those of the MORB mantle due to the lower melting temperatures in arcs20. Second, available geological records do reflect this latitude effect as minor variations, but do not show a significant effect on the global mean sub-arc mantle fO2. For instance, the fragmentation of the supercontinent Rodinia into low-latitude microcontinents could have led to increased low-latitude subduction61,62, potentially resulting in the relatively less oxidized sub-arc mantle fO2 values at ~0.7–0.6 Ga. Conversely, the migration of the continents toward higher latitudes might have led to the positive shift in sub-arc mantle fO2 values during ~0.6–0.5 Ga61–63. Additionally, the aggregation of the continents at low latitudes could have contributed to the relatively less oxidized sub-arc mantle from ~0.5–0.1 Ga63,64. However, these fluctuations are within the 2 s.e.m. errors of the trend (Fig. 3a), and the relatively stable mean V/Sc ratios and sub-arc mantle fO2 since ~0.8 Ga indicate that the latitude effect has had only a limited impact on the long-term evolution of global sub-arc mantle fO2.

It has been suggested that the increased atmospheric and oceanic oxygen levels during the late Neoproterozoic and early Paleozoic may have directly affected the oxidation state of the sub-arc mantle18. However, the relatively stable oxidized state of the sub-arc mantle since ~0.8–0.4 Ga suggests that increased atmospheric and marine oxygen concentrations did not directly lead to the oxidation of the mantle wedge via elevated marine sulfate contents (Fig. 3c, d). Alternatively, serpentinization of mafic and ultramafic rocks can oxidize oceanic rocks and the upper lithospheric mantle, whose eventual subduction could oxidize the sub-arc mantle18,19,24,65–72. Although it is difficult to quantify the degree of serpentinization of the oceanic lithosphere, worldwide serpentinites in subducted oceanic slabs contain abundant carbon, hydrogen, and sulfur, which may contribute to the oxidation and induced melting of the mantle wedge65,71,73–75. If this mechanism were the primary driver of mantle oxidation, we would expect the sub-arc mantle fO2 to have been oxidized since the onset of subduction. Indeed, we observe that the sub-arc mantle has maintained an oxidized state since ~0.8 Ga, supporting this hypothesis. The increased occurrence of blueschists and low-T, high-P metamorphic rocks since the late Neoproterozoic76 suggests that the evolution of modern subduction may have facilitated the deserpentinization of subducted slabs, releasing oxidized materials into the sub-arc mantle (Fig. 3b) and thus maintaining its oxidized state.

This observation suggests that the long-term oxidation of the sub-arc mantle may be driven by geological processes involving serpentinization and subduction, rather than by the direct input of marine dissolved oxygen and sulfate. Consequently, the oxidation of the sub-arc mantle appears to be influenced by deep Earth processes rather than being a direct consequence of changes in surface oxygen levels.

Given the greater mobility of Sr and Rb in fluids compared to Nd and La, Sr/Nd and Rb/La ratios have been used to trace the transport of aqueous fluids into the mantle wedge24,77,78. The enrichment of Th in terrigenous sediments79 implies that elevated Th/La ratios in arc basalts relative to MORBs typically reflect the movement of sediment melts from the subducted slab into the sub-arc mantle19. Our results show significantly higher mean Sr/La, Rb/La, and Th/La ratios in primitive arc basalts compared to those in MORBs through time, indicating that oxidized slab-derived fluids and melts have likely enhanced the oxidation of the sub-arc mantle since ~0.8 Ga (Fig. 3d–f).

The oxidized nature of modern arc magmas compared to MORBs has been attributed to either oxidized materials from subducted slabs19,24,66,71 or differentiation processes80,81. Our results indicate that the sub-arc mantle has been oxidized since the late Neoproterozoic, influencing the long-term oxidation state of arc magmas. Moreover, it has long been suggested that mantle fO2 changes have elevated Earth’s surface oxygen levels (e.g., the GOE) through volcanic degassing over geological time4,8,82–84. However, the sub-arc mantle fO2 did not increase during ~0.8–0.4 Ga, which is asynchronous with the oxidation of the atmosphere and the deep ocean during that period. The oxidation of the sub-arc mantle was therefore not a direct trigger of the NOE (Fig. 3). Therefore, alternative mechanisms must ultimately have driven the NOE: e.g., the prosperity of primary producers (e.g., algae)13, the burial of organic carbon and pyrite17, and/or increased marine phosphorus concentrations85–88. Nonetheless, the relatively stable oxidation of the sub-arc mantle since the late Neoproterozoic may have contributed to the secular oxidation of Earth’s surficial environments by increasing the flux of oxidized volcanic gases to the Earth’s surface and potentially promoting biological evolution (e.g., animal diversification)89,90. Further studies on potential links between the fO2 of the broader mantle and surficial oxidation and biological evolution should integrate records of igneous rocks, sedimentary rocks, and geobiodiversity through time.

Methods
Training dataset
The global arc and non-arc basaltic geochemical datasets (each basalt representing a single sample) were previously compiled and checked by Liu et al.33 from the GEOROC (https://georoc.eu/georoc/new-start.asp; accessed 15 January 2023)91 and PetDB databases (https://www.earthchem.org/petdb/; accessed 18 January 2023). Here, our training dataset includes arc (n=5069) and non-arc (n=8500) basalts (45–54 wt% SiO2, ≤17 wt% MgO). This geochemical training dataset comprises typical modern (most younger than 65 Ma) continental and oceanic arc basalts and non-arc basalts (i.e., oceanic island basalts, MORBs, oceanic plateau basalts, and continental basalts) (Supplementary Fig. S1) (see “Data Availability”).

Feature selection
Before operating the XGBoost training model, the input features in the training dataset were first tested for collinearity to both reduce model dimensions (some elements have similar geochemical behaviors) and save computing resources33,40. Here, we used the Pearson correlation coefficient (−1≤ρ≤1) to test the collinearity of every feature, with |ρ| values closer to 1 representing increased correlation between two features (Supplementary Fig. S2). Following Liu et al.33, we only selected features with |ρ|<0.88. Accordingly, we used 27 input features for the XGBoost classification model.

Scatter and box plots for each geochemical feature included in the arc and non-arc basaltic training datasets are shown in Supplementary Fig. S3. The distribution of each input feature between arc and non-arc basalts is nearly identical, further indicating that no single element can effectively classify these two types of basalts. Furthermore, some features contained missing values because some elements were not measured or reported in the original publications. However, the proportion of missing values was <30% for most features (Supplementary Fig. S4). Nonetheless, the XGBoost ML method is designed to deal with missing values92.

Application dataset
To apply our model, we compiled a global application dataset (~0.85 Ga to present) mainly comprising two data populations: (a) basalts ranging from ~0.85–0.45 Ga (n≈1680) from the EarthChem repository (http://www.earthchem.org/; accessed 11 June 2021) and (b) basalts from ~0.8–0 Ga (n≈12,730) (each basalt representing a single sample), with nearly all samples being Phanerozoic (n≈12,520), from the igneous geochemical dataset of Keller and Schoene41 (Supplementary Fig. S5) (see “Data Availability”). It has been shown that uncorrected geochronological data archived in the EarthChem database cannot be directly used, especially for Precambrian samples33,40,53. Therefore, to control the data quality, we manually checked the basalt data against the original publications via multiple steps, including removing duplicate samples, correcting geochemical and geochronological data, and expert data review33,40. We observed that the geochronological data for numerous Proterozoic samples were inconsistent with the original publications, whereas the Phanerozoic samples matched their sources accurately (Supplementary Fig. S6). Accordingly, the newly refined basaltic dataset was used to calculate secular changes of the mean V/Sc ratio in primitive arc basalts, and thereby estimate the sub-arc mantle fO2 since ~0.8 Ga in 100-Myr bins.

The primitive arc basalts were filtered to include only those with 8–17 wt% MgO and Mg#=60–72 to reduce the influence of mineral crystallization/accumulation, magma mixing, and crustal contamination (Supplementary Fig. S7)20.

XGBoost modeling
XGBoost is a commonly used supervised ML technique that applies gradient-boosted decision trees to solve classification and regression problems92,93. It trains a model on a labeled dataset using decision trees and then predicts outcomes on unseen data. Specifically, it adds new trees iteratively to run gradient boosting, which predicts the residuals of prior trees. The gradient descent algorithm guides this process to minimize the loss function.

In our modeling, we implemented a binary classification for the training dataset. Accordingly, our classification model comprised the following steps. (1) We executed 10-fold cross-validation (i.e., dividing the parental training dataset into training and testing subsets 10 times to evaluate model performance) to test whether our training dataset was influenced by a class imbalance problem. Class imbalance is a prevalent challenge in ML, particularly in classification tasks, where the distribution of classes in the dataset is significantly uneven (see details in the next subsection). This process gives a mean value with a standard deviation (s.d.) based on ten performance scores. (2) We randomly divided the parental training dataset into a training subset (70%) and a testing subset (30%). (3) We optimized hyperparameters (e.g., gamma, learning rate, max depth, and alpha) via grid-search cross-validation and 10-fold cross-validation to obtain the best training classification model. Gamma (≥0) is the minimum loss reduction that controls the complexity of decision trees and prevents overfitting of the model. Overfitting occurs when a ML model achieves high accuracy on the training dataset but performs poorly on new data. The learning rate (0–1) decreases the step size to reduce overfitting. Max depth (≥0) represents the maximum depth of a tree, determining the complexity of the model. Alpha (≥0) refers to a regularization term to prevent overfitting. After hyperparameter tuning, the optimal training model was achieved with the following hyperparameters: gamma=0, learning rate=0.6, max depth=7, and alpha=0.1. (4) We utilized the testing subset to evaluate model performance via a confusion matrix (Fig. 1). (5) We applied the best training model to the application dataset and predicted the probability of a given sample being an arc basalt (Supplementary Fig. S8). Here, we took 0.5 as the threshold probability between arc (yi ≥0.5) and non-arc basalts (yi <0.5) in our model training, validation, and prediction (see “Code Availability”). We performed the XGBoost ML modeling using the scikit-learn package in Python94 and confirmed within the Geochemistry π Python Framework (v.0.7.0)95. The open-source documentation for XGBoost is available at https://github.com/dmlc/xgboost and https://xgboost.readthedocs.io/en/stable/.

Accuracy and the F1 score are commonly used to estimate ML model performance. Accuracy is defined as:
Accuracy= P(arc)correct +P(non-arc)correct / L(total) (1)
where P(arc)correct and P(non-arc)correct represent the number of correct model predictions for arc and non-arc basalts, respectively, and L(total) is the total number of labeled arc and non-arc samples. Here, we focused on the model predictions of arc basalts. The F1 score is defined as the harmonic mean of precision and recall:
F1 score= 2×Precision×Recall / Precision+Recall (2)
Precision= P(arc)correct / P(arc)total (3)
Recall= P(arc)correct / L(arc) (4)
where P(arc)total and L(arc) refer to the total number of predicted and labeled arc basalts, respectively. Compared to traditional accuracy, the F1 score better estimates model reliability in cases of imbalanced classifications36.

Class imbalance in the ML model
Class imbalance problems arise when the amount of data is significantly different in each class of the training dataset, which can result in underestimated probabilities for scarce classes35,96,97. For instance, an imbalance ratio (IR=M/m, with M and m denoting the number of samples in the majority and minority classes, respectively) exceeding ~25 can significantly diminish the accuracy of the training model96. Here, the difference between the number of arc (n=5069) and non-arc basalts (n=8500) in our training dataset (IR≈1.7) is not significant enough to result in a class imbalance problem. That said, if there were an important class imbalance issue in our training dataset, the 10-fold cross-validation procedure would generate very low accuracies and F1 scores. However, our 10-fold cross-validation resulted in a relatively high accuracy of 0.86±0.07 (1 s.d.) and a high F1 score of 0.81±0.10 (1 s.d.) before any model training processes. Accordingly, our training dataset is not strongly affected by class imbalance.

Overfitting by the ML model
Overfitting issues in ML models arise when a model performs well on the training dataset but fails to predict new, unseen data. A prevalent method used to assess overfitting is 10-fold cross-validation, which randomly splits the training and testing subsets ten times to evaluate model performance. After 10-fold cross-validation, our training and testing subsets both exhibited accuracies of 0.95 and F1 scores of 0.94. These relatively high accuracies and F1 scores indicate that our ML model is not affected by overfitting. Furthermore, XGBoost includes regularized objectives and algorithms that contribute to smoothing the final learned weights to avoid overfitting92.

Weighted bootstrap resampling method
We implemented a weighted bootstrap resampling technique to calculate the mean V/Sc (Fig. 2a), Rb/La, Sr/Nd, and Th/La ratios (Fig. 3e–g) of primitive arc basalts through time, which can minimize spatiotemporal preservation bias41,42. To reduce spatiotemporal bias, the resampling technique introduces weights inversely related to each sample’s age and location. During the resampling process, rarer samples are resampled frequently and denser data less frequently. The resampling process was implemented as follows. (1) Each sample was assigned a weight, calculated as the inverse of its spatiotemporal density, to minimize spatiotemporal preservation bias. (2) A Monte Carlo simulation, a statistical method that uses repeated random sampling to obtain numerical results, was applied to resample proportional to the samples’ weights and achieve a resampled dataset. (3) Based on the samples’ age data and their associated uncertainties, we separated the resampled dataset into 100-Myr bins in which we calculated elemental ratios (e.g., V/Sc, Rb/La, Sr/Nd, Th/La). (4) Steps (1) to (3) were repeated 100 times. (5) Finally, based on the 100 simulations, we calculated the mean value for each bin and estimated the 2 s.e.m. uncertainties to quantify the variability of our estimates.

Petrological modeling
We employed a near-fractional melting model to quantitatively simulate V/Sc ratios in primary melts during sub-arc mantle partial melting20. In the melting model, the concentration of element i in the instantaneously produced melt is given as:
Ci,melt n+1 = Ci,residue n / (Di,bulk + F(1 - Di,bulk)) (5)
where Ci,melt n+1 is the concentration of element i in the melt at melting step n+1, Ci,residue n is that of element i in the residue after melt extraction at step n, Di,bulk is the bulk partition coefficient at step n+1, and F is the extracted melt fraction at each step. In addition, the concentration of element i in the aggregate melt at step n is given as:
Ci,aggr = Σ(Pi,melt n * Ci,melt n) / Σ(Pi,melt n) (6)
Where Ci,melt n and Pi,melt n are the concentration of element i in the instantaneous melt and the mass of melt produced at step n, respectively. Ci,aggr and Σ(Pi,melt n) are the overall concentration of element i and the bulk mass of the aggregate melt at step n, respectively.

We calculated the melting P and T conditions of global primitive arc basalts at a water content of 4 wt% using the Fractionated-PT software44,45. Our results show that the average melting P was nearly constant through time at 1.3±0.2 GPa (2 s.d.), which is within the spinel stability field30 (Fig. 2b). Therefore, we modeled the initial mineral assemblage in the sub-arc mantle as a spinel lherzolite (57% olivine (Ol), 28% orthopyroxene (Opx), 13% clinopyroxene (Cpx), 2% spinel (Spl))98 of DMM chemical composition59. The generation of arc magmas was assumed to initiate at ~1150°C (deduced from Supplementary Fig. S15). The water-bearing melting reactions were chosen from Gaetani and Grove99 and Parman and Grove100.

The partition coefficients for element i between mantle minerals and the melt were calculated via the empirical equations of Wang et al.20:
log10 DV melt = -2.30 - 0.258ΔFMQ + 1871/T - 0.24 * NBO/Tetra (7)
log10 DOpx/melt = -4.61 - 0.198ΔFMQ + 5981/T + 4.48 * AlTetra (8)
log10 DV Cpx/melt = -4.24 - 0.267ΔFMQ + 5717/T + 3.64 * AlTetra (9)
log10 DSpl/melt = -1.09 - 0.186ΔFMQ + 2447/T + 0.004 * Cr# (10)
log10 DS Cpx/melt = 3.31 - 7375/T - 0.038 * Mg# (11)
log D Cpx/melt = -1.51 + 2342/T - 160 * P + 2.44 * AlTetra (12)

The ratio of non-bridging oxygens to tetrahedrally coordinated cations (NBO/Tetra) is a measure of melt polymerization101, calculated as:
NBO/Tetra = 4 * X Tetra - 2 * X O / X Tetra (13)
where X Tetra and X O represent the atomic proportions of tetrahedrally coordinated cations and oxygen, respectively. To estimate this, we compiled global primitive arc basalts from the GEOROC repository (n=785) and calculated the major element compositions of primary arc melts assuming a water content of 4 wt%57,58, from which we calculated the average NBO/Tetra value of global primary arc melts.

AlTetra is the tetrahedrally coordinated site (atoms per formula unit) of Al in Opx and Cpx20. We estimated mean AlTetra values for Opx and Cpx. Cr# (100 × Cr2O3 / (Cr2O3 + Al2O3)) and Mg# were employed in empirical Eqs. (10) and (11), respectively20. We determined the mean Cr# and Mg# values for global spinel lherzolites based on the compilations and verifications of Qin et al.37. Finally, combined with a non-modal near-fractional melting model and average melting P-T conditions (Fig. 2b, c), we converted the mean V/Sc values of primitive arc basaltic samples to mean sub-arc mantle fO2.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The paper uses machine learning (ML), specifically an eXtreme Gradient Boosting (XGBoost) model, to classify arc basalts, representing an innovative approach to applying ML techniques in geoscience. The study provides valuable insights into the temporal stability of the oxidation state of the sub-arc mantle, showing it has remained consistently oxidized since the Neoproterozoic. This contributes significantly to understanding the link between Earth's deep processes and surface environmental conditions. The methodology is strong, employing reliable geochemical databases (GEOROC, PetDB) to create a representative dataset that supports the study's conclusions. The ML model achieved high accuracy (95%) and F1 score, showing reliability in distinguishing arc from non-arc basalts. The integration of ML classification with petrological modeling and geochemical analysis of V/Sc ratios gives a comprehensive view of the sub-arc mantle's oxidation state. The paper effectively explores factors affecting mantle oxidation, such as subduction processes and interactions with atmospheric oxygenation. Figures are clear and illustrate key findings effectively, including feature importance and temporal changes in oxidation.\nHowever, the discussion section lacks sufficient emphasis on the broader implications of the findings, such as their impact on biological evolution and atmospheric changes during significant geological intervals. The potential links to animal diversification or broader climate effects during the Neoproterozoic Oxygenation Event should be more thoroughly explored to strengthen these points. The machine learning methodology, while innovative, lacks transparency about critical details like hyperparameter tuning, model validation, and potential biases, which would help confirm the robustness of the model beyond the reported accuracy. Some sections, particularly the methods and results, are dense with technical details, making it difficult for non-specialists to understand. Simplifying or explaining these concepts in more detail would make the paper more accessible. Terms like ΔFMQ or specific details about petrological modeling could benefit from clearer definitions upon first mention. While the figures are helpful, their captions could provide more context to make them understandable without needing to refer back to the text. The manuscript also lacks explicit differentiation from existing studies; clearer comparisons to recent literature would help highlight the unique contributions of this study. Minor formatting inconsistencies, such as author name variations and inconsistent use of terms (\"oxidization\" vs. \"oxidation\"), detract from the paper's professionalism, and ensuring consistency would improve readability.\nOverall, the paper offers strong scientific contributions, particularly through its innovative ML approach and robust data analysis. However, enhancing clarity, providing better context for the findings, and focusing more on their broader significance, especially for non-specialists, would substantially improve the quality and reach of the manuscript.", "reviewer_2": "Liu and others use the V/Sc proxy to investigate redox conditions of sub-arc magmas in the last 0.8 billion years. Sub-arc mafic magmas were classified from global geochemical databases, and the fugacity constraints were calculated from the whole rock V/Sc ratio, which has a correlation with redox, given the incompatible behaviour and fugacity sensitivity nature of V. The lack of variations observed in the V/Sc led the authors to conclude that the sub-arc mantle has remained persistently oxidised since the Neoproterozoic. This is an interesting study that contradicts recent studies using V/Sc and Fe-speciation in arc-magmas (Stolper and Bucholz, 2019, PNAS - S&B). S&B used individual arc magmas V/Sc instead of averaging out ratios of all arcs binned in 100 Myr intervals. This is a different approach than the one used by Liu et al. because it takes individual conditions into account rather than smoothing out any variations by calculating medians/means. The most compelling result of S&B not discussed by Liu et al. is the Fe-speciation results, which show a significant change in fugacity, and it is more reliable than whole-rock elemental ratios simply because it has better resolution and probability of retaining primary signatures. Moreover, V/Sc is known for not resolving minor variations in fO2 compared to Fe3+/Fetotal (Novella et al. 2020, EPSL).\nThis paper could be a good contribution to Nature Comms if a few key points are addressed/clarified:\n1) Instead of using 100 Myr intervals, which unavoidably smooth out variations, the authors could have used 25 or even 10 Myr intervals to identify variations in the V/Sc. Equally, a plot in supplementary material showing all the individual V/Sc points vs. time would be helpful.\n2) The fO2 change observed by S&B via Fe-speciation was not discussed. V/Sc has proven inconclusive in other studies, whereas Fe-speciations is more reliable in constraining the fugacity of sub-arc magmas. Using V/Sc and finding different results could simply be a limitation of this proxy.\n3) Subduction of sediments and latitudinal dependence are presented as potential explanations of studies that observed variations in fugacity of sub-arc magmas, but a connection or implication of those with respect to the overall conclusion of the present study (i.e. that sub-arc magmas do not change fugacity in the last 0.8 Gyr) was not presented. Is this to say that the authors acknowledge the variations in the fugacity of sub-arc magmas since the NOE? Using the expression 'consistent oxidisation' gives the impression that the fO2 remained constant/invariant over that period, and as such, it is incompatible with some of the information presented in the discussions."}, "author_response": "Point-by-point reply\nAll line numbers quoted below refer to those in the clean version of the revised manuscript.\nReviewer #1 (Remarks to the Author):\nThe paper uses machine learning (ML), specifically an eXtreme Gradient Boosting (XGBoost)\nmodel, to classify arc basalts, representing an innovative approach to applying ML techniques in\ngeoscience. The study provides valuable insights into the temporal stability of the oxidation state of\nthe sub-arc mantle, showing it has remained consistently oxidized since the Neoproterozoic. This\ncontributes significantly to understanding the link between Earth's deep processes and surface\nenvironmental conditions. The methodology is strong, employing reliable geochemical databases\n(GEOROC, PetDB) to create a representative dataset that supports the study's conclusions. The ML\nmodel achieved high accuracy (95%) and F1 score, showing reliability in distinguishing arc from\nnon-arc basalts. The integration of ML classification with petrological modeling and geochemical\nanalysis of V/Sc ratios gives a comprehensive view of the sub-arc mantle's oxidation state. The\npaper effectively explores factors affecting mantle oxidation, such as subduction processes and\ninteractions with atmospheric oxygenation. Figures are clear and illustrate key findings effectively,\nincluding feature importance and temporal changes in oxidation.\nReply 1: Thanks for your positive feedback and comments. We have carefully considered all your\nsuggestions and modified our manuscript (see below).\nHowever, the discussion section lacks sufficient emphasis on the broader implications of the\nfindings, such as their impact on biological evolution and atmospheric changes during significant\ngeological intervals. The potential links to animal diversification or broader climate effects during\nthe Neoproterozoic Oxygenation Event should be more thoroughly explored to strengthen these\npoints.\nReply 2: We appreciate the reviewer’s suggestion to expand our discussion on the broader\nimplications of our findings. We agree that exploring the connections between mantle oxidation and\nmajor geological events is crucial. Our study indicates that while changes in mantle fO may have\n2\ninfluenced atmospheric oxygen levels over geological time through volcanic degassing, potentially\ncontributing to the Archean–Proterozoic Great Oxidation Event (Kasting et al., 1993; Kump et al.,\n2001; Holland, 2002; Aulbach and Stagno, 2016), the sub-arc mantle fO did not increase during\n2\n~0.8–0.4 Ga (Figure 3). This period was asynchronous with the oxidation of the atmosphere and the\ndeep ocean, suggesting that while the oxidation of the arc mantle may have played a role, it did not\ndirectly trigger the Neoproterozoic Oxygenation Event (NOE). Alternative mechanisms, such as the\nproliferation of primary producers (Lyons et al., 2014), the burial of organic carbon and pyrite\n(Krause et al., 2022), and increased marine phosphorus concentrations (Reinhard et al., 2017; Kipp\nand Stüeken, 2017; Laakso et al., 2020; Dodd et al., 2023), likely drove the NOE.\nThe oxidation of the arc mantle since ~0.8 Ga likely contributed to the secular oxidation of\nEarth’s surficial environments by increasing the flux of oxidized volcanic gases to the Earth’s\nsurface and potentially promoting biodiversity (Stockey et al., 2024; Kadoya et al., 2020). Because\nour study specifically focuses on the evolution of sub-arc mantle fO , we suggest that future research\n2\nshould integrate comprehensive records of igneous rocks, sedimentary rocks, and geobiodiversity\nthrough time to better understand the potential links between mantle fO and surficial oxidation and\n2\nbiological evolution (lines 294-306).\nThe machine learning methodology, while innovative, lacks transparency about critical details like\nhyperparameter tuning, model validation, and potential biases, which would help confirm the\nrobustness of the model beyond the reported accuracy.\nReply 3: Thanks for your suggestions. We acknowledge the importance of transparency in machine\nlearning (ML) methodology. As a widely used ML technique, eXtreme Gradient Boosting (XGBoost)\nis a supervised ML model, in which a model is trained on a known and labeled dataset using decision\ntrees, then applied to an unknown application dataset to make predictions. Therefore, we trained an\nXGBoost classification machine learning model on geochemical data from modern arc and non-arc\nbasalts (lines 70-74).\nHyperparameter tuning\nWe used grid-search cross‐validation and 10-fold cross‐validation to operate the hyperparameter\ntuning (e.g., gamma, learning rate, max depth, and alpha) to gain the best training classification\nmodel. Gamma (≥ 0) is the minimum loss reduction that controls the complexity of decision trees\nand prevents overfitting of the model. Overfitting occurs when a ML model achieves high accuracy\non the training dataset but performs poorly on new data. The learning rate (0–1) decreases the step\nsize to reduce overfitting. Max depth (≥ 0) represents the maximum depth of a tree, determining the\ncomplexity of the model. Alpha (≥ 0) refers to a regularization term to prevent overfitting. After\nhyperparameter tuning, the optimal training model was achieved with the following\nhyperparameters: gamma = 0, learning rate = 0.6, max depth = 7, and alpha = 0.1 (this text is now\nadded to the manuscript, lines 366-374).\nModel validation\nSome non-arc basalts are influenced by slab-derived fluids and sediments, resulting in arc-like\ngeochemical signatures. These signatures include enrichment in large-ion lithophile elements\n(LILEs) and depletion in high-field-strength elements (HFSEs) (van Hunen and Moyen, 2012; Xu\net al., 2020). Therefore, it is essential to compile independent datasets to test whether our ML model\ncan accurately identify non-arc basalts with arc-like signatures (Liu et al., 2024). One such case is\nCenozoic intraplate basalts in Northeast China, which exhibit high H O/Ce and Ba/Th ratios and\n2\nlow Ce/Pb ratios, suggesting the influence of subducted fluids and sediments from the flat slab in\nthe mantle transition zone beneath the region (Kuritani et al., 2011; Chen et al., 2015; Wei et al.,\n2018). Previous ML models, including random forest and deep neural networks, predicted that most\nof these Cenozoic intraplate basalts were affected by stagnant slab-derived fluids (Zhao et al., 2019).\nOur ML model classified these Cenozoic intraplate basalts (n = 331) from Northeast China (Zhao\net al., 2019) as non-arc basalts with ~99% accuracy.\nThe early Cretaceous Fangcheng intraplate basalts from the Pingyi Basin in Shandong Province\nare characterized by enriched light rare-earth element and LILE contents and depleted HFSEs\n(Zhang et al., 2002). The formation of these Fangcheng basalts likely involved fluids and melts\nreleased from the subducted paleo-Pacific slab (Zhao et al., 2002; Guo et al., 2013; Dai et al., 2019).\nOur ML model classified these Fangcheng basalts (n = 24) as non-arc basalts with ~96% accuracy.\nFurthermore, some island arc basalts, such as those from the Mota arc (Vanuatu), exhibit\natypical arc geochemical signatures, such as Nb enrichment (Sorbadere et al., 2013; Xu et al., 2020).\nImportantly, we incorporated typical Nb-enriched arc basalts, such as those from Panama, Costa\nRica, and Kamchatka, into our training model (Reagan and Gill, 1989; Kepezhinskas et al., 1996).\nOur ML model accurately recognized the atypical Mota arc basalts (n = 6) (Sorbadere et al., 2013).\nAdditionally, we tested whether our ML model can effectively exclude typical non-arc samples,\nsuch as basalts and basaltic andesites from the East Pacific Rise. When classifying these rocks (n =\n28) (Wanless et al., 2012), our model accurately identified all samples as non-arc basalts.\nConsequently, the results of our independent model validation indicate that our ML model robustly\ndistinguishes between arc and non-arc basalts. We stress, though, that our ML model is primarily\ndesigned to classify arc vs. non-arc tectonic settings for basalts and basaltic andesites (45–54 wt.%\nSiO ), i.e., the SiO range included in our training dataset (this text is now added to the manuscript,\n2 2\nlines 135-160).\nPotential bias\nOur ML model incorporates some fluid-mobile elements (e.g., U and Pb) as input features, which\nmay be modified during metamorphism and post-alteration processes. That said, if our model were\nhighly biased by fluid-mobile elements, it would incorrectly classify highly altered samples.\nHowever, the relative importances of U and Pb were <0.04 in our classification model (Figure 1a).\nTo further confirm that our model is not biased by fluid-mobile elements, we applied it to extremely\nweathered Neogene non-arc basalts (n = 21) from Hainan Island, South China (Ma et al., 2007);\nalmost all (~95%) the altered samples were identified as non-arc basalts. Consequently, our refined\ndataset and ML classification model offer a more reliable record of the temporal evolution of V/Sc\nratios in global primitive arc basalts (this text is now added to the manuscript, lines 196-204).\nSome sections, particularly the methods and results, are dense with technical details, making it\ndifficult for non-specialists to understand. Simplifying or explaining these concepts in more detail\nwould make the paper more accessible. Terms like ΔFMQ or specific details about petrological\nmodeling could benefit from clearer definitions upon first mention.\nReply 4: Thanks for your suggestions. We understand that the technical nature of our work,\nparticularly in the methods and results sections, may pose challenges for non-specialist readers.\nSimplification of technical language\nTo address this concern and enhance the clarity of our paper, we have revised sections of the methods\nand results to reduce unnecessary technical jargon. For example, we provided more straightforward\nexplanations for “confusion matrix” in the results section; it is a square matrix that visualizes the\nperformance of a classification model, with rows representing the known classes (i.e., the true labels\nof the data) and columns representing the predicted classes (i.e., the labels predicted by the model)\n(lines 87-91). Furthermore, the weighted bootstrap resampling method incorporates a weight that is\ninverse to a sample’s age and location to minimize spatiotemporal bias (lines 109-110).\nIn the Methods section, we streamlined the description of the XGBoost modeling process and\nprovided detailed explanations of key concepts such as 10-fold cross-validation, class imbalance,\noverfitting, and hyperparameters upon their first mention. For example:\n(1) 10-fold cross-validation refers to divide the parental dataset into training and test subsets\n10 times to evaluate model performance (lines 359-361).\n(2) The class imbalance issue is a common challenge in machine learning, especially in\nclassification tasks, where the distribution of classes in the dataset is significantly uneven (lines 361-\n363).\n(3) Overfitting occurs when a machine learning model achieves high accuracy on the training\ndata but fails to generalize to new, unseen data (lines 369-370).\n(4) Hyperparameter gamma (≥ 0) is a parameter that controls the minimum loss reduction\nrequired to make a further partition in a decision tree, thereby preventing overfitting by managing\nthe complexity of the model (lines 367-369).\nTerm definitions and explanations\nThe term ΔFMQ refers to the deviation of the oxygen fugacity (fO ) of a system from the fayalite-\n2\nmagnetite-quartz (FMQ) buffer (lines 225-226). For petrological modeling, we employed a non-\nmodal partial melting model to simulate the variation of the V/Sc ratio in mantle-derived melts (lines\n64-67). We have provided brief explanations of these terms upon its first mention.\nWhile the figures are helpful, their captions could provide more context to make them\nunderstandable without needing to refer back to the text.\nReply 5: Thanks for your comments. We agree that enhancing the context within the captions will\nimprove the clarity and accessibility of the figures. We have revised each figure caption to include\nmore context to make them more understandable by a wider audience. For example:\nFigure 1. Results after applying our XGBoost model to classify arc vs. non-arc basalts. a The\nrelative feature importance of each input feature in training the model. All feature importances are\n<0.09, indicating that no single feature dominates the classification model. b The confusion matrix\nwhen the model was applied to the testing subset of the training dataset. This square matrix compares\nknown and predicted data labels. The confusion matrix for the testing subset shows a high accuracy\nof 0.95 and an F1 score of 0.94, suggesting the strong performance of our high-dimensional trained\nmodel.\nFigure 3 The evolution of sub-arc mantle fO and geological records over time. a The secular\n2\na The secular mean sub-arc mantle fO2 evolution since ~0.8 Ga. We first simulated arc mantle\nmelting using a non-modal partial melting model to establish the relationship between V/Sc and fO .\nPT software (Lee et al., 2009). By combining the V/Sc−fO relationship, melting P-T conditions,\n2\nand mean V/Sc values, we estimated the temporal evolution of the mean sub-arc mantle fO since\n2\nthe late Neoproterozoic (see “Methods”). The modern arc mantle fO was estimated from primary\n2\nmelt inclusions in Mariana arc basalts (Brounce et al., 2014). The evolution of the ambient upper\nmantle fO was estimated by Zhang et al. (2024). b The occurrence of blueschists and low-T, high-\natmospheric O contents (Lyons et al., 2014; Krause et al., 2022; Stockey et al., 2024) and ocean\n2\ndissolved O contents (Stolper and Keller, 2018; Stockey et al., 2024), respectively. e–g The secular\n2\nevolution of mean Rb/La, Sr/Nd, and Th/La ratios in primitive arc basalts, respectively. Dashed lines\nindicate the average values of modern primitive MORBs (data extracted from the PetDB repository,\nn ≈ 530). The mean Sr/La, Rb/La, and Th/La ratios in primitive arc basalts are consistently higher\nthan those in MORBs through time. Vertical error bars in a and e–g are 2 s.e.m. uncertainties.\nThe manuscript also lacks explicit differentiation from existing studies; clearer comparisons to\nrecent literature would help highlight the unique contributions of this study.\nReply 6: We appreciate the reviewer’s feedback regarding the need for clearer differentiation from\nexisting studies and for providing explicit comparisons to recent literature.\nA previous study suggested that the sub-arc mantle fO increased during ~800–400 Ma, based\n2\non the higher mean Fe3+/ΣFe and V/Sc ratios of Phanerozoic island arc igneous rocks compared to\nthose of their Precambrian counterparts (Stolper and Bucholz, 2019). However, directly calculating\nmean values for individual island arc segments may be susceptible to preservation and sampling\nbiases due to the uneven spatiotemporal sample distribution (Keller and Schoene, 2018), which\ncould lead to highly variable observed mean Fe3+/ΣFe and V/Sc ratios in Precambrian rocks (Stolper\nand Bucholz, 2019). To mitigate this, we employed the weighted bootstrap resampling technique to\nminimize spatiotemporal preservation bias when estimating mean V/Sc ratios through time. Our\nanalysis of V/Sc ratios in primitive arc basalts suggests a relatively stable value since the late\nNeoproterozoic (Figure 2a).\nFurthermore, the island arc igneous rocks identified by Stolper and Bucholz (2019) may have\nbeen compromised by traditional tectonic-magmatic discrimination methods, which are less\naccurate31. Additionally, their compiled dataset of island arc igneous rocks exhibits significant\ncompositional variability, including mafic, intermediate, and felsic compositions (~40–80 wt.%\nSiO ). It is inappropriate to constrain the sub-arc mantle fO using such a broad range of\n2 2\ncompositions, because these rocks originate from heterogeneous sources with distinct geochemical\ncharacteristics. More specifically, medium- to high-silica magmatic rocks are unsuitable for\nconstraining the sub-arc mantle fO , as their geochemical signatures have been significantly altered\n2\nby extensive magmatic evolution and crustal assimilation, obscuring the fO information inherited\n2\nfrom the mantle source.\nMoreover, all the whole-rock Fe3+/ΣFe ratios compiled by Stolper and Bucholz (2019) were\nobtained using wet chemical methods, such as colorimetric measurement that is now known to\noverestimate Fe3+/ΣFe ratios in basaltic samples (Bézos et al., 2021), reducing the reliability of the\ndata analysis. Furthermore, Mariana Trough back-arc basalts systematically more reduced than\nthose from the sub-arc setting (Brounce et al., 2014). Considering that Stolper and Bucholz (2019)\nincluded back-arc rocks in their analysis, the temporal evolution of Fe3+/ΣFe and V/Sc ratios they\nreported may be biased by the preservation and sampling of arc and back-arc rocks.\nIn summary, the secular evolution of Fe3+/ΣFe and V/Sc ratios they reported in arc igneous\nrocks is undermined by issues of sample representativeness and data reliability. Notably, variations\nin these ratios may not fully reflect changes in sub-arc mantle fO because they are also influenced\n2\nby melting pressure, temperature, fO , mantle source compositions, and degree of partial melting.\nfO (this text is now added to the manuscript; lines 163-192).\n(\"oxidization\" vs. \"oxidation\"), detract from the paper's professionalism, and ensuring consistency\nwould improve readability.\nReply 7: We appreciate the reviewer’s attention to detail. In the revised manuscript, we ensured\nconsistent use of terms throughout the paper, e.g., using “oxidation” throughout the manuscript.\nOverall, the paper offers strong scientific contributions, particularly through its innovative ML\napproach and robust data analysis. However, enhancing clarity, providing better context for the\nfindings, and focusing more on their broader significance, especially for non-specialists, would\nsubstantially improve the quality and reach of the manuscript.\nReply 8: We appreciate the reviewer’s positive feedback on our paper. In response to the suggestions\nfor improvement, we have revised the manuscript to address the following areas:\nEnhancing clarity:\nWe have simplified and clarified technical descriptions throughout the paper, particularly in the\nmethods and results sections. This includes providing more detailed explanations of key concepts\nsuch as hyperparameter tuning, model validation, and potential biases (details in Reply 3). We have\nexpanded the captions of figures to include more contextual information, ensuring that they are\nunderstandable without referring back to the main text (details in Reply 5).\nProviding better context for findings:\nWe have strengthened the discussion section by providing clear and detailed comparisons to recent\nliterature. This highlights the significance of our scientific contributions, particularly the insights\ngained from our innovative machine learning approach and reliable data analysis (details in Reply\n6).\nEmphasizing broader significance:\nWe have explored the potential connections between arc mantle oxidation and the oxidation of\natmospheric oxygen and the deep ocean. This analysis underscores the broader implications of our\nresearch for understanding global geochemical cycles (details in Reply 2).\nMaking it accessible to non-specialists:\nTo ensure that our work is accessible to a wider audience, we have revised sections of the results\nand methods to reduce unnecessary technical jargon. We have also provided more detailed\nexplanations of crucial concepts, such as the confusion matrix, class imbalance issue, and ΔFMQ,\nupon their first mention (details in Reply 4).\nThe revision is designed to enhance the clarity, context, and accessibility of our manuscript,\nmaking it more informative and engaging for non-specialists.\nReviewer #1 (Remarks on code availability):\nCant find the code\nReply 9: Thanks for your comment. To make our data and code available, we archived them at\nZenodo (https://doi.org/10.5281/zenodo.14993044).\nReferences\nAulbach, S. & Stagno, V. Evidence for a reducing Archean ambient mantle and its effects on the\ncarbon cycle. 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Nature 541, 386–389 (2017).\nSorbadere, F., Schiano, P., Métrich, N. & Bertagnini, A. Small-scale coexistence of island-arc- and\nenriched-MORB-type basalts in the central Vanuatu arc. Contrib. Mineral. Petrol. 166, 1305–\n1321 (2013).\nStockey, R. G. et al. Sustained increases in atmospheric oxygen and marine productivity in the\nNeoproterozoic and Palaeozoic eras. Nat. Geosci. 17, 667–674 (2024).\nStolper, D. A. & Bucholz, C. E. Neoproterozoic to early Phanerozoic rise in island arc redox state\ndue to deep ocean oxygenation and increased marine sulfate levels. Proc. Natl. Acad. Sci. USA\n116, 8746–8755 (2019).\nStolper, D. A. & Keller, C. B. A record of deep-ocean dissolved O from the oxidation state of iron\n2\nin submarine basalts. Nature 553, 323–327 (2018).\nvan Hunen, J. & Moyen, J.-F. Archean Subduction: Fact or Fiction? Annu. Rev. Earth Planet. Sci.\n40, 195–219 (2012).\nWanless, V. D., Perfit, M. R., Klein, E. M., White, S. & Ridley, W. I. Reconciling geochemical and\ngeophysical observations of magma supply and melt distribution at the 9°N overlapping\nspreading center, East Pacific Rise. Geochem. Geophys. Geosyst. 13, Q11005 (2012).\nWei, W. et al. Seismic evidence for a mantle transition zone origin of the Wudalianchi and Halaha\nvolcanoes in Northeast China. Geochem. Geophys. Geosyst. 20, 398–416 (2018).\nXu, Y. et al. The origin of arc basalts: New advances and remaining questions. Sci. China-Earth Sci.\n63, 1969–1991 (2020).\nZhang, F. et al. The constant oxidation state of Earth’s mantle since the Hadean. Nat. Commun. 15,\n6521 (2024).\nZhang, H.-F. et al. Mesozoic lithosphere destruction beneath the North China Craton: evidence from\nmajor-, trace-element and Sr–Nd–Pb isotope studies of Fangcheng basalts. Contrib. Mineral.\nPetrol. 144, 241–254 (2002).\nZhao, Y., Zhang, Y., Geng, M., Jiang, J. & Zou, X. Involvement of slab-derived fluid in the\ngeneration of cenozoic basalts in Northeast China inferred from machine learning. Geophys.\nRes. Lett. 46, 5234–5242 (2019).\nReviewer #2 (Remarks to the Author):\nLiu and others use the V/Sc proxy to investigate redox conditions of sub-arc magmas in the last 0.8\nbillion years. Sub-arc mafic magmas were classified from global geochemical databases, and the\nfugacity constraints were calculated from the whole rock V/Sc ratio, which has a correlation with\nredox, given the incompatible behaviour and fugacity sensitivity nature of V. The lack of variations\nobserved in the V/Sc led the authors to conclude that the sub-arc mantle has remained persistently\noxidised since the Neoproterozoic.\nReply 1: We appreciate the reviewer’s summary of our methodology and findings.\nThis is an interesting study that contradicts recent studies using V/Sc and Fe-speciation in arc-\nmagmas (Stolper and Bucholz, 2019, PNAS - S&B). S&B used individual arc magmas V/Sc instead\nof averaging out ratios of all arcs binned in 100 Myr intervals. This is a different approach than the\none used by Liu et al. because it takes individual conditions into account rather than smoothing out\nany variations by calculating medians/means.\nReply 2: Thank you for your insightful comment on the contrasting approaches and findings\nbetween our study and that of Stolper and Bucholz (2019). We acknowledge that our study utilizes\naveraged V/Sc ratios over 100 Myr intervals. In contrast, Stolper and Bucholz (2019) estimated the\naverage Fe3+/ΣFe and V/Sc ratios for individual island arc localities through time. However, directly\ncalculating mean values for each island arc segment may be susceptible to preservation and\nsampling biases due to the uneven spatiotemporal distribution of samples (Keller and Schoene,\n2012). This may lead to highly variable Fe3+/ΣFe and V/Sc ratios in Precambrian samples (Stolper\nand Bucholz, 2019). To mitigate this, we employed a weighted bootstrap resampling technique to\nminimize spatiotemporal preservation bias when estimating the mean V/Sc ratios through time.\nThe most compelling result of S&B not discussed by Liu et al. is the Fe-speciation results, which\nshow a significant change in fugacity, and it is more reliable than whole-rock elemental ratios simply\nbecause it has better resolution and probability of retaining primary signatures. Moreover, V/Sc is\nknown for not resolving minor variations in fO2 compared to Fe3+/Fetotal (Novella et al. 2020,\nEPSL).\nReply 3: We appreciate the reviewer’s emphasis on the Fe-speciation results presented by Stolper\nand Bucholz (2019) and their significance in understanding changes in fugacity. We acknowledge\nthat Fe3+/ΣFe measurements in mineral inclusions and glasses offer important insights into mantle\noxygen fugacity (fO ), but such measurements are limited by sample availability and high analytical\n2\ncosts (Huang et al., 2022) (lines 60-61). Moreover, all the whole-rock Fe3+/ΣFe ratios compiled by\nStolper and Bucholz (2019) were obtained using wet chemical methods, such as colorimetric\nmeasurement that is now known to overestimate Fe3+/ΣFe ratios in basaltic samples (Bézos et al.,\n2021), reducing the reliability of the data analysis (lines 181-183).\nFurthermore, if Fe3+/ΣFe offers significantly better resolution for retaining primary signatures\ncompared to V/Sc ratios, we would expect no significant change in the V/Sc ratios of island arc\nrocks. However, the consistent correlation between Fe3+/ΣFe and V/Sc ratios during ~800–400 Ma,\nas observed by Stolper and Bucholz (2019), suggests that the ability of V/Sc to resolve mantle fO\n2\nin island arc rocks is not systematically inferior to that of the Fe3+/ΣFe ratio. This indicates that V/Sc\ncan be a reliable proxy for tracking changes in mantle fO .\nhigher oxidation states, while the homovalent element Sc behaves incompatibly during mantle\npartial melting (Lee et al., 2005; Mallmann and O’Neill., 2009). Accordingly, petrological modeling\nof non-modal partial melting indicates that the V/Sc ratio in basalts is a reliable proxy of mantle fO\n2\nbecause V and Sc exhibit analogous partitioning behaviors during mantle melting processes and are\nrelatively insensitive to mantle lithologies and chemical composition (Liu et al., 2025).\nConsequently, the V/Sc ratio in basaltic melts serves as a robust redox proxy for tracing the evolution\nof mantle fO , offering valuable insights into the redox histories of the Earth (lines 61-67).\n1) Instead of using 100 Myr intervals, which unavoidably smooth out variations, the authors could\nhave used 25 or even 10 Myr intervals to identify variations in the V/Sc. Equally, a plot in\nsupplementary material showing all the individual V/Sc points vs. time would be helpful.\nReply 4: We appreciate the reviewer’s suggestion to explore finer temporal resolutions for analyzing\nV/Sc variations and providing a supplementary plot of individual V/Sc data points. However, using\nshorter intervals would result in fewer data points per interval, increasing the risk of sampling bias\nand reducing the statistical robustness of the analysis. Accordingly, we now present the temporal\nevolution of V/Sc using 50 Myr and 25 Myr intervals (Figure S9). The results demonstrate that the\nsecular evolution of mean V/Sc in primitive arc basalts is consistent regardless of the chosen time\ninterval, indicating that our estimated mean V/Sc is not biased by the choice of interval (Figure 2a;\nFigure S9) (lines 106-109). Notably, we acknowledge that certain periods (e.g., ~0.7–0.6 Ga) with\nlimited sample availability may reduce the time resolution of the estimated mean V/Sc ratio. Further\nresearch should focus on collecting more samples to minimize sampling bias and enhance time\nresolution.\nFigure S9. Variations of the mean V/Sc ratio in global primitive arc basalts in 50 Myr and 25 Myr\nbins. The gray scatter points are individual V/Sc data points through time. Error bars are 2 s.e.m.\nuncertainties. The relatively large uncertainty on V/Sc at ~0.7–0.6 Ga is due to the scarcity of basalts\nerupted during that period.\n2) The fO2 change observed by S&B via Fe-speciation was not discussed. V/Sc has proven\ninconclusive in other studies, whereas Fe-speciations is more reliable in constraining the fugacity\nof sub-arc magmas. Using V/Sc and finding different results could simply be a limitation of this\nproxy.\nReply 5: We appreciate the reviewer’s feedback regarding the need for providing explicit\ncomparisons to the fO change observed by Stolper and Bucholz (2019) via Fe-speciation.\ninsights into mantle oxygen fugacity (fO ), but such measurements are limited by sample availability\n2\nand high analytical costs (Huang et al., 2022) (lines 60-61). Moreover, all the whole-rock Fe3+/ΣFe\nratios compiled by Stolper and Bucholz (2019) were obtained using wet chemical methods, such as\ncolorimetric measurement that is now known to overestimate Fe3+/ΣFe ratios in basaltic samples\n(Bézos et al., 2021), reducing the reliability of the data analysis (detailed discussions about Stolper\nand Bucholz (2019) in lines 163-192).\nFurthermore, if Fe3+/ΣFe offers significantly better resolution for retaining primary signatures\ncompared to V/Sc ratios, we would expect no significant change in the V/Sc ratios of island arc\nrocks. However, the consistent correlation between Fe3+/ΣFe and V/Sc ratios during ~800–400 Ma,\nas observed by Stolper and Bucholz (2019), suggests that the ability of V/Sc to resolve mantle fO\n2\nin island arc rocks is not systematically inferior to that of the Fe3+/ΣFe ratio. This indicates that V/Sc\ncan be a reliable proxy for tracking changes in mantle fO .\nwith higher oxidation states, while the homovalent element Sc behaves incompatibly during mantle\npartial melting (Lee et al., 2005; Mallmann and O’Neill., 2009). Accordingly, petrological modeling\nof non-modal partial melting indicates that the V/Sc ratio in basalts is a reliable proxy of mantle fO\n2\nbecause V and Sc exhibit analogous partitioning behaviors during mantle melting processes and are\nrelatively insensitive to mantle lithologies and chemical composition (Liu et al., 2025).\nConsequently, the V/Sc ratio in basaltic melts serves as a robust redox proxy for tracing the evolution\nof mantle fO , offering valuable insights into the redox histories of the Earth (lines 61-67).\n2\n3) Subduction of sediments and latitudinal dependence are presented as potential explanations of\nstudies that observed variations in fugacity of sub-arc magmas, but a connection or implication of\nthose with respect to the overall conclusion of the present study (i.e. that sub-arc magmas do not\nchange fugacity in the last 0.8 Gyr) was not presented. Is this to say that the authors acknowledge\nthe variations in the fugacity of sub-arc magmas since the NOE? Using the expression 'consistent\noxidisation' gives the impression that the fO2 remained constant/invariant over that period, and as\nsuch, it is incompatible with some of the information presented in the discussions.\nReply 6: Thanks for your comment regarding the potential explanations for observed variations in\nsub-arc magma fO and the apparent inconsistency with our conclusion of consistent oxidation in\n2\nsub-arc magmas over the last ~0.8 Ga. We understand that the use of the term “consistent oxidization”\nmay have given the impression of an invariant fO , which was not our intention.\nemphasize that there is no significant variation of long-term evolution of the sub-arc mantle fO\n2\nassociated with the latitude effect. Although we acknowledge that the mean sub-arc mantle fO\n2\nvalues may be associated with the latitude effect, the relatively stable mean V/Sc ratios and sub-arc\nmantle fO since ~0.8 Ga indicate that the latitude effect has had a limited impact on the long-term\n2\nevolution of sub-arc mantle fO (Figure 2a, 3a) (lines 254-267). Accordingly, after excluding the\n2\ninfluence of the latitude effect in the discussion, we use the phrase “relatively consistent oxidation”\nto emphasize our findings that the sub-arc mantle has maintained a relatively stable oxidized state\nover the long run.\nReviewer #2 (Remarks on code availability):\nApologies for not assessing the reproducibility of the code. The data discrimination seems\nstraightforward, and I considered the output valid in my review.\nReply 7: Thanks for your suggestion. To make our data and code available, we archived them at\nZenodo (https://doi.org/10.5281/zenodo.14993044).\nReference:\nBézos, A., Guivel, C., La, C., Fougeroux, T. & Humler, E. Unraveling the confusion over the iron\noxidation state in MORB glasses. Geochim. Cosmochim. Acta 293, 28–39 (2021).\nHuang, W. et al. Estimating ferric iron content in clinopyroxene using machine learning models. Am.\nMineral. 107, 1886–1900 (2022).\nKeller, C. B. & Schoene, B. Statistical geochemistry reveals disruption in secular lithospheric\nevolution about 2.5 Gyr ago. Nature 485, 490–493 (2012).\nLee, C.-T. A, Leeman,W. P.,Canil, D. &Li, Z.-X. A. Similar V/Sc systematics in MORB and arc\nbasalts: implications for the oxygen fugacities of their mantle source regions. J. Petrol. 46,\n2313–2336 (2005).\nLiu C.-T., Ye, C.-Y. & J. ZhangZhou. Modelling redox state via V--Sc--Ti--Yb partitioning in mantle\nderived melts. Geochem. Perspect. Let. (2025)\nMallmann, G. & O’Neill, H. St. C. The crystal/melt partitioning of V during mantle melting as a\nfunction of oxygen fugacity compared withsome other elements (Al, P, Ca, Sc, Ti, Cr, Fe, Ga,\nY, Zr and Nb). J. Petrol. 50, 1765–1794 (2009).\nStolper, D. A. & Bucholz, C. E. Neoproterozoic to early Phanerozoic rise in island arc redox state\ndue to deep ocean oxygenation and increased marine sulfate levels. Proc. Natl. Acad. Sci. USA\n116, 8746–8755 (2019)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Dear Rebecca,\nI have read the responses to both comments from reviewers #1 and #2. I believe the authors have done a great job in\naddressing the comments and revising the manuscript.\nThe new title feels somewhat underwhelming and could benefit from further consideration. While the conclusion regarding a\nsteady oxidation state is important, the term \"relatively\" weakens its impact. However, I am confident this can be refined\nduring proof editing. Similarly, the last sentence of the abstract could be strengthened.\nThat said, the manuscript is now much clearer in explaining the machine method used in this study. All necessary details\nand information have been provided, making it more useful for readers. Overall, all my concerns have been addressed.\nBest regards,\nLuc Doucet, Perth, the 14/03/2025", "reviewer_2": "The revised version of the paper by Liu et al. presents a more robust discussion of the pitfalls of the V/Sc methods and a\ncomparison with the Fe-speciation approach. I find it interesting that the authors persist in the usability of the V/Sc over\nFe3+/FeTOTAL, as the V/Sc is an indirect method and less precise. The correlation between the two methods indicates that\nthe V/Sc proxy works, but it by no means proves that the consistent oxidation of a specific slice of geological time is not a\nreflection of the resolution of the V/Sc proxy. One point that remains valid is the classification used by Liu et al. (which differs\nfrom S&B by not using individual arcs and by averaging out the data per 100 Myr intervals), and as such, a way forward is to\ntest the same sample dataset used for V/Sc but as Fe3+/FeTOTAL calculations. If the authors can provide this comparison,\nit can potentially resolve/explain the difference between them. I think this is important as the manuscript dismisses the\nFe3+/FeTOTAL without providing compelling arguments. Some of the new sentences included in the revised manuscript\nshould be modified as they are either unclear or incorrect.\nThe new title “Relatively consistent oxidation” does not reflect the results obtained in the study. For example, fluctuations in\nredox conditions are presented and discussed (e.g., latitude-controlled fugacity) but then dismissed as unimportant. The\n100-Myr bins data points have uncertainties that do not overlap throughout the 0.8-0 Ga interval, suggesting that the redox\nstate is not “consistent”. If it were consistent, one would understand that the oxidation had remained constant since the\nNeoproterozoic and Phanerozoic. Perhaps a better title would be “Relatively oxidised sub-arc mantle…” if the main point is\nto acknowledge variations and highlight that although they are presented, the oxidation state of the sub-arc mantle remained\nabove the ambient mantle throughout the interval studied.\nIt would also be helpful to show how simply using V/Sc basalts over time would look compared to the ML+bootstrap\napproach. Is it possible that the misclassified samples are not enough to change the overall observation if they were\nincluded in the V/Sc averages?\nLines 79-80: What are the implications for removing the back-arc and fore-arc basalts from the dataset? Can we see the\nV/Sc of all basalts over time (perhaps in supplementary material?) to evaluate if the overall values are affected by including\nthese other basalt types?\nLines 97-99: It remains unclear how much better the ML+bootstrap method is compared to simply using V/Sc of basalts over\ntime. In other words, it is difficult to assess how much better this technique is compared to using an untreated dataset.\nLine 149: This new discussion on ‘Validation of the ML classification model’ is too long to say that the ML model works and\ncould be simplified. Some explanation on the effects of inadvertently including non-basaltic arcs could be added instead.\nLines 197-200 state that “medium- to high-silica magmatic rocks are unsuitable for constraining the sub-arc mantle fO2, as\ntheir geochemical signatures have been significantly altered by extensive magmatic evolution and crustal assimilation,\nobscuring the fO2 information inherited from the mantle source.” This statement may be valid but is not necessarily true as\nhigh-silica rocks can preserve their original mantle fugacity if partial melting, fractional crystallisation and assimilation are\nwell understood (see for example, Meng et al., 2022 and Moreira et al., 2023 in Nature Geoscience). I recommend clarifying\nthat it is possible to preserve original fugacity in medium to high-silica magmas.\nLines 201-203: “Moreover, all the compiled whole-rock Fe3+/ΣFe ratios compiled by Stolper and Bucholz were obtained\nusing wet chemical methods, such as colourimetric measurement that is now known to overestimate Fe3+/ΣFe ratios in\nbasaltic samples” This statement is misleading and it implies that all wet chemical methods overestimate the ratio, which is\nnot true as titration methods do not overestimate Fe3+/FeTOTAL and not all measurements presented in S&B were obtained\nvia wet chemical methods.\nLine 204: Mariana Trough back-arc basalts ‘are’ systematically…\nLine 206-207: It remains a question here whether using your dataset before classifying the samples as arc-basalts would\nresult in the same shift observed by S&B or not.\nLines 209-211: “Notably, variations in these ratios may not fully reflect changes in sub-arc mantle fO2, because they are also\ninfluenced by melting pressure, temperature, fO2, mantle source compositions, and the degree of partial melting.” There’s a\ntautological issue here as those factors intrinsically control fugacity, so fugacity should not be quoted as a cause of itself.\nLine 213: I don’t think the added word ‘application’ makes sense here.\nLines 216-226: This part is confusing. It is argued that altered/weathered samples are not misclassified due to fluid-mobile\nelements being included in the ML model, but the samples used to support this argument are not arc-basalts. The way to\nsupport this argument is to either say that altered samples are not used or that altered samples (based on fluid-mobile\nelements) can still be recognised as arc-basalts.\nLines 304-306: “It has been suggested that the increase of atmospheric and oceanic oxygen levels during the late\nNeoproterozoic and early Paleozoic may have inversely affected the oxidation state of the sub-arc mantle17” This is not\ncorrect. S&B concluded the opposite. In other words, it has directly affected the oxidation state of the sub-arc mantle.\nLine 308: If there is no direct effect between NOE, sulphate and oxidation of the mantle wedge, what is the alternative\nexplanation? It is not clear how the following paragraph (lines 309-314) offers a fundamentally different explanation based\non the serpentinisation of the ocean floor and the subduction of sediments enriched in sulphate.\nBased on Figure S9, some intervals seem to have no individual V/Sc data points. However, the diagram in Figure 2a shows\nthat the sample size seems to be between 1 and 100 datapoints. Is this because the data points are out of scale?"}, "author_response": "Point-by-point reply\nAll line numbers quoted below refer to those in the clean version of the revised manuscript.\nReviewer #1 (Remarks to the Author):\nI have read the responses to both comments from reviewers #1 and #2. I believe the authors have done a great\njob in addressing the comments and revising the manuscript.\nReply 1: Thanks for your positive feedback and comments.\nThe new title feels somewhat underwhelming and could benefit from further consideration. While the\nconclusion regarding a steady oxidation state is important, the term \"relatively\" weakens its impact. However,\nI am confident this can be refined during proof editing. Similarly, the last sentence of the abstract could be\nstrengthened.\nReply 2: Thanks for your suggestions. We believe that “The sub-arc mantle has remained oxidized since the\nNeoproterozoic Oxygenation Event” would be a better title.\nRegarding the last sentence of the abstract, we have taken your suggestion into account and propose the\nfollowing revision for improving clarity and precision: “Furthermore, the oxidation of the sub-arc mantle\nsuggests that sub-arc mantle fO2 has predominantly controlled the long-term oxidation of arc magmas and thus\ninfluenced the secular oxidation of Earth’s surficial environments since the NOE. Nonetheless, sub-arc mantle\nfO2 was not the primary driver of the NOE”.\nThat said, the manuscript is now much clearer in explaining the machine method used in this study. All necessary\ndetails and information have been provided, making it more useful for readers. Overall, all my concerns have\nbeen addressed.\nReply 3: Thanks for your positive feedback and comments.\nBest regards,\nLuc Doucet, Perth, the 14/03/2025\nReviewer #2 (Remarks to the Author):\nThe revised version of the paper by Liu et al. presents a more robust discussion of the pitfalls of the V/Sc\nmethods and a comparison with the Fe-speciation approach. I find it interesting that the authors persist in the\nusability of the V/Sc over Fe3+/FeTOTAL, as the V/Sc is an indirect method and less precise. The correlation\nbetween the two methods indicates that the V/Sc proxy works, but it by no means proves that the consistent\noxidation of a specific slice of geological time is not a reflection of the resolution of the V/Sc proxy. One point\nthat remains valid is the classification used by Liu et al. (which differs from S&B by not using individual arcs\nand by averaging out the data per 100 Myr intervals), and as such, a way forward is to test the same sample\ndataset used for V/Sc but as Fe3+/FeTOTAL calculations. If the authors can provide this comparison, it can\npotentially resolve/explain the difference between them. I think this is important as the manuscript dismisses\nthe Fe3+/FeTOTAL without providing compelling arguments. Some of the new sentences included in the\nrevised manuscript should be modified as they are either unclear or incorrect.\nReply 1: Thank you for your detailed feedback and insightful comments on the revised version of our manuscript.\nWe appreciate your thorough review and have addressed each of your points as follows:\n(1) Addressing the V/Sc vs. Fe3+/ΣFe Methods\nAlthough the V/Sc ratio is an indirect method compared to the Fe3+/ΣFe approach, recent petrological\nmodeling demonstrates that V/Sc is largely insensitive to mantle source characteristics and the degree of melting,\nwhile remaining sensitive to variations in mantle fO (Table R1, Fig. R1). Furthermore, in a comparison with\n2\nfO estimates derived from Fe-XANES datasets, Liu et al. (2025) analyzed basalts from the Mariana arc\n2\nvolcanoes in the Central Island Province (Brounce et al., 2014) and the central Southwest Indian Ridge (SWIR)\n(Birner et al., 2018). Their results indicated that the fO values of modern arc and MORB mantles, as evaluated\n2\nthrough the V/Sc ratios of primitive arc basalts, are consistent with the fO values constrained by Fe3+/ΣFe ratios\n2\nfrom the Mariana and SWIR samples, respectively (Liu et al., 2025) (Fig. R2). Therefore, given the availability\nof V and Sc data, the V/Sc ratio serves as a reliable redox proxy for tracing the evolution of mantle fO .\nfrom Liu et al., 2025). PM, primitive mantle (Palme and O’Neill, 2014); DMM, depleted MORB mantle (Salters and\nStracke, 2004). Ol, olivine; Opx, orthopyroxene; Cpx, clinopyroxene; Spl, Spinel; Amp, amphibole; Grt, garnet. See more\ndetails in Liu et al. (2025; https://doi.org/10.7185/geochemlet.2504).\nSource Sub-arc mantle\nMineral Spinel Hydrous Hydrous spinel Garnet\nassemblages lherzolite harzburgite harzburgite lherzolite\nOl (wt. %) 57.0 58.0 58.0 53.1\nOpx (wt. %) 28.0 31.6 31.6 17.7\nCpx (wt. %) 13.0 — — 27.3\nSpl (wt. %) 2.0 — 2.0 —\nAmp (wt. %) — 10.4 8.4 —\nGrt (wt. %) — — — 3.0\nChemical\nDMM PM DMM PM DMM PM DMM PM\ncompositions\nV (µg/g) 79 86 79 86 79 86 79 86\nTi (µg/g) 798 1265 798 1265 798 1265 798 1265\nSc (µg/g) 16.3 16.4 16.3 16.4 16.3 16.4 16.3 16.4\nYb (µg/g) 0.40 0.48 0.40 0.48 0.40 0.48 0.40 0.48\nFigure R1 Modelling results for sub-arc mantle melting (see Table R1) (modified from Liu et al., 2025). Variations in\nmodelled (a) mineral proportions and (b, c) bulk partition coefficients (D) for V, Sc, Ti and Yb are shown, as well as (d–f)\nratios of V/Sc, 100 × V/Ti and V/Yb during partial melting of DMM and PM chemical compositions. Abbreviations are as\ndefined in Table R1. See more details in Liu et al. (2025; https://doi.org/10.7185/geochemlet.2504).\nFigure R2 Average sub-arc and MORB mantle fO values estimated via V/Sc across the different source mineral\n2\nassemblages and chemical compositions (modified from Liu et al., 2025). Horizontal error bars illustrate 1 s.d.\nuncertainties. The vertical green and blue color bands show the mean values of global sub-arc and MORB mantle fO with\n2\n2 s.e.m. uncertainties. The grey horizontal bands show ranges of previously determined modern sub-arc and MORB mantle\nfO values. See more details in Liu et al. (2025; https://doi.org/10.7185/geochemlet.2504).\n2\n(2) Fe3+/ΣFe Analysis Using Our Dataset\nWe agree that calculating Fe3+/ΣFe ratios using our basaltic dataset would be a useful test. However, our\ncompiled basaltic dataset lacks Fe3+ data because they were rarely measured and reported in the original\npublications. This scarcity of ferric iron data is even more pronounced for ancient samples (e.g., see below Fig.\nR4), highlighting the challenges in obtaining comprehensive Fe3+/ΣFe data.\n(3) Analysis of the S&B2019Fe Dataset\nTo provide a comparison, we utilized the Fe3+/ΣFe data on island arc rocks from the dataset compiled by\nStolper and Bucholz (2019; hereafter referred to as the “S&B2019Fe dataset”, available in their supplementary\nfile “pnas.1821847116.sd02”). We selected primitive arc basaltic samples using the same filtering criteria as in\nour study: SiO (45–54 wt.%), MgO (8–17 wt.%), and Mg# (60–72) (molar Mg# = 100 × MgO/(MgO + FeO ))\n2 tot\n(Fig. R3). We then calculated the mean Fe3+/ΣFe ratios of these primitive arc basaltic samples in 100-Myr bins\nthrough time without using the bootstrap resampling method (Fig. R4a).\nAdditionally, we applied our machine learning (ML) model to the island arc basaltic samples in the\nS&B2019Fe dataset and selected the primitive island arc basaltic rocks using the same filters. We then calculated\nthe mean Fe3+/ΣFe ratios of these samples without using the bootstrap resampling method, as spatial data (i.e.,\nlatitude and longitude) were not available (Fig. R4b).\nThe results reveal that the number of Fe3+ data points for primitive island arc basalts is quite limited. For\nexample, the S&B2019Fe dataset contains only 84 and 28 primitive island arc samples erupted during 0.8–0\nGa and 2.5–0.8 Ga, respectively (Fig. R4a). Moreover, mean Fe3+/ΣFe ratios do not show a clear shift during\n~0.8–0.4 Ga beyond the range of errors (Fig. R4a, b). The high variability in Fe3+/ΣFe ratios during ~0.6–0 Ga\nmay be influenced by the scarcity of data (i.e., the issue of sample representativeness) and potential\nspatiotemporal bias among the samples (Supplementary Figs. S11 and S12).\nFigure R3 a Fe3+/ΣFe vs. MgO and b Fe3+/ΣFe vs. Mg# for island arc basalts from Stolper and Bucholz (2019), hereafter\nreferred to as the “S&B2019Fe” dataset (available in their supplementary file “pnas.1821847116.sd02”). For comparison\nwith our results, we selected primitive arc basaltic samples from their dataset using the same filtering criteria as in our\nstudy: 45–54 wt.% SiO , 8–17 wt.% MgO, and Mg# = 60–72 (gray shaded areas). We then calculated the mean Fe3+/ΣFe\n2\nratios of these primitive arc basaltic samples in 100-Myr bins through time without using the bootstrap resampling method\n(Fig. R4).\nFigure R4 Secular changes in the mean Fe3+/ΣFe ratio of primitive island arc basaltic samples in the S&B2019Fe dataset\n(Stolper and Bucholz, 2019). Primitive island arc basaltic samples a extracted directly from the S&B2019Fe dataset and\nb after application of our ML classification model to select only arc samples. The primitive arc samples were selected using\nthe same filtering criteria as in our study: 45–54 wt.% SiO , 8–17 wt.% MgO, and Mg# = 60–72 (Fig. R3). The results\n2\nreveal that the number of Fe3+/ΣFe data points for primitive island arc basalts in the S&B2019Fe dataset is quite limited.\n(4) Analysis of the S&B2019V-Sc Dataset\nFurthermore, we utilized the V/Sc ratios of island arc rocks from the dataset compiled by Stolper and\nBucholz (2019; hereafter referred to as the “S&B2019V-Sc dataset”, accessible in their supplementary file\n“pnas.1821847116.sd04”). We filtered the primitive arc basaltic samples using the criteria of SiO (45–54 wt.%)\n2\nand MgO (8–17 wt.%) (Fig. R5), but did not apply the Mg# filter due to the unavailability of FeO data in this\ntot\ndataset. Subsequently, we calculated the mean V/Sc ratios of these primitive island arc basaltic samples in 100-\nMyr bins through time without employing the bootstrap resampling method (Fig. R6). Given the absence of\ntrace element data in the S&B2019V-Sc dataset, we did not apply our ML model to this dataset.\nThe S&B2019V-Sc dataset contains a relatively limited number of V/Sc data points for primitive island\narc basalts. Specifically, the dataset includes 149 and 136 primitive island arc samples erupted during 0.8–0 Ga\nand 2.5–0.8 Ga, respectively (Fig. R6a). Despite this, the results indicate that the mean V/Sc ratios did not\nclearly increase during the period from ~0.8 to 0.4 Ga, considering the range of errors (Fig. R6) (Supplementary\nFigs. S13 and S14).\nAccordingly, our refined dataset, ML classification model, and V/Sc ratios offer a reliable record of the\ntemporal evolution of sub-arc mantle fO . Furthermore, we have recalculated the mean V/Sc ratios using simple\n2\ntraditional methods instead of the ML and bootstrap methods (see details in Reply 5). Moreover, we have revised\nthe unclear and incorrect expressions as you suggested (see details in subsequent replies).\nFigure R5 V/Sc vs. MgO content in island arc basalts from Stolper and Bucholz1, hereafter referred to as the “S&B2019V-\nSc” dataset (accessible in their supplementary file “pnas.1821847116.sd04”). We selected primitive arc basaltic samples\nbased on SiO (45–54 wt.%) and MgO content (8–17 wt.%) (gray shaded area), but we did not apply the Mg# filter due to\n2\nthe unavailability of FeO data in this dataset. Subsequently, we calculated the mean V/Sc ratios of these primitive island\ntot\narc basaltic samples in 100-Myr bins through time without employing the bootstrap resampling method (Fig. R6).\nFigure R6 Secular changes in the mean V/Sc ratios of primitive island arc basaltic samples extracted directly from the\nS&B2019V-Sc dataset (Stolper and Bucholz, 2019). The primitive arc samples were selected based on SiO (45–54 wt.%)\n2\nand MgO content (8–17 wt.%) (Fig. R5). Given the absence of trace element data in the S&B2019V-Sc dataset, we did\nnot apply our ML model to this dataset. The S&B2019V-Sc dataset contains a relatively limited number of V/Sc data\npoints for primitive island arc basalts.\nThe new title “Relatively consistent oxidation” does not reflect the results obtained in the study. For example,\nfluctuations in redox conditions are presented and discussed (e.g., latitude-controlled fugacity) but then\ndismissed as unimportant. The 100-Myr bins data points have uncertainties that do not overlap throughout the\n0.8-0 Ga interval, suggesting that the redox state is not “consistent”. If it were consistent, one would understand\nthat the oxidation had remained constant since the Neoproterozoic and Phanerozoic. Perhaps a better title would\nbe “Relatively oxidised sub-arc mantle…” if the main point is to acknowledge variations and highlight that\nalthough they are presented, the oxidation state of the sub-arc mantle remained above the ambient mantle\nthroughout the interval studied.\nReply 2: Thank you for your detailed feedback on the title and the points raised regarding the consistency of the\noxidation state in our study. We understand your concern that the title “Relatively consistent oxidation” does\nnot fully capture the nuances of our results, particularly the fluctuations in redox conditions and the uncertainties\nassociated with the 100-Myr bins. Your suggestion to use “Relatively oxidized sub-arc mantle...” is well taken,\nand we agree that it more accurately reflects the key findings of our study. Accordingly, after also addressing\ncomments from Reviewer #1, our revised title is “The sub-arc mantle has remained oxidized since the\nNeoproterozoic Oxygenation Event”.\nIt would also be helpful to show how simply using V/Sc basalts over time would look compared to the\nML+bootstrap approach. Is it possible that the misclassified samples are not enough to change the overall\nobservation if they were included in the V/Sc averages?\nReply 3: Thank you for your insightful suggestion regarding the comparison between using a simple V/Sc\napproach over time and our ML + bootstrap approach. We present the mean V/Sc variations via simple methods\nin detail in Reply 5, below. The results show that the evolution of mean V/Sc ratios of primitive arc basalts is\nhighly biased by the choice of geochemical filters.\nLines 79-80: What are the implications for removing the back-arc and fore-arc basalts from the dataset? Can we\nsee the V/Sc of all basalts over time (perhaps in supplementary material?) to evaluate if the overall values are\naffected by including these other basalt types?\nReply 4: Thank you for your question regarding the implications of removing the back-arc and fore-arc basalts\nfrom our dataset and for suggesting the inclusion of the V/Sc ratios of all basalts over time in the supplementary\nmaterial. The back-arc and fore-arc samples exhibit relatively low fO values compared to arc basalts due to\n2\n(Brounce et al., 2014; Cottrell et al., 2022), primarily due to less effects of subduction related processes. To\nexclusively constrain the sub-arc mantle fO , we excluded back-arc and fore-arc samples from our training\n2\ndataset. Accordingly, however, this process may reduce the probability of recognizing back-arc and fore-arc\nsamples as arc ones.\nFurthermore, we plotted mean the V/Sc ratios of all primitive basalts over time (Fig. R7a). The results\nshow that the mean V/Sc ratios of all primitive basalts exhibit a different trend compared to the that obtained\nfrom the mean V/Sc ratios of primitive arc basalts alone (Fig. R7b).\nFigure R7 Secular changes in the mean V/Sc ratios of our compiled basalts over time, calculated for 100-Myr bins. a The\noverall primitive basalts were filtered by SiO content (45–54 wt.%), MgO content (8–17 wt.%), and Mg# (60–72) without\n2\napplying our ML method. b The primitive arc basalts were filtered by the same criteria as a but with ML applied. The mean\nV/Sc ratios in a and b were calculated via the bootstrap resampling technique. Error bars represent 2 s.e.m. uncertainties.\nScatter points show V/Sc ratios against their average ages.\nLines 97-99: It remains unclear how much better the ML+bootstrap method is compared to simply using V/Sc\nof basalts over time. In other words, it is difficult to assess how much better this technique is compared to using\nan untreated dataset.\nReply 5: Thank you for your comment regarding the comparison between the ML + bootstrap method and\nsimply using the V/Sc ratios of basalts over time without any treatment. Notably, traditional binary\ndiscrimination diagrams exhibit low accuracy in classifying arc and non-arc basalts. Therefore, we classified\narc and non-arc basalts via two traditional methods, i.e., (Nb/La) < 0.75 (PM, primitive-mantle-normalized;\nPM\nGao et al., 2022) and (Ba/La) > 2 (CH, chondrite-normalized; Perfit et al., 1980) (Liu et al., 2024). Then, we\nCH\ncalculated the mean V/Sc ratios against their mean ages in 100-Myr bins without and with the bootstrap\nresampling method over time (Fig. R8). The results show that the temporal evolution of the mean V/Sc ratios\nare remarkably biased by the choice of geochemical filters (e.g., Nb/La vs. Ba/La; Fig. R8a, b). The results also\nfurther indicate that traditional binary discrimination diagrams yield poor accuracy when classifying arc vs. non-\narc basalts compared to the high-accuracy ML classification model (e.g., Figs. R9 and R10; modified from Liu\net al., 2024). Moreover, the highly variable mean V/Sc ratios obtained using traditional selection methods may\nhave been influenced by spatiotemporal bias. Specifically, the V/Sc ratio during ~0.6–0.7 Ga is missing because\nthere are no corresponding samples during this period (Fig. R8b). However, the bootstrap resampling technique\nconsiders the age error of every sample, thus providing a more robust estimation of V/Sc over time (e.g., Fig.\nR8c, d). Accordingly, using the ML + bootstrap method, we present a more reliable V/Sc record through time.\nFigure R8 The evolution of V/Sc of primitive arc basalts through time without and with the ML + bootstrap method. Arc\nbasalts were filtered by traditional geochemical methods, i.e., (a, c) (Nb/La) < 0.75 (PM, primitive-mantle-normalized;\nPM\nGao et al., 2022) and (b, d) (Ba/La) > 2 (CH, chondrite-normalized; Perfit et al., 1980). Error bars in (a, b) represent 1\nCH\ns.d. uncertainties, whereas those in (c, d) show 2 s.e.m. uncertainties. The scatter points are V/Sc ratios against their average\nages.\nFigure R9 Traditional bivariate discrimination plots of modern arc and non-arc basalts (modified from Liu et al., 2024).\n(a) The accuracy of (Nb/La) in distinguishing between arc and non-arc basalts is 77%; (b) that of (Ba/La) is 67%.\nPM CH\nSubscripts PM and CH indicate normalization to the primitive mantle and chondrites, respectively. See more details in Liu\net al. (2024; https://doi.org/10.1029/2023GL107996).\nFigure R10 Results of XGBoost ML model when classifying arc vs. non-arc basalts (modified from Liu et al., 2024). (a)\nThe relative feature importance scores of input features in the training dataset. (b) Confusion matrix of results when the\nmodel was applied to the testing dataset. The high accuracy (~95%) indicates that the ML model is capable of reliably\nclassifying arc and non-arc basalts based on their geochemical characteristics. See more details in Liu et al. (2024;\nhttps://doi.org/10.1029/2023GL107996).\nLine 149: This new discussion on ‘Validation of the ML classification model’ is too long to say that the ML\nmodel works and could be simplified. Some explanation on the effects of inadvertently including non-basaltic\narcs could be added instead.\nReply 6: Thanks for your suggestions. We agree that it could be more concise. Therefore, we have streamlined\nthis section (lines 134-152).\nAdditionally, we recognize the importance of addressing the potential effects of inadvertently including\nnon-basaltic arcs in our analysis. Moreover, it is possible that our model may inadvertently identify non-arc\nbasalts (e.g., MORBs) as arc basalts, which could affect the calculated V/Sc ratios of arc basalts and the\nestimated fO . However, our validation results further indicate that our ML model can robustly discriminate\n2\nbetween arc and non-arc basalts, minimizing misclassifications (lines 194-197).\nLines 197-200 state that “medium- to high-silica magmatic rocks are unsuitable for constraining the sub-arc\nmantle fO2, as their geochemical signatures have been significantly altered by extensive magmatic evolution\nand crustal assimilation, obscuring the fO2 information inherited from the mantle source.” This statement may\nbe valid but is not necessarily true as high-silica rocks can preserve their original mantle fugacity if partial\nmelting, fractional crystallisation and assimilation are well understood (see for example, Meng et al., 2022 and\nMoreira et al., 2023 in Nature Geoscience). I recommend clarifying that it is possible to preserve original\nfugacity in medium to high-silica magmas.\nReply 7: We appreciate your insight and the references provided, which highlight the potential for preserving\noriginal mantle fO in high-silica rocks under certain conditions. In the revised version, we acknowledge that it\n2\nis possible to constrain the sub-arc mantle fO using medium- to high-silica magmatic rocks if the degrees of\n2\npartial melting, fractional crystallization and assimilation are well understood (lines 166-170).\nLines 201-203: “Moreover, all the compiled whole-rock Fe3+/ΣFe ratios compiled by Stolper and Bucholz were\nobtained using wet chemical methods, such as colourimetric measurement that is now known to overestimate\nFe3+/ΣFe ratios in basaltic samples” This statement is misleading and it implies that all wet chemical methods\noverestimate the ratio, which is not true as titration methods do not overestimate Fe3+/FeTOTAL and not all\nmeasurements presented in S&B were obtained via wet chemical methods.\nReply 8: We appreciate your insights regarding the limitations of wet chemical methods. We understand that the\noriginal statement may be misleading, as it implies that all wet chemical methods overestimate Fe3+/ΣFe ratios.\nWe have revised the sentence as “Moreover, some whole-rock Fe3+/ΣFe data compiled by Stolper and Bucholz\n(2019) were obtained using wet chemical methods, including colorimetry and titration. Colorimetric\nmeasurements are known to overestimate Fe3+/ΣFe ratios in basaltic samples, whereas titration methods are\nmore reliable” (lines 172-175).\nLine 204: Mariana Trough back-arc basalts ‘are’ systematically…\nReply 9: Thanks. Modified accordingly (line 175).\nLine 206-207: It remains a question here whether using your dataset before classifying the samples as arc-\nbasalts would result in the same shift observed by S&B or not.\nReply 10: Thanks for your insightful comment. To address your question, we have examined the V/Sc ratios in\nour dataset both before and after classifying the samples as arc-basalts. Our findings indicate that, regardless of\nwhether the samples are classified as arc-basalts, we do not observe the same increasing trend in mean V/Sc\nratios between ~0.8 and 0.4 Ga as reported by Stolper and Bucholz (2019) (Fig. R7, Reply 4). This observation\nsuggests that the absence of such a trend in our data is not solely dependent on the classification of samples as\narc-basalts.\nLines 209-211: “Notably, variations in these ratios may not fully reflect changes in sub-arc mantle fO2, because\nthey are also influenced by melting pressure, temperature, fO2, mantle source compositions, and the degree of\npartial melting.” There’s a tautological issue here as those factors intrinsically control fugacity, so fugacity\nshould not be quoted as a cause of itself.\nReply 11: Thanks for your comment. We have modified this sentence (lines 180-182).\nLine 213: I don’t think the added word ‘application’ makes sense here.\nReply 12: Thanks for your comment. We have modified this sentence (line 184).\nLines 216-226: This part is confusing. It is argued that altered/weathered samples are not misclassified due to\nfluid-mobile elements being included in the ML model, but the samples used to support this argument are not\narc-basalts. The way to support this argument is to either say that altered samples are not used or that altered\nsamples (based on fluid-mobile elements) can still be recognised as arc-basalts.\nReply 13: We appreciate your feedback and have revised this section based on your suggestion. To address the\nconcern regarding the classification of altered samples, we have conducted additional analyses using a dataset\nof weathered Cretaceous island arc basaltic rocks (n = 8) from the Benbow Inlier in eastern Jamaica (Hastie et\nal., 2007). When we applied our high-dimensional ML model to these altered samples, we found that nearly all\nof them (n = 7) were correctly identified as arc basalts. This result demonstrates that our model is robust against\nalteration processes. The robustness of our model can be attributed to the low relative importance of fluid-\nmobile elements such as U and Pb (with relative importance scores <0.04) in our classification scheme.\nFurthermore, the top five features of our ML model (e.g., Nb/La, Ti, U/Nb, La, and Nb, to infer their weight in\nthe optimized ensemble tree model) are primarily indicators of deep geological processes, rather than alteration\nor weathering effects. This further supports the conclusion that our classification model is predominantly\ncontrolled by factors related to the mantle source and magmatic processes, rather than surface alteration (lines\n187-197).\nLines 304-306: “It has been suggested that the increase of atmospheric and oceanic oxygen levels during the\nlate Neoproterozoic and early Paleozoic may have inversely affected the oxidation state of the sub-arc mantle17”\nThis is not correct. S&B concluded the opposite. In other words, it has directly affected the oxidation state of\nthe sub-arc mantle.\nReply 14: Thanks for your comment. We have modified this sentence by replacing “inversely” with “directly”\n(lines 267-269).\nLine 308: If there is no direct effect between NOE, sulphate and oxidation of the mantle wedge, what is the\nalternative explanation? It is not clear how the following paragraph (lines 309-314) offers a fundamentally\ndifferent explanation based on the serpentinisation of the ocean floor and the subduction of sediments enriched\nin sulphate.\nReply 15: We appreciate your feedback and understand that the current explanation may not be entirely clear.\nThe initial hypothesis posited that the oxygenation of the deep ocean, accompanied by an increase in marine\nsulfate concentrations, could oxidize oceanic crustal materials (Stolper and Bucholz, 2019). These oxidized\nmaterials, once subducted, were thought to contribute to the oxidation of the mantle wedge and arc magmas. If\nthis were the case, we would expect to see a corresponding increase in the V/Sc ratios of arc magmas during the\nNeoproterozoic–Phanerozoic boundary (Stolper and Bucholz, 2019). However, our analysis reveals that the\nevolution of the sub-arc mantle’s oxygen fugacity (fO ) does not align with the significant rise in surface oxygen\n2\nlevels during the NOE. This observation suggests that the increase in atmospheric and marine oxygen\nconcentrations may not have directly led to the oxidation of the sub-arc mantle through elevated marine sulfate\ncontents (lines 267-271).\nAlternatively, serpentinization of mafic and ultramafic rocks can also oxidize the oceanic rocks and the\nupper lithosphere mantle (Alt et al., 2012; Evans, 2012; Maurice et al., 2020), which can be subducted into the\nmantle, thus oxidizing the sub-arc mantle (Stolper and Bucholz, 2019). If this mechanism were the primary\ndriver of mantle oxidation, we would expect the sub-arc mantle fO to have been oxidized since the onset of\n2\nsubduction. Our findings support this hypothesis, as we observe that the sub-arc mantle has maintained an\noxidized state since ~0.8 Ga (lines 272-282).\nThis observation suggests that the long-term oxidation of the sub-arc mantle may be driven by geological\nprocesses involving serpentinization and subduction, rather than by the direct input of marine dissolved oxygen\nand sulfate. Consequently, the oxidation of the sub-arc mantle appears to be influenced by deep Earth processes\nrather than being a direct consequence of changes in surface oxygen levels (lines 283-287).\nWe believe that this revised explanation more clearly articulates the relationship between the NOE,\nserpentinization, and the oxidation of the sub-arc mantle. Thank you for your valuable feedback, which has\nhelped us refine our argument and clarify this study.\nBased on Figure S9, some intervals seem to have no individual V/Sc data points. However, the diagram in\nFigure 2a shows that the sample size seems to be between 1 and 100 datapoints. Is this because the data points\nare out of scale?\nReply 16: Thank you for your insightful comment. We appreciate your attention to this detail and would like to\nclarify the matter. In Figure S9, we plotted individual V/Sc data points against their average ages, with each\npoint representing a specific measurement accompanied by its own age and associated uncertainty.\nConsequently, there are intervals, such as ~0.7–0.6 Ga, where no individual V/Sc data points are present (Fig.\nS9). However, Figure 2a shows a histogram of the number of primitive arc basalts erupted over time, and it\nappears that there are samples from the ~0.7–0.6 Ga period. This discrepancy arises because, although basaltic\nsamples exist during this period, V/Sc data have not been reported for those particular samples. If we were to\nplot a histogram of the number of V/Sc data points within the primitive arc basaltic dataset, there would indeed\nbe no bars during the ~0.7–0.6 Ga interval (Fig. R11).\nTo address the issue of data sparsity, our analysis employs a bootstrap resampling method that accounts for\nthe age error of each data point. This means that for a given sample, the resampled data point can be selected\nfrom a range of ages, not strictly limited to the exact average age. The age range is modeled as a normal\ndistribution, with the average age of the samples as the mean and the reported error as the standard deviation.\nFor example, in the period between 0.6 and 0.5 Ga, where there are limited data points, the resampling process\ncan still select data points if their age errors extend into this range. In summary, the bootstrap resampling method,\nwhich considers age uncertainties, enables a more reliable estimation of the mean V/Sc values, even in periods\nwith sparse data.\nFigure R11 Histogram of the number of V/Sc data points against their average ages over time. The red curve illustrates the\nkernel density estimate.\nReferences\nAlt, J. C. et al. Recycling of water, carbon, and sulfur during subduction of serpentinites: a stable isotope study\nof Cerro del Almirez, Spain. Earth Planet. Sci. Lett. 327–328, 50–60 (2012).\nBirner, S. K., Cottrell, E., Warren, J.M., Kelley, K. A. & Davis, F. A. Peridotites and basalts reveal broad\ncongruence between two independent records of mantle fO despite local redox heterogeneity. Earth Planet.\nBrounce M. N., Kelley K A, Cottrell E. Variations in Fe3+/ΣFe of Mariana arc basalts and mantle wedge fO . J.\nCottrell et al. Magma Redox Geochemistry Ch. 3 (Wiley-American Geophysical Union, Hoboken, 2022).\nEvans, K. A. The redox budget of subduction zones. Earth-Sci. Rev. 113, 11–32 (2012).\nGao, L. et al. Oxidation of Archean upper mantle caused by crustal recycling. Nat. Commun. 13, 3283 (2022).\nHastie, A. R., Kerr, A. C., Pearce, J. A. & Mitchell, S. F. Classification of altered volcanic island arc rocks using\nimmobile trace elements: Development of the Th–Co discrimination diagram. J. Petrol. 48, 2341–2357\n(2007).\nLiu C.-T., Ye C.-Y. & ZhangZhou J. Modelling redox state via V-Sc-Ti-Yb partitioning in mantle derived melts.\nGeochem. Perspect. Let. 33, 1–7 (2025).\nLiu, C.-T., Ye, C.-Y. & ZhangZhou, J. Secular changes in the occurrence of subduction during the Archean.\nGeophys. Res. Lett. 51, e2023GL107996 (2024).\nMaurice, J. et al. The intrinsic nature of antigorite breakdown at 3 GPa: Experimental constraints on redox\nconditions of serpentinite dehydration in subduction zones. Contrib. Mineral. Petrol. 175, 94 (2020).\nPalme, H. & O’Neill, H. St. C. Treatise on Geochemistry Ch. 3.1 (Elsevier Ltd., Oxford).\nPerfit, M. R., Gust, D. A., Bence, A. E., Arculus, R. J. & Taylor, S. R. Chemical characteristics of island- arc\nbasalts: implications for mantle sources. Chem. Geol. 30, 227–256 (1980).\nSalters, V. J. M. & Stracke, A. Composition of the depleted mantle. Geochem. Geophys. Geosyst. 5, Q05B07\n(2004).\nStolper, D. A. & Bucholz, C. E. Neoproterozoic to early Phanerozoic rise in island arc redox state due to deep\nocean oxygenation and increased marine sulfate levels. Proc. Natl. Acad. Sci. USA 116, 8746–8755 (2019)."}, {"round": 3, "reviewer_comments": {"reviewer_2": "The revised version of the manuscript by Liu et al is more nuanced and addresses the key points raised in the last round of\nreviews. Based on the new plots provided in the rebuttal letter, it is clear that the ML+bootstrap model is valid when the data\nare scarce or absent, but overall, it provides a similar understanding of the sub-arc mantle fugacity over the last 800 Myr\ncompared to simpler classification methods. It implies that misclassification of the basaltic rocks is not severely detrimental\nto the overall conclusion of this manuscript. I believe this point could be more directly mentioned in the discussion of the\npaper. Otherwise, the latest version of the manuscript is interesting, timely and would stimulate discussions on the same\nsubject, making it a good contribution to Nature Communications."}, "author_response": "Reply: Thank you for your positive feedback and constructive comments. We appreciate your recognition that the ML + bootstrap model yields consistent insights into mean V/Sc over the past 800 million years, even when compared to simpler classification methods.\nAs you noted, the similarity in V/Sc trends between the ML approach and simpler methods\n(e.g., Nb/La vs. Ba/La plots, Figure R1) suggests that misclassification does not drastically\nalter the core conclusion. However, we would like to emphasize that accurate identification of\narc basalts remains critical for robustly quantifying fO evolution. For example, while modern\n2\narc basalts and MORBs exhibit comparable mean V/Sc ratios, the calculated fO of the sub-arc\n2\nmantle is higher than that of MORB mantle—largely because arc magmas form at lower\nmelting temperatures (Wang et al., 2019; Liu et al., 2025). Thus, the ML model’s ability to\nreduce misclassification (especially for ambiguous ancient samples) helps avoid potential\nbiases in fO estimates, ensuring a more reliable reconstruction of long-term redox trends.\nbootstrap method. Arc basalts were filtered by traditional geochemical methods, i.e., (a, c) (Nb/La) <\nPM\n0.75 (PM, primitive-mantle-normalized; Gao et al., 2022) and (b, d) (Ba/La) > 2 (CH, chondrite-\nCH\nnormalized; Perfit et al., 1980). Error bars in (a, b) represent 1 s.d. uncertainties, whereas those in (c, d)\nshow 2 s.e.m. uncertainties. The scatter points are V/Sc ratios against their average ages.\nReferences:\nLiu C.-T., Ye C.-Y. & ZhangZhou J. Modelling redox state via V-Sc-Ti-Yb partitioning in\nmantle derived melts. Geochem. Perspect. Let. 33, 1–7 (2025).\nWang, J. et al. Oxidation state of arc mantle revealed by partitioning of V, Sc, and Ti between\nmantle minerals and basaltic Melts. J. Geophys. Res.: Solid Earth 124, 4617–4638 (2019)."}]

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