Earth system instability explains redox paradox during late Cambrian SPICE event

Abstract

The late Neoproterozoic–early Paleozoic (~600 to 520 million years ago) witnessed a fundamental shift under atmosphere-ocean redox conditions, where pulsed ocean oxygenation events (OOEs) were replaced by episodic ocean anoxic events (OAEs). The Cambrian Steptoean positive carbon isotope excursion (SPICE) event (494.5 to 492.5 million years ago) represents a major early Paleozoic OAE, yet its drivers and underlying dynamics remain controversial. Here, we present carbonate uranium isotope (δ²³⁸U_carb) data from North and South China, revealing a sharp decrease from −0.29 ± 0.12 per mil to −0.85 ± 0.03 per mil at the onset of the SPICE event, followed by a return to pre-excursion values. This indicates a rapid onset of global ocean anoxia before the rise of δ¹³C_carb values, followed by a transition to oxic conditions. Integrating δ²³⁸U_carb data with refined COPSE (Carbon, Oxygen, Phosphorus, Sulphur, and Evolution) biogeochemical modeling reconciles the pre-SPICE redox paradox of low atmospheric pO₂ coexisting with limited seafloor anoxia. We propose that the SPICE and its associated excursions reflect a non-steady-state Earth system behavior, involving oscillations in coupled phosphorus-oxygen-carbon-sulfur and uranium cycles, which influenced the evolution of early animals through redox-dependent biodiversity filters.

Uranium isotopes and biogeochemical modeling suggest that Earth system instability drove a redox-paradox during the SPICE.

INTRODUCTION

The late Neoproterozoic–early Paleozoic transition [~600 to 520 million years ago (Ma)] was characterized not only by a simple stepwise rise in atmospheric oxygen (pO₂) but also by marked oscillations under both the carbon cycle and marine redox conditions (1–5). This dynamic interval coincided with the rise and evolution of early animals, as well as the subsequent Cambrian Explosion, during which most major animal phyla first appeared (3, 6, 7). Geochemical evidence (i.e., δ¹³C_carb and δ²³⁸U_carb) indicates a fundamental Earth system transition from stable, widespread anoxia (pre–800 Ma) to recurring redox oscillations (~800 to 520 Ma) (3, 8)—a shift recently recognized as an Earth system Hopf bifurcation (9, 10). This Neoproterozoic oxygenation event (NOE) (11) ultimately paved the way for more stable oxic conditions that established modern biogeochemical cycles and laid the foundation for the evolution and diversification of morphologically and phylogenetically complex animals.

However, key debates persist regarding the timing and geochemical expression of this transition and when pO₂ rose to near-modern levels. One hypothesis posits delayed oxygenation [~0.2 present atmospheric level (PAL)] until the middle Paleozoic with the expansion of land plants ultimately driving the rise to modern levels, termed the Paleozoic oxygenation event (12). This is supported by multiple lines of evidence, including (i) redox proxy data (Mo isotopes and Ce anomalies) showing shifts at ~435 to 392 Ma (13, 14), (ii) low seawater sulfate levels inferred from sulfur isotope mass balance, suggesting a high burial ratio of pyrite to gypsum (15), (iii) the absence of pre–400 Ma charcoal (16), and (iv) modeling results from inverse [data-driven; GEOCARBSULFOR; (17)] and forward models [process-driven; COPSE; (18, 19)]. In contrast, evidence from halite fluid inclusions (20) and alternative modeling results [GEOCARB, GEOCARBSULF, and MAGic; (21–23)] argue for higher early Paleozoic pO₂ (~0.8 PAL).

Therefore, this study aims to (i) reconcile discrepancies among redox-sensitive isotope systems—particularly uranium versus sulfur isotopes—to help resolve the critical redox paradox of coexisting low atmospheric pO₂ (0.3 ± 0.1 PAL) and a low fraction of seafloor anoxia (10 ± 10%) in the early Paleozoic (2) and (ii) assess whether the early Paleozoic Earth system transitioned out of an unstable, oscillatory regime. We achieved these goals by presenting new geochemical data and modeling results focused on the Steptoean positive carbon isotope excursion (SPICE; 494.5 to 492.5) (24, 25), a well-studied chronostratigraphic marker long regarded as the first major ocean anoxic event (OAE) of the Phanerozoic (26) and noted for its unusual biogeochemical signals.

Uranium isotopes

The uranium isotope composition (²³⁸U/²³⁵U ratio, denoted as δ²³⁸U) of marine carbonates is a well-established global seafloor redox proxy due to its redox sensitivity at a globally integrated scale (27). Uranium has two dominant oxidation states in surface environments: the sparsely soluble U(IV) and the soluble U(VI) (28). Under anoxic conditions, the reduction of U(VI) to U(IV) results in a large and detectable isotopic fractionation, with the reduced U(IV) being enriched in the heavier ²³⁸U isotope. During periods of anoxia, the enhanced reduction of U(VI) to U(IV) and the subsequent removal of heavy isotopes from seawater would shift the δ²³⁸U values of seawater toward lower values. Uranium has a long residence time in the modern ocean [~500 thousand years (kyr)] relative to the ocean mixing time (1 to 2 kyr) (29), which leads to a relatively uniform δ²³⁸U composition of seawater (30). This global homogeneity persisted even during periods of extensive marine anoxia, when uranium residence times were likely reduced due to smaller oceanic reservoirs (31, 32).

Neoproterozoic-Paleozoic carbonates exhibit relatively consistent δ²³⁸U baselines, with cross-sectional differences typically ranging from 0.1 to 0.2 per mil (‰). In contrast, major negative carbon isotope excursions—such as the Ediacaran Shuram event (~574 Ma)—reach magnitudes of ~0.8‰ and occur synchronously across different continents (3, 33). An anticorrelation between δ²³⁸U and δ¹³C_carb is widely observed during the Neoproterozoic-Paleozoic transition (5): Positive carbon isotope excursions coincide with negative uranium isotope excursions during OAEs, whereas negative carbon isotope excursions coincide with positive uranium isotope excursions during ocean oxygenation events (OOEs) (34).

Biogeochemical models

We built on the Carbon, Oxygen, Phosphorus, Sulphur, and Evolution (COPSE) model (18, 19) and its extended configurations to test two competing explanations for the SPICE event and coeval geochemical anomalies: (I) an enhanced nutrient (phosphorus) influx to the oceans triggered increased primary production and organic carbon burial within an early Paleozoic steady state (35–37) or (II) that these patterns reflect the continuation of Earth system oscillations initiated in the Neoproterozoic. Furthermore, we incorporated stochastic forcing to illustrate the dynamic relationship between SPICE and the associated oscillations in configuration (III).

Scenario I was explored using the baseline COPSE reloaded model with the inclusion of an oceanic uranium cycle [see tables in (19, 27)]. The early Paleozoic steady state (pO₂ = ~0.2 PAL) was achieved by fixing all physical forcings inherited from the GEOCARB and COPSE models to values corresponding to 500 Ma (18, 19, 22). We varied the atmosphere-ocean oxygen reservoir (O) from 0.1 to 0.9 PAL to explore the response. The resulting nine stable states produced corresponding shifts in other reservoirs (normalized to present-day levels): atmosphere-ocean carbon-alkalinity (A) = 3.75 ± 0.25, ocean phosphorus (P) = 2 ± 1, sulfur (S) = 0.3 ± 0.3, and uranium (U) = 0.375 ± 0.375 (fig. S1). To achieve a background δ¹³C_carb of ~0‰ at pO₂ = 0.9 PAL, we assigned δ¹³C values of +3.0 and −24‰ for the carbonate (oxidized) and sedimentary organic (reduced) carbon reservoirs, respectively. In our notation, uppercase bold italic lettering (e.g., A) indicates reservoir size normalized to present-day levels.

Scenario II used an “excitable” extension of the COPSE model, which replaces the zero-dimensional ocean with a multicolumn ocean structure, following the excitable P-O-C cycle (EPOC) model (38). This framework explicitly considers heterogeneous seafloor redox conditions by partitioning marine burial fluxes of organic carbon, phosphorus, and sulfur into 100 idealized ocean columns (fig. S2). The oxygen demand in each column varies according to the nutrient-uptake efficiency parameter k_Uⁱ (i = 1 to 100; k_Uⁱ_minimum = 0.23 and k_Uⁱ_maximum = 0.25) (39), producing relatively uniform redox conditions across the seafloor. Marine export production is assumed to be proportional to P, and organic carbon burial is considered proportional to export production and thus also proportional to P.

One of the key controls on whole-system dynamic is the cycling of phosphorus—the ultimate limiting nutrient for primary production over geological timescales (40, 41)—and, more specifically, the dependence of seafloor redox conditions on the burial ratio of organic carbon to total phosphorus (C_org:P_total) (42, 43). This coupling operates through two competing effects: Higher marine P concentration fuels productivity, increasing P burial, but the resulting oxygen consumption in the water column and the expansion of anoxia suppress P burial. Under uniform redox conditions, a threshold P level exists beyond which widespread anoxia is triggered (fig. S3A), producing a nonmonotonic relationship between P levels and the globally integrated P burial flux (fig. S3B). This nonlinear, redox-sensitive feedback amplifies system instability and can generate limit cycle oscillations with periods of ~3 to 30 million years (Myr). Mathematically, the coupled C-O-P-S-U differential equations yield periodic solutions (9, 10, 38, 44).

In this configuration, we introduce a scaling factor (or hyperparameter) Corgb_f (multiplying the globally integrated organic carbon burial flux). For example, when the Corgb_f is set to 1.0, the model predicts a burial flux of approximately modern levels, at 4.5 × 10¹² mol C/year. This factor facilitates three distinct dynamical regimes separated by two tipping points (fig. S3, C to O): (i) anoxic steady state (Corgb_f < 0.5; blue lines in fig. S3), where marine organic carbon burial is insufficient to accumulate oxygen once balanced by oxidative weathering and organic carbon degassing, causing the atmosphere-ocean oxygen reservoirs to remain stable at low values (<0.1 PAL; fig. S3E); (ii) long-term non-steady-state or unstable regime (0.5 < Corgb_f < 1.2; orange lines in fig. S3), where crossing the anoxic tipping point imbalances the P-O-A plus S-U cycles, driving sharp rises and drops in reservoir sizes within the ranges roughly consistent with the stable state in scenario I: P = 2 ± 1.0; O = 0.4 ± 0.1; A = 4 ± 0.5; S = 0.02 ± 0.01; U = 1.5 ± 1.5; and (iii) an oxic steady state (Corgb_f > 1.2; red lines in fig. S3, above the oxic tipping point), where stronger marine organic carbon burial elevates pO₂ until burial and oxygen sinks are again balanced, locking the system into a high-oxygen steady state. Therefore, the anoxic (≈0.5) and oxic (≈1.2) tipping points of the factor Corgb_f define the non-steady-state where oscillations emerge. Within the non-steady-state, Corgb_f determines the pace and shape of the oscillation (fig. S3, G to I).

Scenario III builds on the Scenario II with two additional modifications: (i) a step increase in Corgb_f from 1.0 to 1.5 to illustrate the system’s behavior as it crosses the oxic threshold and (ii) the introduction of stochastic forcing by adding a noise term to the differential equation for A. Physically, this noise term represents random fluctuations in the volcanic-metamorphic degassing flux

$$\frac{\mathrm{d}A}{\mathrm{d}t}=F_{\mathit{\text{Ainput}}}-F_{\mathit{\text{Aoutput}}}+{\mathrm{\eta }}_A\left(t\right)$$

$${\mathrm{\eta }}_A\left(t\right)=\frac{\mathrm{\alpha }}{\sqrt{{\mathrm{\tau }}_{\mathrm{{\rm A}}}}}\ast \mathit{dW}\left(t\right)$$

The noise term η_Α(t) (unit: mol C/year) is defined using two parameters—α and the residence time of A τ_A—together with a standard Wiener process dW(t). We set α ≈ 3 × 10¹⁵ mol C year^−0.5 and τ_A ≈ 1 × 10⁶ years, such that the resulting perturbation yield normally distributed fluctuations with a mean magnitude of ~3 × 10¹² mol year⁻¹ when averaged over 10⁶-year intervals. This level of variability is consistent with the order of magnitude of the long-term carbon inputs and outputs (~1 × 10¹³ mol year⁻¹) of the A reservoir.

RESULTS

The SPICE event at the Jiulongshan (JLS) and Duibian (DB) sections is characterized by a globally recognized positive carbonate carbon isotope excursion, with the δ¹³C_carb shifting from −0.16 to +4.40‰ (Fig. 1, C and E). The δ²³⁸U_carb data show a smooth negative excursion, the peak of which coincides with the onset of the rising limb of the positive δ¹³C_carb excursion, followed by a gentle positive excursion that persists into the falling limb of the δ¹³C_carb curve (Fig. 1, D and F). In the northern China JLS section, carbonate δ²³⁸U_carb values decline from −0.41‰ to a negative peak of −0.82‰ at the Miaolingian-Furongian boundary (Fig. 1D). With the beginning of the Paibian stage, δ²³⁸U_carb rebounds to −0.26‰ and then stabilizes around −0.50‰ (range: −0.61 to −0.37‰), mirroring its initial pre-SPICE level. A nearly identical pattern is observed in the southern China Duibian section (Fig. 1F), where δ²³⁸U_carb decreases from −0.18 to −0.88‰ before the SPICE and then gradually increases to −0.10‰ at ~56 m, before returning to around −0.50‰. The decline in δ²³⁸U_carb begins before the rise in δ¹³C_carb, and its positive excursion persists until roughly midway down the falling limb of the δ¹³C_carb curve.

Fig. 1. Paleogeography and trends in isotopic data.

(A) Global paleogeographic map at ~495 Ma (66). (B) Locations of the two study sections on the North China Platform and Yangtze Platform (67). Abbreviations: JLS, Jiulongshan; DB, Duibian. (C and D) Paired δ¹³C_carb and δ²³⁸U_carb data from the JLS section. (E and F) Paired δ¹³C_carb and δ²³⁸U_carb data from the DB section. Modern carbonate δ²³⁸U_carb values are from (68). The SPICE interval spans the late Guzhangian to Paibian stages (blue shading) (69). NUIE, negative uranium isotope excursion. The red solid line denotes the trend line derived from locally estimated scatterplot smoothing (LOESS) fitting, and the gray shaded area represents the 90% confidence interval.

DISCUSSION

Interpretation of the carbonate uranium isotope records across the SPICE

Multiple lines of evidence suggest that the carbonate uranium isotope records observed during the SPICE event represent a primary seawater signal documenting secular variations in seawater uranium isotope compositions, rather than being related to depositional diagenesis. First, there is no statistically significant covariation between δ²³⁸U_carb values and δ¹⁸O_carb and δ¹³C_carb values. Second, our samples exhibit very low Mn/Sr and Rb/Sr ratios, high U/Al ratios, minimal dolomitization, and uniformly low Al contents, indicating negligible diagenetic alteration and detrital contamination (see the Supplementary Materials for details; figs. S5 to S9). Third, the close correspondence in the timing and magnitude of the carbon and uranium isotope shifts between the North and South China sections, coupled with consistent carbonate δ²³⁸U_carb trends from Australia (36), strongly indicates a globally homogeneous response.

Our understanding of the uranium redox cycle in modern environments suggests that the negative and positive excursions observed during the SPICE event reflect changes under global marine redox conditions. Specifically, the negative shift at the onset of the SPICE event indicates an expansion of marine anoxia, whereas the positive shift during the event suggests a return to oxic conditions. However, the positive excursion may relate to a transition from strong euxinic conditions to strong ferruginous conditions, considering that some recent studies suggest muted uranium isotope fractionations between ferruginous water columns and underlying sediments (45, 46). Nevertheless, this alternative interpretation is deemed highly unlikely due to inconsistency with published redox proxy data from various basins. Published iron speciation data across the SPICE event, including sections from Avalonia, Baltica, Laurentia, and Gondwana, a powerful proxy for distinguishing between euxinic and ferruginous conditions, do not show a statistically significant decrease in the Fe_Py/Fe_HR ratio, suggesting no evidence for a shift from euxinic to ferruginous anoxia (35, 47). Meanwhile, carbonate records from the Durness Group in the UK indicate persistent dysoxia to ferruginous conditions without evidence of widespread euxinia before or during the event (48).

Therefore, a pronounced positive δ²³⁸U_carb excursion driven primarily by a large-scale transition from globally euxinic to ferruginous conditions lacks the necessary preconditions. Consequently, the observed positive δ²³⁸U_carb excursion is more parsimoniously explained by a genuine contraction of the anoxic seafloor area, implying an increase in the proportion of oxic waters, rather than a major internal shift in the dominant mode of anoxia from euxinic to ferruginous. This interpretation aligns consistently with independent evidence for increased organic carbon and pyrite burial during the SPICE and its hypothesized consequence of a net rise in atmospheric-oceanic oxygen levels (49).

Failure of the steady-state explanation for the late Cambrian SPICE Earth system

Building on Berner’s inverse modeling approach (21, 22), coupled δ¹³C_carb-δ³⁴S_CAS and δ²³⁸U_carb records have been used to reconstruct atmospheric pO₂ and the fraction of anoxic seafloor (f_ANOX), respectively. Applying this method to the Terreneuvian (early Cambrian) yields a paradoxical redox scenario: pO₂ ≈ 0.3 ± 0.1 PAL coexists with f_ANOX ≈ 10 ± 10% (2), although the mechanism behind this paradox remains elusive. This redox paradox challenges the widely accepted nonlinear pO₂-f_ANOX relationship, which predicts a steep increase in seafloor anoxia as pO₂ declines (e.g., from ~20 to ~70% f_ANOX when pO₂ falls from 0.6 to 0.4 PAL). Although refinements in ocean circulation or biogeochemical feedbacks can modify the exact shape of this relationship (50–52), the first-order principle—that lower pO₂ should correspond to greater seafloor anoxia—remains valid. Because the SPICE event exhibited δ¹³C_carb and δ²³⁸U_carb excursions similar to those observed in the Terreneuvian, this redox paradox may have persisted into the late Cambrian (Fig. 2A). The observed lead of the δ²³⁸U_carb negative excursion before the δ¹³C_carb rise could be explained by a mechanism where redox changes precede carbon cycle variations, such as redox-driven organic carbon remineralization (5). However, this alternative hypothesis does not resolve the paradox itself as it offers no explanation for the long-term coexistence of low atmospheric pO₂ and a limited fraction of anoxic seafloor.

Fig. 2. Modeling results display the early Paleozoic redox paradox.

(A) Relationship between atmospheric pO₂ and the fraction of seafloor anoxia (f_ANOX) showing the nonlinear transition from anoxic (0.4, 0.77) to oxic (0.6, 0.23) states based on the COPSE model (19), with the paradoxical early Cambrian redox state constrained by (2). (B) Phosphorus influx to the oceans. (C) Testing different atmosphere-ocean oxygen levels (0.1 to 0.9 PAL). (D) Predicted variations in f_ANOX. (E to G) Model-data comparisons for δ¹³C_carb, δ²³⁸U_carb, and δ³⁴S_CAS records [data sources: this study and (36)]. Refer to fig. S1 for an extended version showing normalized size of P-O-A-S-U reservoirs.

To test whether nutrient-driven perturbations could explain this (Scenario I; see the section “Biogeochemical models” for details), we applied a single phosphorus pulse designed to reproduce the +4‰ positive δ¹³C_carb excursions across a range of fixed pO₂ steady states (0.1 to 0.9 PAL; Fig. 2C) in the COPSE model. Although the model reproduces the positive δ¹³C_carb excursions under all pO₂ states, only low-pO₂ scenarios (<0.2 PAL; Fig. 2G, blue lines) fit the δ³⁴S_CAS values (~40‰), whereas high-pO₂ scenarios (>0.8 PAL; Fig. 2F, red lines) match the pre- and post-SPICE δ²³⁸U_carb baseline values (−0.4‰) and its negative excursion.

The failure of the steady-state explanation is multifaceted. First, the phosphorus influx required to trigger a +4‰ positive δ¹³C_carb excursions from a steady state (dR/dt = 0, where R denotes the reservoir size in mol) is unrealistically large, exceeding the estimated total phosphorus delivery to the modern ocean (~4 × 10¹⁰ mol/year) (19). Identifying a plausible geological process or source rock capable of supplying such an input is highly challenging. Second, there is a substantial incompatibility between the constraints imposed by sulfur and uranium isotope mass balances.

We propose that the SPICE event may reflect a persistently non-steady-state or oscillatory Earth system regime initiated in the Neoproterozoic (9, 10). In this view, the observed geochemical anomalies arose from sustained source-sink imbalances rather than a single transient physical forcing. Similar dynamics—where nonlinear redox feedbacks on marine P burial generate periodic isotopic excursions—have been invoked to explain the recurrence of Cretaceous and Early Triassic OAEs (38, 44).

SPICE occurred against a long-lasting Earth system non-steady-state

To simulate non-steady-state Earth system dynamics (Scenario II), we used the “excitable” extension of the COPSE model (38). We set the organic carbon burial flux to near-modern levels, Corgb_f = 1.0. Although elevated bioturbation during the Cambrian could have locally reduced organic carbon burial efficiency and thus the integrated burial flux (53, 54), independent modeling indicates that marine organic carbon burial flux had increased to modern levels during the Neoproterozoic–early Paleozoic transition (55).

Our model experiment successfully reproduces the paradoxical atmosphere-ocean redox state associated with SPICE. Before the positive δ¹³C_carb excursion, the system exhibits low pO₂ (~0.25 PAL), a low C_org:P_total burial ratio, and limited f_ANOX (<0.1) (Fig. 3B), characterized by oxic water columns and efficient P removal. In this redox state, the oxygen cycle is in source-sink imbalance: the integrated sink—comprising oxidative weathering, organic carbon degassing, and pyrite weathering—exceeds the combined sources from organic carbon and pyrite burial (Fig. 3A). In contrast, the atmosphere-ocean carbon-alkalinity (A) and ocean phosphorus (P) reservoirs remain source-sink balanced due to their relatively short residence times (reservoir size in mol divided by flux in mol/year) and response times (P ≈ 0.5 Myr; A ≈ 1.0 Myr), which are shorter compared to that of oxygen (Fig. 3, D and F).

Fig. 3. Biogeochemical modeling results from the non-steady-state.

(A, D, and F) Overall source and sink of the reservoirs of atmosphere-ocean oxygen (O), carbon-alkalinity (A), and ocean phosphorus (P). (B) Model predicted f_ANOX and pO₂ (PAL). (C, E, and G) Comparison between modeled and observed C-U-S isotope records (data sources as in Fig. 2). The factor Corgb_f was set to constant 1.0 to obtain a near-modern-level marine organic carbon burial flux.

Oxygen depletion continues until pO₂ falls below a threshold (~0.25 PAL in this model), triggering widespread ocean anoxia. This anoxia releases P, stimulating primary production and enhancing the burial flux of C_org and pyrite. Consequently, this process eventually results in positive excursions of C-S isotopes. Simultaneously, prolonged anoxic conditions promote the removal of ²³⁸U-enriched U(IV), driving a negative excursion in uranium isotopes (Fig. 3, C, E, and G). Meanwhile, the recovery of pO₂ to ~0.5 PAL is an intrinsic feature of the system, with the duration of this process—and the reversal of isotopic excursions—controlled by the rate of oxygen accumulation. In our model, widespread ocean anoxia during the SPICE event allowed the integrated oxygen source to exceed the sink by ~1.0 × 10¹³ mol/year. It took ~1 to 2 Myr to accumulate enough oxygen; eventually, the system crossed the higher pO₂ threshold, eliminating most of the anoxia and reversing all isotopic excursions. This is exemplified by the positive shift in δ²³⁸U_carb following the δ¹³C_carb peak, which is consistent with the chronostratigraphic duration of the SPICE event.

It is important to note that recent zircon chemical abrasion–isotope dilution–thermal ionization mass spectrometry (CA-ID-TIMS) geochronology and astronomical age models highlight uncertainty in the duration of the SPICE event, with estimates ranging from 1.6 to 2.6 Myr (24, 25, 56). However, this variability does not affect our conclusions as the period of the full limit cycle in our model also varies widely—from ~5 to 25 Myr within the unstable regime (fig. S3). The positive δ¹³C_carb excursion occupies roughly 25% of each cycle, yielding durations of ~1.25 to 6.25 Myr. Therefore, the model inherently accommodates the plausible range of SPICE durations, and our interpretations remain robust even if the event were somewhat longer or shifted within the Guzhangian-Paibian interval.

Dynamic relationship between SPICE and Neoproterozoic oscillations

The dynamics driving the SPICE event exhibit important similarities to, as well as key distinctions from, the periodic carbon cycle and redox oscillations documented in the Neoproterozoic (57) and earliest Paleozoic (2). To explicitly compare these time intervals, we examined model trajectories across the oxic threshold by prescribing a stepwise increase in the organic carbon burial flux (Corgb_f) under both deterministic and noise-influenced configurations (Fig. 4). This increase may have been driven by enhanced productivity from eukaryotic algae, which would improve the efficiency of the biological pump that transfers particulate organic matter to the sediment (1, 57). This increase is further substantiated by the transition to higher total organic carbon levels in the early Cambrian compared to the Ediacaran, as compiled in (58). This suggests that the parameter Corgb_f was approaching the oxic threshold (57)—specifically, the transition from unstable to stable oxic conditions—beginning in the Cambrian period.

Fig. 4. Modeling results display the dynamic relationship between SPICE and Neoproterozoic oscillations.

(A) Step increase in the hyperparameter Corgb_f, which is used to scale the overall marine organic carbon burial flux. (B) Noise term added to the differential equation for the atmosphere-ocean carbon-alkalinity reservoir (A), representing random fluctuations in the volcanic-metamorphic degassing flux. (C and D) Modeling results of long-term carbon isotope evolution with and without white noise (stochastic forcing), respectively. t_a, activation time; t_e: excursion time.

In the deterministic, or noise-free, system, increasing Corgb_f from 1.0 to approximately 1.2 lengthens the full limit cycle period to around 25 Myr while preserving a positive δ¹³C_carb excursion of about 2 Myr (t_e is the excursion time). Further increases push the system into a fully stable oxic state, eliminating self-sustained oscillations (Fig. 4C). Thus, although the SPICE excursion occurs within an inherently oscillatory regime, it occupies a narrow dynamical corridor, positioned closer to the transition between unstable and stable behavior than in previous time intervals.

When stochastic forcing is introduced, the system responds very differently. The noise term—representing uncertainty in volcanic–metamorphic degassing—produces irregular limit cycles, with timing controlled by the activation time (t_a) (Fig. 4D), which is the interval required for oxygen to accumulate to a higher pO₂ threshold. At Corgb_f ≈ 1.0, the system displays regular oscillations, with periods influenced by both the activation time (t_a) and the excursion time (t_e). However, at Corgb_f ≈ 1.2, the limit cycle becomes highly sensitive to noise: t_a >> t_e, and the period is dominated almost entirely by t_a (Fig. 4D). This behavior is consistent with coherence resonance in noisy nonlinear systems, where random forcing enhances the likelihood of threshold-crossing events (59).

These insights provide a unified dynamical explanation for the apparently sporadic and isolated nature of the SPICE excursion. We propose that the SPICE event is related to the continuous oscillations observed from the Neoproterozoic to the Early Cambrian, likely representing a stochastically triggered excursion that occurred during a phase of prolonged activation time. This made it challenging for the system to reach the anoxic threshold and prevented major δ¹³C_carb excursions between the SPICE event and the Terreneuvian. Thus, the gap separating these events is a natural consequence of threshold dynamics and the noise-dependent activation process, rather than evidence for a fundamentally stable P-O-A cycle state.

In summary, we present evidence that the SPICE event and its coeval isotopic excursions occurred against a fundamentally non-steady-state Earth system background. Although the traditional view linking positive δ¹³C_carb shifts to large phosphorus inputs remains valid, such “large inputs” need not derive directly from rivers and weathering; instead, they can arise from sustained imbalances between nutrient sources and sinks. This same source-sink imbalance explains the observed discrepancies between uranium and sulfur isotope records and resolves the atmosphere-ocean redox paradox (low pO₂ coexisting with a low fraction of ocean anoxia). Our results suggest that this non-steady-state Earth system, initiated in the Neoproterozoic, persisted at least through the late Cambrian—and possibly much longer—indicating that the stepwise rise of pO₂ to modern levels and the establishment of a permanently stable oxic regime had not yet occurred. Instead, atmospheric oxygen likely oscillated throughout early Paleozoic.

MATERIALS AND METHODS

A total of 326 δ¹³C_carb data and 89 δ²³⁸U_carb data are reported here and available in Supplementary Datasets. The age model for geochemical profiles follows the frameworks in previous studies (24, 25). The detailed geological background and study sections are provided in the Supplementary Materials.

Carbonate powder (0.5 to 1.0 g) was dissolved in 0.5 M HCl for 12 hours at room temperature and then centrifuged at 4000 rpm to separate the insoluble residues. The supernatants were dried down, redissolved in 3 ml of concentrated HNO₃, and dried down again. Major and trace element concentrations were measured on Thermo Fisher Scientific iCAP Pro ICP-OES and Thermo Fisher Scientific Element HR-ICP-MS, respectively. Typical precision was better than 5% based on repeated analysis of in-run check standards. Before U purification, aliquots containing 200 ng of U were taken from each stock solution and mixed with a ²³³U-²³⁶U double spike (IRMM-3636) at a U_spike:U_sample molar ratio of 0.0363. The spiked samples were then dried down completely and dissolved in 5 ml of 3 M HNO₃ for U purification. Uranium was purified using the UTEVA resin method for isotope analysis. The final purified samples were measured at a concentration of 50 parts per billion (ppb) in 0.32 M HNO₃ on the Thermo Scientific Neptune Plus MC-ICP-MS in the Isotope Laboratory at the Institute of Global Environmental Change, Xi’an Jiaotong University. The U isotope data are reported in standard notation relative to the CRM-112a isotopic standard: δ²³⁸U = [(²³⁸U/²³⁵U)_sample/(²³⁸U/²³⁵U)_CRM-112a − 1] × 1000‰. Double-spiked CRM145 (50 ppb U) was analyzed by bracketing every group of three samples. The δ²³⁸U values of the samples were normalized to the average bracketing standards. The overall reproducibility and accuracy of our procedure were monitored by repeated analyses of the geostandards SH-1 (δ²³⁸U = −0.38‰ ± 0.04‰, 2SD, n = 13) and JDO-1 (δ²³⁸U = −0.11‰ ± 0.06‰, 2SD, n = 11). The δ²³⁸U results and geochemical data are summarized in Supplementary Datasets.

Numerical methods

Models were implemented in the Julia programming language (60) using the PALEOtoolkit framework (https://github.com/PALEOtoolkit). Numerical ODE integration was performed using the Julia SciML interface (61) to the SUNDIALS CVODE package (62). Numerical integration of stochastic differential equations was performed using the SOSRA solver from the Julia StochasticDiffEq.jl package (61). The detailed model description is provided in the Supplementary Materials.

Model limitations

The ocean domain used in this study—a simplified “column ocean”—necessarily omits realistic paleogeographic features and water-depth gradients. The uranium module assumes that riverine U input scales with silicate weathering and that all marine U sinks vary linearly with oceanic U concentration. In this framework, the anoxic U sink is proportional to the COPSE-derived fraction of anoxic seafloor. We should note that this assumption may oversimplify the redox controls on the marine U cycle. Recent studies demonstrate that ferruginous condition can also facilitate U removal without substantial isotope fractionation (45, 46, 63). Implying that the shift from euxinic to ferruginous anoxia has the ability to generate U isotope excursions. Consequently, in our model, the U cycle only functions as an external isotope mass-balance module appended to the P-A cycles: It contains no internal nonlinearities and does not feed back into the other biogeochemical reservoirs. The oceanic U inventory is therefore not a state variable in the model. This structural simplification largely explains why the model’s U isotope predictions cannot reproduce the observed sharp recovery from negative U isotope excursion or other finer-scale features.

Here, we adopt a narrow range of k_Uⁱ values (0.23 to 0.25), the nutrient-uptake efficiency parameter, to impose nearly uniform seafloor redox conditions and thereby maintain the system in an excitable P-O-A regime. Sensitivity tests targeting this critical parameter are presented by Daines and Li (10). Notably, the Corgb_f-defined positions of the anoxic and oxic thresholds shift only modestly across different k_Uⁱ values, indicating that the unstable regime occupies a broad region of parameter space. This suggests that invoking intrinsic system instability to explain the early Paleozoic redox paradox is both reasonable and robust.

It is important to recognize that system instability is not the sole hypothesis for the periodic oscillations observed during the Ediacaran-Cambrian transition. The introduction of periodic external forces, such as eustatic sea level changes and orbitally driven nutrient inputs, may also account for these oscillations (64, 65). However, the underlying causes of the periodic fluctuations in these external drivers remain an area that requires further investigation.

Supplementary Materials

The PDF file includes:

Supplementary Text

Figs. S1 to S10

Table S1

Legends for data S1 to S4

References

Other Supplementary Material for this manuscript includes the following:

Data S1 to S4