While photosynthesis is the proximate source of molecular oxygen, maintaining an oxidized atmosphere over geological time requires the burial of photosynthetically produced organic carbon (OC) in sediments, which prevents its re-reaction with O2 (ref. 1). Availability of the limiting nutrient phosphorus is believed to be the main driver for the production and thus the final burial of OC2, and it is usually the supply of P that is considered to modulate atmospheric O2 over Earth history3,4,5. In the modern ocean, however, only a minor amount (~13%) of OC that reaches the sediment is buried because the majority is microbially remineralized back into carbon dioxide6.

The lack of a simple link between the export of biomass from the surface seawater and the long-term burial of OC in sediments raises questions about the connection between nutrient availability in the photic zone and long-term atmospheric oxygenation. It is reasonable to expect, therefore, that changes to the reactivity of OC, through either local temperature changes or the protection against microbial remineralization afforded to OC by binding with seafloor minerals7,8,9, could be important for the geological O2 cycle and may provide alternative explanations for the long-term rise in O2 over Earth history. For example, many minerals that can bind OC are sourced from the continents and may therefore have undergone substantial increases in abundance over Earth history during continental emergence, with the potential to dramatically increase the preservation potential of OC and thus oxygenate the Earth.

The binding of OC with iron minerals, Fe (oxyhydr)oxides in particular, is a ubiquitous process in soils and sediments7,10 in which Fe (oxyhydr)oxides can sequester OC in multiple ways, including via adsorption of OC onto mineral surfaces, coprecipitation of OC with mineral particles and complexation between reactive Fe phases and OC to form macromolecules and nanoparticulate organominerals11,12,13. Through sequestration with Fe (oxyhydr)oxides, OC is less susceptible to chemical and microbiological attack12,14,15. In marine sediments, Fe reduction experiments show that 21.5 ± 8.6% of all OC is bound with reactive Fe phases, most likely via coprecipitation with Fe (oxyhydr)oxides and complexation to form macromolecules composed of OC and Fe (oxyhydr)oxide nanoparticles7. Reactive Fe phases are therefore invoked as a ‘rusty sink’ for OC that can protect bound carbon from microbial remineralization and enhance its long-term burial7,16,17.

A global biogeochemical model with mineral OC burial

In this Article, we develop a global biogeochemical ocean–atmosphere–sediment model to test the effect that mineral protection of OC might have on the global carbon, O2 and nutrient cycles. Specifically, we investigate how Fe mineral protection alters the relationship between limiting nutrient availability and carbon burial, and how changing the supply of Fe (oxyhydr)oxides would influence the long-term planetary redox state. We note that clay minerals may also have played a substantial role in OC preservation18,19,20, and while we do not model this process, because both iron and clay minerals can be sourced from terrigenous material, they may further promote OC preservation when material delivery is high.

Our model is developed from a series of well-established conceptual models of global marine biogeochemistry21,22,23,24,25,26. The model tracks the global cycles of organic and inorganic carbon, sulfate and sulfide anions, Fe, O2 and P in a five-box ocean system representing the shallow shelf, deep shelf, surface open ocean, surface high latitude and deep ocean and has explicit air–sea exchange with a single well-mixed atmosphere box (Fig. 1 and Supplementary Fig. 1). The majority of fluxes and other process information is taken directly from these previous works and adapted onto our six-box scheme. To calibrate the model using known geological records, carbonate precipitation and the cycling of carbon isotopes are also included in the model.

Fig. 1: Schematic diagram of the global biogeochemical model.
figure 1

a, Iron cycle. Dissolved iron in water bodies exists as dissolved Fe(ii) (DFe(ii)) or Fe(iii) (DFe(iii)). A terrigenous source of particulate Fe(iii) (oxyhydr)oxides (PFe) is also supplied to marine sediments. b, Carbon cycle. Carbon in the oceanic reservoirs exists as dissolved inorganic carbon (DIC) or OC. Boxes with a blue background represent oceanic reservoirs. White boxes represent reservoirs of chemical components, grey arrows represent thermohaline transport fluxes and yellow arrows represent mixing fluxes. SS, shallow shelf; DS, deep shelf; S, surface open ocean; H, surface high latitude; D, deep ocean. Redu., reduction; Oxid., oxidation; Scav., scavenging. Prod., production; Remi., remineralization; Prot., OC protected by Fe(iii) (oxyhydr)oxides; Unpr., OC unprotected.

The dissolved Fe in all ocean boxes is divided into Fe(ii) and Fe(iii) (Fig. 1). The input fluxes of dissolved Fe to the ocean are the riverine influx of dissolved Fe(iii), the release of dissolved Fe(iii) to the surface ocean due to dissolution of dust, the hydrothermal dissolved Fe(ii) flux and the benthic dissolved Fe(ii) flux generated by Fe reduction in the sediments. Dissolved Fe is free to redistribute around the ocean via circulation and mixing between ocean boxes. The reaction pathways for the Fe cycle in the ocean boxes are taken to be Fe reduction, pyrite formation, siderite precipitation, aerobic Fe oxidation and Fe(iii) scavenging by particles (the formation of nanoparticulate Fe (oxyhydr)oxides, which aggrade with other particles and sink to the sediments), following recent works by Wallmann et al.24 and van de Velde et al.26. Another flux of Fe (oxyhydr)oxides to the sediments is the weathering and transport of particulate Fe directly from land (through both river and dust; Fig. 1).

Primary production in all three surface oceanic boxes is determined by P and Fe concentrations through nutrient co-limitation24. The degradation of OC in the water column is determined by the availability of electron acceptors in the priority order of O2, Fe(iii), SO42− (refs. 26,27). We have added a mineral-protected OC burial term in sediments to mimic OC burial due to the protection by Fe (oxyhydr)oxides. This is done by dividing the burial of OC into two parts: mineral-protected OC burial associated with Fe (oxyhydr)oxides and unprotected OC that is degraded through the cascade of electron acceptors. Following the findings of Lalonde et al.7, we have parameterized the fraction of OC burial associated with Fe (oxyhydr)oxides using a fixed OC/Fe ratio in the range of 4 ± 2. Due to this ratio, the net effect of Fe(ii) and/or Fe(iii) input into seawater, if buried as Fe (oxyhydr)oxides, is expected to be an increase in O2 level in the ocean and atmosphere system16. The OC burial that is not associated with Fe (oxyhydr)oxides is calculated using a fixed burial efficiency, following the majority of previous work25,28. Oxidative weathering of fossil OC on land is described as a function of O2 level29.

Our model is constructed around the assumption of a present-day steady state, but we also validate its general function by testing it in a simulation of the Permian–Triassic boundary (Supplementary Fig. 2). During this time, the emplacement of the Siberian Traps Large Igneous Province resulted in an extreme CO2 input event, which is well documented through shifts in ocean acidity, carbon burial systematics and ocean oxygenation25,30,31,32. Our model produces a reasonable fit to the changes in ocean pH and carbonate δ13C across the carbon input event32 and predicts a notable reduction in marine O2 concentration and a rise in water-column H2S concentration. Thus, we conclude it represents the long-term carbon and O2 cycles in a manner consistent with current scientific understanding. The longer-term recovery in our model is slower than in ref. 32, probably because we do not impose changes to erosion rates or enhanced weathering of igneous rocks. The full model outline and computer code is included in Supplementary Information.

An independent driver for Earth’s oxygenation

Figure 2 shows the key steady states of our model under changes to the weathering input of dissolved P (x axis) and co-varying fluxes of particulate Fe (oxyhydr)oxides from rivers and dissolved Fe(iii) from the dissolution of dust—collectively termed ‘terrigenous Fe flux’ (y axis). A decoupling between P and Fe inputs to the ocean may be achieved because Fe and P can be hosted in different minerals in igneous rocks, such as feldspar and apatite, with different susceptibilities to dissolution and transport. Therefore, a change in weathering regime—the relative intensities of physical and chemical weathering processes—or dust flux may alter the proportions of Fe and P delivered to the ocean from the continents.

Fig. 2: Influence of Fe and P delivery to the ocean on OC burial and the oceanic redox state under mineral protection of OC.
figure 2

a, O2 concentration in the deep ocean. b, SO4 concentration in the deep ocean. c, Percentage of mineral-protected OC burial in total OC burial. PL, present level.

Here the burial of OC associated with Fe (oxyhydr)oxides increases with an increase in the terrigenous Fe flux because the overall delivery of Fe to sediments is greater. This results in increased amounts of O2 and SO4 in the model ocean because more OC is protected by Fe and therefore less of the oxidized species are consumed during remineralization. The effects of this mechanism can cause O2 levels averaged across the model boxes to vary by one to two orders of magnitude for a similar variation in the Fe flux. The effects are also greater when P weathering inputs are lower because this results in a reduced flux of OC to sediments and therefore a proportionally greater protected fraction of OC (Fig. 2c).

As in previous studies, our model continues to show that increasing P availability, and therefore photosynthetic gross primary production (Supplementary Fig. 4), can drive increased dissolved O2 and SO4 in the oceans33,34, but our analysis adds two important pieces of information to this general view. First, supply of Fe to the oceans, and the direct effect of this on mineral preservation and OC burial, constitutes an independent control on electron acceptor availability, which may also drive large changes in marine O2 and SO4 concentrations. Second, changes in P availability may have a substantially different effect depending on the Fe supply flux. When Fe supply is high, a reduction in P availability may not drive a large reduction in oxidant availability (for example, top right of Fig. 2a,b) as previous models have predicted35. Supplementary Figs. 57 show model sensitivity tests where we rerun Fig. 2 under a different rate of ocean circulation, input of sulfate and degree of redox-dependent P recycling. These figures confirm that the overall behaviour of the model shown in Fig. 2 is robust to these considerations.

Empirical evidence

Geological evidence is consistent with our hypothesis that the variations in Fe delivery from the continents may have played an important role in the evolution of ocean–atmosphere O2 (Fig. 3). To estimate the broad changes in Fe (oxyhydr)oxide delivery to the oceans over Earth history, we consider the increase in exposed continental land area over time and plot the elevation of active continental crust and the normalized strontium isotope curve36,37, which are expected to track changes in overall terrigenous delivery from the continents to the oceans and thus changes in Fe (oxyhydr)oxide delivery as a fraction of terrigenous material. Such an enhancement of continental erosion may have acted as the root driver for the increase in OC burial associated with Fe (oxyhydr)oxides and, thus, atmospheric oxygenation.

Fig. 3: The evolution of Fe fluxes, oceanic redox and atmospheric \(p_{{\mathrm{O}}_2}\).
figure 3

a, The evolution of continental area. The results of ref. 40 for fast and slow plate tectonics are based on the continental growth model of ref. 45. b, Mean elevation of active continental crust based on records of zircon europium anomaly37. The shadow represents a 95% confidence interval. c, Normalized 87Sr/86Sr curve of continental weathering versus mantle influence36, where normalization removes the effects of 87Rb decay over Earth history. d, The evolution of concentration of Fe (oxyhydr)oxides in shale through time (see Supplementary Information for the description of data compiling). The panel on the upper left shows the frequency distributions of bootstrap resampled mean concentrations of Fe (oxyhydr)oxides in shale (n = 10,000) before 830 Ma (grey) and after 830 Ma (green). e, Current understanding of the evolution of atmospheric \(p_{{\mathrm{O}}_2}\) relative to present atmospheric level (PAL), after ref. 33. The oceanic redox in e is adapted from ref. 5.

Although there is large uncertainty in the estimation of the evolution of land area with time38,39,40, most models show a substantial increase in land masses during 3.0–2.3 billion years ago (Ga), and between the Archaean and Palaeoproterozoic the strontium isotope record shows a drift towards higher values, consistent with increased continentally sourced Sr36 (Fig. 3). Continental elevation and strontium isotope records are also consistent with further increases in material delivery during 1000–500 million years ago (Ma) (Fig. 3). Between 3.0 and 2.3 Ga, the emergence of land masses probably brought substantial terrigenous material to seawater and hence substantial amounts of Fe, which is also consistent with the occurrence of major Fe formations after 2.75 Ga (ref. 41; Fig. 3). This Fe influx corresponds with the Great Oxygenation Event (~2.4-2.2 Ga) and multiple independent lines of evidence for ‘whiffs’ of O2 before it42,43. Between 1000 and 500 Ma, the further increases in continental elevation and terrigenous inputs correspond with the Neoproterozoic Oxygenation Event (~800-550 Ma)36,37. We therefore suggest that an increase in terrigenous inputs into the ocean and an associated increase in the terrigenous Fe flux may have resulted in substantial OC burial, contributing to the oxygenation of the ocean and atmospheric system. While we focus on iron in this Article, the evidence here also supports the potential for a wider link between terrigenous material delivery and Earth’s oxygenation, which may also include other minerals and processes.

It is difficult to track the global burial rate of Fe (oxyhydr)oxides directly. This is because sedimentary concentrations can reflect Fe transport in the ocean as well as redox-dependent conversion of Fe oxides to authigenic minerals such as pyrite. A compiled dataset (see Supplementary Information for the description of the compilation) for the content of Fe (oxyhydr)oxides in shales shows a particularly substantial increase during the Neoproterozoic Oxygenation Event (Fig. 3). The mean content of Fe (oxyhydr)oxides of post-Tonian age (<830 Ma) is more than twice that of the pre-Cryogenian (>830 Ma)—0.43 ± 0.12 wt% versus 0.19 ± 0.06 wt% (2 s.d.). The unpaired Student’s t test shows that the difference between these two mean values is significant (P < 0.001, α = 0.01), and the increase in mean contents of Fe (oxyhydr)oxides remains robust during bootstrap resampling (Fig. 3). This increase in the abundance of Fe (oxyhydr)oxides may have been driven by the progressive oxygenation of the ocean interior during the late Precambrian. If so, then this may constitute a positive-feedback regime where more OC is mineral preserved, which drives further oxygenation (for example, Supplementary Fig. 8).

We conclude that mineral protection of OC, driven by supply of Fe from the continents, probably has been an independent driver of increased marine O2 and SO4 concentrations and has led to a system that is more resilient to deoxygenation by restriction of P supply to the oceans. This adds weight to the hypothesis that the ultimate driver of Earth’s oxygenation is the emergence and/or uplift of continental land masses38,43,44, a process that in our model would raise atmospheric \(p_{{\mathrm{O}}_2}\) and marine O2 and SO4 levels and buffer the system against collapses in biological productivity. We suggest that the direct effect of Fe minerals on OC preservation and burial should be included in subsequent analyses of the long-term oxygenation of Earth.


Model structure

Our model is developed from a series of well-established conceptual models of global biogeochemical cycles21,22,23,24,25,26,28. The model has five ocean boxes (Supplementary Fig. 1): shallow margin (sm), deep margin (dm), surface (s), surface high latitude (h) and deep (d). Following the results of ref. 46, the shallow-margin box is defined from 0–100 m water depth and occupies 10% of the ocean surface and 5% of the seafloor. The deep-margin box is 100–1,000 m water depth and occupies a further 5% of the seafloor. The surface box is 100 m deep and represents 76.5% of the ocean surface, while the surface high-latitude box is 250 m deep and represents 13.5% of the ocean surface. The species, fluxes, main equations, parameters and reactions in the model are shown in Supplementary Tables 14. Supplementary Table 1 shows the model species and their sizes at present (based on refs. 5,21,22,25,47,48,49,50,51,52,53,54), Supplementary Table 2 shows the chemical/biological reactions, Supplementary Table 3 shows the flux equations and Supplementary Table 4 shows the model parameters. A schematic of the model structure is shown in Supplementary Fig. 1. The following sections explain key reactions and burial fluxes of the model. See Supplementary Information for a more detailed description of the model.


The model approximates the main reactions of C, O, S and Fe cycles in the water column (Supplementary Table 2). These reactions include photosynthesis, aerobic degradation of organic matter, iron reduction, sulfate reduction, pyrite formation, aerobic iron oxidation, aerobic sulfide oxidation, sulfide-mediated iron reduction, siderite formation and Fe(iii) scavenging. The reaction rate laws of photosynthesis and respiration are discussed below. See Supplementary Information for the description of all the reactions in the model.

Primary production in the surface boxes (Pripri) is calculated considering nutrient co-limitation by P and Fe24:

$${\mathrm{Pripr}}_i = K_{{\mathrm{PP}}_i} \times {{{\mathrm{min}}}}\left[ {C_{{\mathrm{DP}}_i} \times \frac{{C_{{\mathrm{DP}}_i}}}{{C_{{\mathrm{DP}}_i} + K_{\mathrm{P}}}},\frac{{C_{{\mathrm{FeIII}}_i}}}{{r_{{\mathrm{FeP}}}}} \times \frac{{C_{{\mathrm{FeIII}}_i}}}{{C_{{\mathrm{FeIII}}_i} + K_{{\mathrm{Fe}}}}}} \right]$$

where KPPi is the kinetic constant of primary productivity in box i, CDPi is the P concentration in box i, CFeIIIi is the Fe(iii) concentration in box i, rFeP is the atomic ratio between Fe and P in phytoplankton biomass, and KP and KFe are Monod constants.

The rates for the pathways of organic matter degradation via aerobic respiration (ARi), iron reduction (ironRi) and sulfate reduction (sulfRi) are calculated using a Monod scheme55,56 as the sequence of these pathways is controlled by their energy yields27. Thus, the reaction rate laws of these pathways are:

$${\mathrm{AR}}_i = K_{{\mathrm{Remin}}_i} \times C_{{\mathrm{POC}}_i} \times \frac{{C_{{{{\mathrm{O}}}}2_i}}}{{C_{{{{\mathrm{O}}}}2_i} + K_{{\mathrm{O}}2}}}$$
$${{{\mathrm{ironR}}}}_i = K_{{\mathrm{Remin}}_i} \times C_{{\mathrm{POC}}_i} \times \frac{{K_{{\mathrm{O}}2}}}{{C_{{{{\mathrm{O}}}}2_i} + K_{{\mathrm{O}}2}}} \times \frac{{C_{{\mathrm{FeIII}}_i}}}{{C_{{\mathrm{FeIII}}_i} + K_{{\mathrm{FeIII}}}}}$$
$${{{\mathrm{sulfR}}}}_i = {{{\mathrm{{\Psi}}}}} \times K_{{\mathrm{Remin}}_i} \times C_{{\mathrm{POC}}_i} \times \frac{{K_{{\mathrm{O}}2}}}{{C_{{{{\mathrm{O}}}}2_i} + K_{{\mathrm{O}}2}}} \times \frac{{K_{{\mathrm{FeIII}}}}}{{C_{{\mathrm{FeIII}}_i} + K_{{\mathrm{FeIII}}}}} \times \frac{{C_{{\mathrm{SO}}4_i}}}{{C_{{\mathrm{SO}}4_i} + K_{{\mathrm{SO}}4}}}$$

where \(K_{{\mathrm{Remin}}_i}\) is the rate constant for organic matter degradation in box i, \(C_{{\mathrm{POC}}_i}\) is the concentration of particulate OC (POC) in box i, \(C_{{{{\mathrm{O}}}}2_i}\) is the concentration of oxygen in box i, \(C_{{\mathrm{FeIII}}_i}\) is the concentration of Fe(iii) in box i,\(C_{{\mathrm{SO}}4_i}\) is the concentration of SO42− in box i, Ψ is the attenuation factor for sulfate reduction, KO2 is the limiting concentration for aerobic respiration and KFeIII is the limiting concentration for iron reduction. The total remineralization rate (Remini) in each ocean box is the sum of aerobic respiration (ARi), iron reduction (ironRi) and sulfate reduction (sulfRi):

$${\mathrm{Remin}}_i = {\mathrm{AR}}_i + {{{\mathrm{ironR}}}}_i + {{{\mathrm{sulfR}}}}_i$$

Burial fluxes

The modern burial fluxes of OC in the shallow margin (\(f_{{\mathrm{mocb}}_{{\mathrm{sm}}}}\)), deep margin (\(f_{{\mathrm{mocb}}_{{\mathrm{dm}}}}\)) and deep sea (\(f_{{\mathrm{mocb}}_{\mathrm{d}}}\)) are set as 4.5 Tmol yr–1, 1.5 Tmol yr–1 and 1 Tmol yr–1, respectively, following ref. 22. This also follows the findings of ref. 57 that roughly 20% of the marine OC burial occurs in the deep sea. The modern POC fluxes to the sediment–seawater interface in the shallow margin (\({\mathrm{Sed}}_{{\mathrm{sm}}}\)) and deep margin (\({\mathrm{Sed}}_{{\mathrm{dm}}}\)) are estimated to be 30 Tmol yr–1 and 10 Tmol yr–1 using \(f_{{\mathrm{mocb}}_{{\mathrm{sm}}}},f_{{\mathrm{mocb}}_{{\mathrm{dm}}}}\) and assuming a burial efficiency (BE) of ~15 % for the sediments on the continental margin6. Similarly, the modern POC flux to the sediment–seawater interface in the deep ocean (\({\mathrm{Sed}}_{\mathrm{d}}\)) is estimated to be 10 Tmol yr–1 using \(f_{{\mathrm{mocb}}_{\mathrm{d}}}\) and a BE of ~10% for the deep-ocean sediments6. The OC burial is divided into two parts: OC burial associated with Fe and ‘unprotected’ OC burial. The OC burial fluxes associated with Fe (\(f_{{\mathrm{mocb}}_i}^{\,{\mathrm{Fe}}}\)) are estimated using the burial flux of Fe and an OC: Fe burial ratio (\(\gamma _{{\mathrm{OCFe}}}^{\mathrm{b}}\); ref. 7) such that:

$$f_{{\mathrm{mocb}}_{{\mathrm{sm}}}}^{\,{\mathrm{Fe}}} = \gamma _{{\mathrm{OCFe}}}^{\mathrm{b}} \times \left( {f_{{\mathrm{FeIIIsolid}}_{{\mathrm{sm}}}} + f_{{\mathrm{FeIIIscaveng}}_{{\mathrm{sm}}}} - f_{{\mathrm{beniFeII}}_{{\mathrm{sm}}}}} \right)$$
$$f_{{\mathrm{mocb}}_{{\mathrm{dm}}}}^{\,{\mathrm{Fe}}} = \gamma _{{\mathrm{OCFe}}}^{\mathrm{b}} \times \left( {f_{{\mathrm{FeIIIsolid}}_{{\mathrm{dm}}}} + f_{{\mathrm{FeIIIscaveng}}_{{\mathrm{dm}}}} - f_{{\mathrm{beniFeII}}_{{\mathrm{dm}}}}} \right)$$
$$f_{{\mathrm{mocb}}_{\mathrm{d}}}^{\,{\mathrm{Fe}}} = \gamma _{{\mathrm{OCFe}}}^{\mathrm{b}} \times \left( {f_{{\mathrm{FeIIIsolid}}_{\mathrm{d}}} + f_{{\mathrm{FeIIIscaveng}}_{\mathrm{s}}} + f_{{\mathrm{FeIIIscaveng}}_{\mathrm{h}}} + f_{{\mathrm{FeIIIscaveng}}_{\mathrm{d}}} - f_{{\mathrm{beniFeII}}_{\mathrm{d}}}} \right)$$

where \(f_{{\mathrm{FeIIIsolid}}_i}\) represents the particulate Fe(iii) flux from continental weathering, and \(f_{{\mathrm{beniFeII}}_{\mathrm{d}}}\) represents the benthic flux of Fe(ii). The burial fluxes of OC (\(f_{{\mathrm{mocb}}_i}\)) are therefore calculated as:

$$f_{{\mathrm{mocb}}_i} = \left\{ {\begin{array}{*{20}{c}} {f_{{\mathrm{mocb}}_i}^{\,{\mathrm{Fe}}} + \left( {{\mathrm{Sed}}_i - f_{{\mathrm{mocb}}_i}^{\,{\mathrm{Fe}}}} \right) \times {\mathrm{BEO}}_i,{\mathrm{Sed}}_i > f_{{\mathrm{mocb}}_i}^{\,{\mathrm{Fe}}}} \\ {{\mathrm{Sed}}_i,{\mathrm{Sed}}_i < f_{{\mathrm{mocb}}_i}^{\,{\mathrm{Fe}}}} \end{array}} \right.$$

where BEOi represents BE of organic matter that is not associated with Fe. BEOi is calculated using modern values of \(f_{{\mathrm{mocb}}_i}\), \(f_{{\mathrm{mocb}}_i}^{\,{\mathrm{Fe}}}\) and Sedi.

The burial flux of sulfate as evaporites in the shallow-margin box (fSO4b) is scaled with sulfate concentration28:

$$f_{{{{\mathrm{SO}}}}4{\mathrm{b}}} = k_{{\mathrm{SO}}4{\mathrm{b}}} \times \frac{{C_{{\mathrm{SO}}4_{{\mathrm{sm}}}}}}{{C_{{\mathrm{SO}}4_{{\mathrm{sm}}0}}}}$$

where \(f_{{\mathrm{SO}}4{\mathrm{b}}}\) is the present burial flux of sulfate in the shallow-margin box.

The P burial fluxes include three components: organic P, iron-bound P and authigenic P. The burial fluxes of organic P (POPburi) are scaled with the burial fluxes of organic matter using a fixed C/P ratio in marine sediments (\(\gamma _{{\mathrm{CP}}}^{\mathrm{b}}\)):

$${{{\mathrm{POPbur}}}}_i = f_{{\mathrm{mocb}}_i}/\gamma _{{\mathrm{CP}}}^{\mathrm{b}}$$

The burial flux of iron-bound P (FePi) is scaled with the P concentration (DPi) in the oceanic box that is in contact with sediments:

$${{{\mathrm{FeP}}}}_i = k{\mathrm{FeP}}_i \times {{{\mathrm{DP}}}}_{{{{i}}}}/{{{\mathrm{DP}}}}_{{{{{i}}}}_0}$$

where \({\mathrm{DP}}_{i_0}\) is the initial dissolved P concentration in oceanic box i. The burial flux of authigenic P (Pauthi) is also scaled with seawater P concentration:

$${{{\mathrm{Pauth}}}}_i = k{\mathrm{Pauth}}_i \times {{{\mathrm{DP}}}}_{{{{i}}}}/{{{\mathrm{DP}}}}_{{{{{i}}}}_0}$$

Model testing

We test the model behaviour by running a large perturbation experiment from Earth history—the Permian–Triassic carbon injection from the Siberian Traps. The purpose of this is to test whether the model is consistent with previous modelling approaches—we do not make any conclusions on the Permian–Triassic. Here the CO2 injection flux and isotopic composition follow recent modelling work using a similar type of model32. The response of our model to this flux (Supplementary Fig. 2) compares well to the recent modelling work and to the geological record for carbonate δ13C and marine pH. Our model also produces marine deoxygenation and an increase in the amount of free sulfide in the water column31,58,59. We also run a test of a large P input flux roughly modelled on an often-hypothesized trigger for the Cretaceous ocean anoxic events (Supplementary Fig. 3). The model outputs for this event show deoxygenation and a positive carbon isotope excursion, again generally consistent with the prevailing views on the global biogeochemical response to massive P inputs60. We conclude in this section that our model behaviour in response to changes in carbon and nutrient cycles is broadly in line with other modelling efforts and with current understanding of Earth’s biogeochemical functions.