## Main

The rise of free oxygen (O2) in the Earth’s atmosphere and oceans enabled the evolution of aerobic life1. Oxygenic photosynthesis (OP) in microbial mats was a substantial source of O2 for the Great Oxidation Event (GOE) ~2.4 billion years ago (Ga), during the stable low-O2 conditions that followed and for the Neoproterozoic Oxygenation Event (NOE) ~600 Ma (ref. 2). The biological3,4, tectonic5 and geochemical6,7 mechanisms that determined this stepwise pattern of oxygenation are still debated. Here we explore a previously unconsidered link between Earth’s oxygenation pattern and rotation rate, which decelerated over geological time due to tidal friction8,9. We establish a mechanistic link between daylength and export fluxes of solutes from microbial mats. Experimental measurements and models of Proterozoic cyanobacterial mat analogues show that longer daylength increases benthic O2 export, changes the balance between aerobic and anaerobic remineralization, and thus enhances the diel organic carbon (Corg) burial. We then investigated the remarkable similarity between the timing and pattern of increase in atmospheric O2 ($$p{{\rm{O}}_2}$$ as a fraction of the present atmospheric level (PAL)) and daylength. We found that increases in daylength could plausibly have influenced Earth’s oxygenation, particularly around key oxidation events, and thus helped to pave the way for the evolution of plants and animals of the modern world.

## Longer days increase net benthic O2 export fluxes

Earth’s rotation period is 24 hours at present, but may have been as low as 6 hours at ages older than 4 Ga (refs 8,10,11). Thus, daylength (that is, one rotational or diel period) and the illumination period may have increased more than threefold since the evolutionary origin of photosynthesis. This implies that the dynamics of illumination (rate of increase and decrease) within the diel period changed substantially. The rate of gross photosynthetic production (GPP) is governed by the instantaneous photon flux, irrespective of illumination dynamics and daylength. The net production rate, equivalent to diel Corg burial, is the result of this GPP and the rate of Corg consumption. As opposed to GPP, the net production of benthic ecosystems is expected to be influenced by changes in the illumination dynamics. In such systems, rates of net productivity are not only shaped by the instantaneous photon flux, but also by fluxes of metabolic substrates and products, which are governed by molecular diffusion. Thus, import, export and accumulation of metabolites should be sensitive to daylength due to the interaction between illumination dynamics and diffusive mass transfer.

We developed a modelled understanding of this interaction and first explored the implications for the export fluxes of the photosynthetic product O2. Our modelling framework12 formulates benthic ecosystems as diffusive–reactive systems with OP, anoxygenic photosynthesis (AP), aerobic respiration (Raero), sulfate reduction (anaerobic respiration (Ranaero)) and abiotic sulfide oxidation (SOX) (Extended Data Fig. 1 and Supplementary Video 1). Starting with a simple in silico mat with only OP and Raero, simulations with the same rate of GPP showed that longer days yield higher export fluxes, that is, an increase in O2 escape to the overlying water (Fig. 1a,b). The mechanism behind this relationship is apparent in the duration between the maxima of gross O2 production and export (Fig. 1a), which illustrates how mass transfer resistance delays the O2 escape. The export-limiting delay represents a smaller fraction of the day for longer daylengths. Longer days build up steeper O2 gradients and therefore higher fluxes, both upward and downward (Extended Data Fig. 2a). In thin mats, the latter would interact with the mat substrate (for example, pyrite), and possibly create a daylength-driven increase in preserved weathering signals13. The daylength-driven increase in O2 fluxes also alters the availability of O2 within the mat, boosts the fraction of produced Corg that escapes Raero and thus decreases remineralization efficiency (Fig. 1b). Consequently, daylength interacts with the net productivity of benthic systems, which relates to the short-term (that is, diel) Corg excess, and possibly the long-term Corg burial rate, a crucial determinant for the state of global $$p{{\rm{O}}_2}$$ (refs 1,14). Overall, although GPP rates are unaffected by changes in daylength, Corg burial is modulated through the physics of molecular diffusion.

## Daylength increases O2 export more than reductant export

A more realistic scenario includes Ranaero as an additional sink of Corg, which we implemented in the form of sulfate reduction. Conceptually, sulfate and sulfide, the substrate and product, respectively, can be exchanged with any other redox couple, such as Fe(III)/Fe(II). We focus on the sulfur cycle because of the early evolutionary onset of sulfate reduction15 and because sulfide was transiently abundant in Precambrian coastal habitats16. We first chose a mat scenario with the Ranaero rate fixed to a constant value, to isolate the effect of daylength on diffusion-driven dynamics of sulfide export (Fig. 1c). Like O2 fluxes, the reductant export fluxes are shaped by molecular diffusion and rates of production and consumption within the mat (Ranaero and SOX). The latter is an additional sink of O2 and is thus competitive with Raero. Consequently, the Corg that escapes both anaerobic and aerobic remineralization can be represented as the difference between the O2 and H2S export fluxes (Fig. 1c,d and Extended Data Fig. 1). As both fluxes increase with daylength, the rates of SOX decrease. Owing to this moderating effect of SOX, Raero is less sensitive to daylength than it is in a reductant-free scenario. The effect of an increased O2 export on the diel Corg burial rate is therefore counteracted, but not overwhelmed, by concomitant increases in H2S export (Fig. 1d). To further explore if the increase of diel Corg burial is maintained when Ranaero is affected by local solute dynamics, we implemented sulfate-reducing bacteria (SRB) that are inhibited by O2 and H2S, as observed in modern mats17,18,19. Across a range of inhibition strengths, diel Corg burial consistently increases with daylength (Fig. 2 and Extended Data Fig. 3).

Given that the Earth’s redox landscape changed along with daylength through geological time, we studied the sensitivity of daylength-driven diel Corg burial to reductant and O2 availability in the water column. Diel O2 export and Corg burial fluxes increased with daylength across all O2 boundary conditions (Fig. 2). Increasing O2 in the water column had a strong enhancing effect on Raero and negative effect on O2 export fluxes. For the diel Corg burial rate, determined by both Raero and Ranaero, the effect of O2 levels in the water column was variable (Extended Data Fig. 3). Depending on the inhibition strength of O2 on Ranaero, Corg burial either increases or decreases with the O2 boundary conditions. Given that Ranaero is O2 sensitive, the negative impact of $$p{{\rm{O}}_2}$$ is overwhelmed by the positive effect of daylength enhancing diel benthic Corg burial over Earth’s history.

To explore the interactions between reductant availability and Corg burial with daylength, we also included AP using H2S as an electron donor that competes with OP for the contribution to GPP based on mat-intrinsic reductant and light levels20 (Extended Data Fig. 4). With AP present in mats, the fraction of the day that exports O2 is reduced for shorter daylengths because of the time required for AP to deplete the local sulfide concentration below the thresholds that allow OP to occur (Extended Data Fig. 5). Although the total GPP (AP + OP) is unaffected by daylength, the fraction of the day during which O2 is produced decreases markedly with daylength. Concomitantly, Ranaero decreases with daylength due to the increasing inhibition by O2. Although counterintuitive, Raero decreases with daylength because SOX becomes more competitive for O2 due to the increasing fractions of the day with O2 production. Consequently, across a range of sulfide and O2 levels in the overlying water, we found that the Corg burial of systems with AP is more steeply modulated by daylength compared with that for communities with only OP (Fig. 2). Interestingly, the dependency of the diel Corg burial on the reductant boundary condition was negligible compared to that on daylength. Therefore, the metabolic repertoire, rather than the water column redox conditions, shapes the response of benthic systems to daylength in terms of diel Corg burial.

Overall, we show that the net productivity, that is, the short-term Corg burial of benthic ecosystems, and thus a crucial determinant of the source strength for global $$p{{\rm{O}}_2}$$, can increase with daylength over Earth’s age without assuming a decrease in the global O2 sink strength or an increase in GPP. However, the range of global GPP probably varied substantially, for example, due to new evolutionary avenues of primary production21, redox and phosphate oscillations related to weathering during the ‘boring billion’ years6, continental reconfiguration22, long-term changes in insolation23 or even daylength-related changes in ocean circulation and nutrient supply by upwelling24. We therefore evaluated the sensitivity of daylength-driven increases in benthic O2 export to the rates of GPP. As expected, O2 export displays a steep dependency on GPP, but daylength-driven changes in Corg burial are substantially less sensitive to GPP (Fig. 2). This implies that the areal coverage of benthic habitats rather than the evolution of GPP by the inhabitants is of greatest relevance for daylength-driven effects.

## Empirical verification of the daylength effect

To reify the concept of export fluxes being modulated by daylength, we measured rates of photosynthesis and O2 export in cyanobacterial mats from the Middle Island Sinkhole (MIS), an extant analogue of Proterozoic mats under low-O2 conditions25. Net O2 production consistently occurred only after extended exposure time to light (Fig. 3a). White sulfur-oxidizing bacteria (SOB) atop the mat during night and morning reduced the light availability for photosynthesis26. The cyanobacteria exclusively performed AP, and thereby depleted the sulfide underneath the SOB layer (Fig. 3b,c). The sudden onset of O2 production during the phase of high light in the early afternoon (Fig. 3d) coincided with the downward migration of the light-reflecting white SOB, which was probably induced by depletion of sulfide by cyanobacterial AP (Extended Data Fig. 6a). This migration was triggered only after an additional lag of 1–8 hours after sulfide depletion, depending on the O2 and sulfide levels in the overlying water (Extended Data Fig. 6b). The ensuing exposure of cyanobacteria to a higher photon flux at the mat surface resulted in high rates of OP and AP and the onset of net O2 export. As the vertical structure of the mat persisted during subsequent lower light intensities, rates of both OP and AP remained high (Fig. 3e).

The chemosynthetic SOB modulated the locally availability of light for cyanobacteria and caused delayed O2 production, which implies a strong effect of daylength on the net O2 export from mats that host competitive photosynthetic and chemosynthetic communities. We assessed this prediction by measuring the net O2 production in these mats during different daylengths simulated in the laboratory under low O2 conditions (Figs. 2a and 3f, and Extended Data Fig. 7). For daylengths of <12 hours, no O2 was produced and the mats were a net sink for O2. For a daylength of 16 hours (that is, late Archean) and longer, a net diel O2 export occurred, with 21 hour (late Proterozoic) and 24 hour daylengths exporting two and three times, respectively, more O2 than 16 hour one.

Although similar competitive effects have been observed in other extant mat systems26, the applicability of these analogues to Precambrian mats is uncertain. However, several other mechanisms also result in a delayed O2 production due to a dramatic variation of the redox conditions in microbial mats within diel timescales. Some microbial groups are equipped with mechanisms to regulate or delay the onset of certain metabolic processes20,27,28,29. Similar to the MIS mat, the implementation of a delayed recovery of OP after exposure to sulfide27 in our modelled mat showed that GPP and Corg burial decreased sharply with decreasing daylength (Extended Data Fig. 8). Overall, the combined effect of mass transfer limitation, metabolic regulation and whole-community interactions in living microbial mats strengthens the dependency of O2 export and Corg burial on increasing daylength (Fig. 2).

The regulation of Corg burial by daylength and by the corresponding diel O2 dynamics is conceptually consistent with empirical observations in modern sediments, in which the long-term burial efficiency decreases with the exposure time to O2 (ref. 14). As longer days export more O2, the ratio between Raero and Ranaero decreases (Extended Data Fig. 3), the average diel O2 penetration depth decreases (Extended Data Fig. 2b) and the non-photosynthetic layers of mats are exposed to O2 for a shorter fraction of the day (Extended Data Fig. 2c). This suggests that daylength also promotes long-term Corg burial independent of the effect of daylength on the dynamic response of respiratory processes with specific metabolic traits. Additionally, mat accretion rates must be accounted for because they shape the residence time of Corg in the oxic zone. Modern mats reach stunning accretion rates30 (for example, 0.5–5 mm yr−1), similar to estimates from ancient microbialites31 (0.5–15 mm yr−1). Given that longer days decreased the diel local O2 availability and enhanced the burial efficiency, the accretion rate would have increased, thereby possibly establishing a positive feedback effect on long-term burial. This is because both regulatory factors result in shorter exposure times of benthic Corg to O2, but on different timescales. Thus, the daylength effect on net productivity and long-term burial could possibly be more pronounced for growing mats than for our modelled mats with a stagnant biomass.

## Spinning down to oxygenation

The fundamental effect of changing planetary rotation rate on benthic export fluxes would have applied for most of Earth’s photosynthetic history until the end of the ‘matworld’32. Quantitative assessment requires parameterizing global benthic Corg burial along with Earth’s rotation rate, which decreased over Earth’s history as inferred from geological proxies33,34 and models10,35. A precise reconstruction of the rotation rate is currently beyond reach owing to uncertainties in the strengths of tidal friction, which includes effects from oceanic33,36, atmospheric10,37 and solid Earth tides35. Although there is no consensus on the exact pattern, the rate of oceanic tidal dissipation normalized to the strength of the astronomical forcing must have been lower than modern rates for long stretches of Earth’s history because the current rate implies an Earth–Moon collision at ~1.5 Ga, for which there is no evidence36. Recent models that consider the effect of changes in the continental configuration on tidal dissipation rates suggest that Earth’s rotational deceleration was lowest in the mid-Proterozoic33. Another long-standing hypothesis even predicts a period with a stable rotation rate in the Proterozoic due to a resonant atmospheric thermal tide10,37. The dissipation of oceanic and solid Earth tides cause rotational deceleration that is counteracted by atmospheric thermal tides, which depend on daylength37. This hypothesized period of stability and the subsequent marked increase in daylength coincide with the boring billion years of O2 stasis and the NOE, respectively. The remarkable correlation between the patterns of Earth’s oxygenation and rotation rate (Fig. 4) invites a quantitative evaluation of the potential mechanistic link between daylength and oxygenation.

We extended our estimates of diel benthic Corg burial to global scales over Earth’s history. Considerations of Corg fluxes on planetary and geological scales require several uncertain assumptions, and thus our estimates represent a possible range of the effect of rotation rate on $$p{{\rm{O}}_2}$$. To quantitatively implement Earth’s rotational deceleration, we used a recent model10, which predicts deceleration before 2.2 Ga followed by resonant stability during the mid-Proterozoic until ~650 Ma, and subsequent return to deceleration towards the modern 24 h daylength. To model the quasi-steady-state evolution of global $$p{{\rm{O}}_2}$$, we considered that daylength-driven changes in global Corg burial and solute export fluxes interacted with sinks of O2 beyond the benthic domain, namely, atmospheric reduction by metamorphism- and volcanism-derived gases and erosional weathering (Extended Data Fig. 1). As the relative contributions of benthic and pelagic to total marine Corg burial are highly uncertain38,39,40,41,42, we expressed the benthic term as a fraction of total marine burial, assumed to be at modern levels. Beyond the marine realm, we considered the possible effect of terrestrial mats in the Precambrian43. As we expect long-term burial rates to be substantially lower than the diel Corg burial14, we implemented a weathering-based negative feedback effect between $$p{{\rm{O}}_2}$$ and terrestrial diel, and implicitly on long-term, Corg burial (Extended Data Figs. 1 and 9). This analysis showed that daylength-driven changes in Corg burial could account for the offset between pre- and post-GOE O2 levels without having to assume any changes in atmospheric reductant fluxes or GPP (Fig. 4b). Mat scenarios with no net Corg burial in the pre-GOE Archean (18 h daylength) support 50% of the global marine Corg burial in the mid-Proterozoic (21 h daylength), but only occupy 3.7% of the modern oceanic area (see Methods). For the modern continental arrangement, this mat coverage is comfortably less than the neritic zone (7.5%)44, the primary habitat for benthic photosynthesis. The daylength effect implies an increase up to ~0.28$$p{{\rm{O}}_2}$$ at around 0.55 Ga (Fig. 4b), consistent with an early NOE and a later Palaeozoic oxidation event (POE), possibly connected to the Great Ordovician Biodiversity Event, at ~0.4 Ga (refs 2,45).

We suggest that changes in daylength rebalance remineralization. Positive carbon isotope excursions associated with oxygenation events are interpreted as signals of increased Corg burial, caused by increasing GPP or decreasing remineralization efficiency46,47,48. How these parameters imprint on the isotope record in the case of microbial mats is uncertain due to mass transfer limitation of dissolved inorganic carbon supply and the resultant negligible isotope fractionation observed in modern mats49,50,51. Yet, the daylength-driven enhancement of O2 export and Corg burial is consistent with proxies for weathering and total organic carbon contents in the record (Extended Data Fig. 9). Despite the predicted increase in weathering, we have not included the response of phosphorus fluxes to increasing $$p{{\rm{O}}_2}$$. Increased weathering would have further boosted the global primary production7,52—but probably only transiently as a pulse, followed by a return to the previous quasi-steady state $$p{{\rm{O}}_2}$$ (refs 3,6) for a given daylength. Although nutrient supply and the corresponding GPP determine the absolute range of $$p{{\rm{O}}_2}$$ levels, daylength effects on benthic burial could have shaped the overall oxygenation pattern before the POE (Fig. 4b).

Overall, we show that increasing daylength is a monotonic driver of net productivity pervasive across all ranges of metabolic parameters (Fig. 2). Relatively abrupt changes in daylength, as caused by escape or entry into resonance locking, could therefore be among the triggers for the global oxidation events. In this respect, our proposed mechanism is similar to that of other abrupt events that cause imbalances in the global $$p{{\rm{O}}_2}$$ budget, such as plate tectonics (including supercontinent formation)5,53,54,55 or new prospects for productivity in the oceans and on land4,45,56. As Earth’s rotation rate, governed by planetary physics, does not share any assumptions with these geological or biological triggers, the daylength effect operates in parallel to these other Earth-bound mechanisms. Even if we assume a more gradual decrease in rotation rate, our study clearly suggests that net productivity would have increased. Previous studies show that gradual changes in sources and sinks of O2 can cause relatively abrupt shifts in $$p{{\rm{O}}_2}$$, such as those due to H2 escape, insolation, continental phosphorus supply, continental growth or volcanic reductant input6,23,47,57,58. The exact magnitude of the daylength effect remains uncertain as it relies on several assumptions, particularly the relationship between diel and long-term burial efficiency and the detailed pattern of rotational deceleration. Further, we have not considered the effects of changes in the limiting factors of gross productivity, such as phosphorus, insolation or strength of O2 sinks, other than daylength-related increases in terrestrial Corg weathering. Yet, the peculiarity of daylength-driven increases in benthic net productivity is that no such changes are required to produce substantial changes in $$p{{\rm{O}}_2}$$. Thus, the dynamics of the Earth–Moon system possibly had major impacts on global O2 levels during critical turning points of Earth’s biogeochemical evolution towards a profusely oxic world.

## Methods

### Modelling microbenthic O2 export

We explored how microbial processes and export fluxes of their metabolic substrates and products from ancient benthic photosynthetic ecosystems were influenced by daylength, environmental conditions and various regulatory mechanisms of photosynthetic production and respiration using an in silico microbenthic model. Model scenarios were constructed and simulated using MicroBenthos software12. MicroBenthos model definitions and parameters for the described scenarios are provided with this article. The software and usage instructions are available at https://microbenthos.readthedocs.io.

The modelling framework is an adaptation of de Wit et al.61. Briefly, benthic systems are constructed as a diffusive–reactive system in a 1D computational domain, with discrete cells used to represent the spatial distribution of the state and parameter variables. While the study by de Wit et al.61 focused on biomass growth running over long simulation times, our interest was to study the dynamics of process rates and solute fluxes over diel timescales. Therefore, we set a fixed biomass for the microbial groups, added a water subdomain on top of the sediment as a diffusive boundary layer and ran simulations until a diel steady state was reached (5 days). Our model domain used 5 µm cells, with an 8 mm sedimentary subdomain and 1 mm diffusive boundary layer of water on top. O2 and sulfide concentrations were the state variables that we solved for. Photosynthetically active radiation (PAR) was expressed as a percent of the maximum intensity at the diel zenith, and followed a cosinusoidal pattern similar to that of diel insolation dynamics.

Raero and SOX were formulated to occur throughout the sediment. Microbial groups (cyanobacteria and SRB) were represented as biomass distributions in the sediment subdomain, and biomass-dependent metabolism kinetics were expressed as multiplications of the response functions of salient environmental and state variables. Coupled partial differential equations of the state variables (O2 and H2S) were composed from the reaction terms that accounted for sediment porosity and were solved with finite-volume numerical approximations62.

Our in silico mat allowed us to explore how diffusive mass transfer shapes the interplay between illumination dynamics, gross production and consumption rates, and diel O2 export. The effect of daylength was studied by varying the period of the illumination from 12 h to 24 h, the range of estimated daylengths over Earth’s history after the earliest estimates for the origin of OP63. We report the calculated average diel net export and process rates in units of mmol m−2 h−1 because the hour is the largest temporal unit unaffected by changes in the Earth’s rotation and thus allows for comparison across daylengths.

First, we explored the simplest case of O2 production, which is with light availability. Two microbial processes were considered: OP performed by cyanobacteria and Raero. The parameters for the biotic reactions were re-expressed as a biomass-specific maximal yield (Qmax). A fundamental assumption is that the photosynthesis rate is strictly correlated to the instantaneous photon flux:

$${\rm{OP}} = Q_{{\rm{max}}}\times {\rm{biomass}}\times {\rm{sat}}\left( {{\rm{PAR}},\,K_{{\rm{PAR}}}} \right),$$
(1)

where sat is a Michaelis–Menten function with KPAR = 15% and the cyanobacterial biomass with a log-normal distribution with a peak value of 12 mg cm−3 at 0.5 mm depth (Supplementary Video 1). The only source of O2 is OP, and the sinks are aerobic (sedimentary) respiration (Raero). For the production and consumption rates of Corg, we assumed a stoichiometry of:

$${\mathrm{H}}_2{\mathrm{O}} + {\mathrm{CO}}_2 \to {\mathrm{O}}_2 + {\mathrm{CH}}_2{\mathrm{O}}$$
(2)

with respect to O2 cycling rates, where CH2O refers to one Corg equivalent. Assuming that Corg is predominantly particulate, with negligible diffusional transport, diel Corg burial was thus calculated as:

$${\mathrm{C}}_{{\mathrm{org}}}\ {\mathrm{buried}} = \smallint {\mathrm{OP}}-\smallint {\mathrm{R}}_{{\mathrm{aero}}},$$
(3)

where ∫OP and ∫Raero are the diel depth-integrated rates of O2 production and consumption and are equivalent to Corg production and consumption according to equation (2). Thus, diel burial can also be represented through the export flux of O2 at the top and bottom interfaces of the sedimentary domain:

$${\mathrm{C}}_{{\mathrm{org}}}\ {\mathrm{buried}} = {\mathrm{O}}_{2}\ {\mathrm{export}} = \smallint {\mathrm{OP}}-\smallint {\mathrm{R}}_{{\mathrm{aero}}},$$
(4)

which allowed us to assess the dynamic steady state of the diel model when the average diel depth-integrated rates equalled the export fluxes.

To calibrate the O2 productivity for unitless PAR intensities, we determined the Qmax that caused a maximum O2 export that corresponded to the median maximal flux from illuminated benthic photosynthetic systems13. A Qmax of 4.0022 mmol g−1 h−1 produced the target export flux of 5.76 mmol m−2 h−1 under a sedimentary respiration load of 0.1 mM h−1. Note that by calibrating the productivity to the maximum diel illumination, the model represents a ‘mean solar day’ of a given Earth year59. This allowed us to disentangle the effect of daylength from geological-scale changes in the insolation intensity, such as in the ‘faint young Sun’ paradigm reviewed thoroughly by Feulner23, or changes in the solar spectrum related to atmospheric composition64.

Next, we explored the effect of Ranaero on the daylength dependency of the process rates and export fluxes. We used the example of sulfate reduction performed by SRB with a log-normal biomass distribution with a peak value of 2 mg cm−3 (Supplementary Video 1). The Ranaero rate was either defined as a constant rate process for the scenario ‘OP SRB constant’ as:

$${\mathrm{R}}_{{\rm{anaero}}} = Q_{{\rm{max}}}\times{\rm{biomass}}$$
(5)

or as an O2- and H2S-sensitive process as:

$$\begin{array}{rcl}{\mathrm{R}}_{{\rm{anaero}}} & = & Q_{{\rm{max}}} \times {\rm{biomass}}\times {\rm{inhibition}}([{\rm{O}}_2],\,K_{{\rm{max}},{{\rm{O}}_2}},\,K{_{{\rm{half}},{{\rm{O}}_2}})}\\ && \times {\rm{inhibition}}\left( [{{\rm{H}}_2{\rm{S}}],\,K_{{\rm{max}},{\rm{H}}_2{\rm{S}}},\,K_{{\rm{half}},{\rm{H}}_2{\rm{S}}}} \right)\end{array}$$
(6)

where inhibition is a function of the local H2S and O2 concentration (x) of the form:

$$\frac{{K_{{\rm{max}}} - x}}{{2\times K_{{\rm{max}}} - K_{{\rm{half}}} - x}}$$
(7)

when x < Kmax and 0 when x ≥ Kmax. Inhibition factors chosen for both scenarios with O2- and H2S-sensitive SRB (‘OP SRB’ and ‘OP SRB inhibited’) were 3 mM for $$K_{{\rm{max}},{\rm{H}}_2{\rm{S}}}$$, 0.5 mM for $$K_{{\rm{half}},{\rm{H}}_2{\rm{S}}}$$ and 1 µM for $$K_{{\rm{half}},{\rm{O}}_2}$$. $$K_{{\rm{max}},{\rm{O}}_2}$$ was 0.8 mM for the scenario with a moderate inhibition, ‘OP SRB’, and 0.3 mM for the scenario with a strong inhibition, ‘OP SRB inhibited’.

SOX was formulated as:

$${\rm{SOX}} = k\times {\rm{O}}_2\times{\rm{H}}_2{\rm{S}},$$
(8)

where k = 351 l mol−1 h−1 (ref. 65). For Ranaero we assumed the stoichiometry:

$${{\mathrm{SO}}_4}^{2 - } + 2{\mathrm{CH}}_2{\mathrm{O}} \to {\mathrm{H}}_2{\mathrm{S}} + 2{\mathrm{CO}}_2 + 2{\mathrm{H}}_2{\mathrm{O}},$$
(9)

and therefore calculated diel burial as:

$${\mathrm{C}}_{{\mathrm{org}}}\ {\mathrm{buried}} = \smallint {\mathrm{OP}}-\smallint {\mathrm{R}}_{{\mathrm{aero}}}-2\times\smallint {\mathrm{R}}_{{\mathrm{anaero}}},$$
(10)

where ∫Ranaero is the depth-integrated rate of sulfide production by SRB. The export flux of O2 is shaped by mat-intrinsic rates of Raero, OP and SOX according to:

$${\mathrm{O}}_{2}\ {\mathrm{export}} = \smallint {\mathrm{OP}}-\smallint {\mathrm{R}}_{{\mathrm{aero}}}-\smallint {\mathrm{SOX}},$$
(11)

where ∫SOX is the depth-integrated rate of O2 consumption by SOX. Assuming the complete oxidation of H2S to sulfate, H2S export can be formulated as:

$${\mathrm{H}}_2{\mathrm{S}}\ {{\rm{export}}} = \smallint {\mathrm{R}}_{{\mathrm{anaero}}}-0.5\times\smallint{\mathrm{SOX}}.$$
(12)

According to equations (10)–(12), diel burial can thus be represented as:

$${\mathrm{C}}_{{\mathrm{org}}}\ {\mathrm{buried}} = {\mathrm{O}}_2\ {\mathrm{export}}-2\times {\mathrm{H}}_2{\mathrm{S}}\ {{\mathrm{export}}}$$
(13)

This illustrates that the control of diel burial is related to the export of O2 and the reduced product of Ranaero (such as H2S), as the former is an equivalent source and the latter an equivalent sink of Corg within the mat. This means that an increase in O2 export would not result in an increase of burial if H2S export increased proportionally in terms of Corg equivalents.

To calibrate the productivity for SRB scenarios, we determined values of Qmax for OP and SRB, which yielded the target maximum export flux of 5.76 mmol m−2 h−1 at 24 h under 250 µM O2 boundary conditions and negligible burial fluxes at 18 h under anoxic boundary conditions, that is, in pre-GOE conditions (see Supplementary Data 1 for model parameters).

We tested the sensitivity of diel burial to O2 concentration in the water column (0–250 µM) for all three SRB scenarios. For the least O2-sensitive scenario (‘OP SRB’), we also tested sensitivity of burial to gross productivity by varying the maximal photosynthetic yield Qmax over the range 0.5–10 mmol g−1 h−1. Note that the variation in Qmax can be considered equivalent to variations in other factors that influence gross production, such as nutrient supply and irradiance levels.

We then explored the effect of AP and reductant supply to the mat. Reductants that served as electron donors for AP were available in Precambrian phototrophic habitats, and supported diverse forms of photosynthesis even after the GOE and the evolution of OP66,67,68. Although the extent and ecological niches of AP and OP over Earth’s history remain unclear, AP and OP probably co-existed, with spatially and temporally variable partitioning of the total GPP between them69. Analogous to modern systems, the partitioning probably depended on the limiting factors of both metabolisms, such as light and nutrients, with AP additionally limited by electron donor supply, and on the onset of novel evolutionary avenues or geochemical transitions that facilitated shifts in the outcome of competition.

We implemented this concept by adapting the ‘OP SRB’ scenario to include metabolic flexibility in the modelled photosynthetic community, analogous to cyanobacteria that can partition harvested light energy towards OP and sulfide-driven AP (Extended Data Fig. 4). Transitions between photosynthetic modes are based on the local sulfide and light availability with the rate of OP regulated by the rate of AP20. In this ‘OP SRB + AP’ scenario, the modelled cyanobacteria produced O2 according to:

$$\begin{array}{rcl}{\rm{OP}} & = & Q_{{\rm{max}}}\times {\rm{biomass}}\times{\rm{sat}}({\rm{PAR}},\,K_{{\rm{PAR}}})\\ && \times\left( {1-{\rm{normsat}}\left( {{\rm{H}}_2{\rm{S}},\,{\rm{H}}_2{\rm{S}}_{{\rm{thr}}}} \right)} \right),\end{array}$$
(14)

where normsat is a normalized Michaelis–Menten function with a value of 1 for H2S ≥ H2Sthr, where H2Sthr is the threshold sulfide level. Conversely,

$$\begin{array}{rcl}{\rm{AP}} & = & Q_{\rm{max}}\times{\rm{biomass}}\times{\rm{sat}}({\rm{PAR}},K_{{\rm{PAR}}})\\ && \times{\rm{normsat}}\left. {({\rm{H}}_2{\rm{S}},\,{\rm{H}}_2{\rm{S}}_{{\rm{thr}}})} \right)\end{array}$$
(15)

The metabolic behavior is such that OP occurs only below H2Sthr, which is light dependent. Below this threshold level, the harvested light energy is partitioned towards AP and OP, with a higher affinity for AP. Above the threshold, only AP occurs and OP is suppressed. The resulting metabolic response is that the sum of OP and AP follows the form of equation (1), whereas Ranaero, Raero, SOX and other processes work as in previous scenarios. The interplay of illumination, mat processes and the resultant depth-resolved dynamics of O2 and H2S under this scenario can be seen in the Supplementary Video 1. Assuming sulfate as the product of AP according to:

$${\mathrm{H}}_2{\mathrm{S}} + 2{\mathrm{CO}}_2 + {\mathrm{H}}_2{\mathrm{O}} \to {{\mathrm{SO}}_4}^{2 - } + 2{\mathrm{CH}}_2{\mathrm{O}},$$
(16)

diel burial in this scenario was calculated as

$${\mathrm{C}}_{{\mathrm{org}}}\ {\mathrm{buried}} = \smallint {\mathrm{OP}} + \smallint {\mathrm{AP}}-\smallint {\mathrm{R}}_{{\mathrm{aero}}}-2\times \smallint {\mathrm{R}}_{{\mathrm{anaero}}},$$
(17)

where ∫AP is the depth-integrated rate of CO2 fixation by AP. As in the other scenarios, diel burial can alternatively be calculated according to equation (13). Values of Qmax for OP and Ranaero were adjusted to produce the same maximum O2 export flux at 24 h (O2 boundary at 250 µM) and diel Corg flux at 21 h (25 µM O2 boundary) as in ‘OP SRB’. This allowed us to establish directly comparable upscaling calculations for global $$p{{\rm{O}}_2}$$ at the same areal coverage and diel burial by ‘OP SRB’ and ‘OP SRB + AP’ mats (see below).

Besides the effect of daylength, we also studied the effect of the availability of O2 and H2S as electron donors from the water column on the scenario with AP. Water column O2 levels from 0 to 250 µM and H2S levels from 0 to 20 µM were tested.

Photosynthetic inhibitory mechanisms were also tested by modelling cyanobacteria that exhibit a 30 min recovery time of OP after the local sulfide levels fall below a certain level27.

### Microsensor measurements

We sampled cores from cyanobacterial mats that formed in the MIS (Michigan, United States) in October 2015, May 2016 and June 2016. Cores and bottom water sampled from above the mats were transported to the lab in Ann Arbor. Cores were either used directly or kept on the seasonal day–night light cycle at 8 °C until the measurements were made. During the measurements in the cores, a circular flow of the water column above the mat surface was adjusted using peristaltic pumps connected to an external temperature-controlled reservoir of bottom water. Water column O2 and sulfide concentrations were adjusted in this separate reservoir of bottom water using N2, air and neutralized Na2S solution. After adjustment, the reservoir was covered with paraffin oil to prevent gas exchange and maintain constant conditions in the water column. The total sulfide concentration in the water column was regularly checked by subsampling and colorimetric determination according to Cline70. Both the water column reservoir and the core were kept at 10 °C during the measurements.

Illumination was provided by a broadband halogen lamp (Schott KL-1500). In situ spectral light quality was simulated using optical filter foils (Roscolux 375, Rosco Laboratories). The incident irradiance at the surface of the mat was determined with a submerged cosine-corrected quantum sensor connected to a LI-250A light meter (both LI-COR Biosciences GmbH). O2, pH and H2S microsensors with a tip diameter of 10–50 µm and a response time of <1 s were built, calibrated and employed as previously described71,72,73. The microsensor tips were always separated by <500 µm during simultaneous O2, pH and H2S measurements.

The volumetric rates of gross OP were estimated based on the dynamics of O2 concentration after a light–dark shift, as described previously74. Analogously, the volumetric rates of gross AP were calculated from the increase of H2S concentration and pH directly after a light–dark transition (that is, light-driven Stot consumption rates), as previously described26,27,75. Net rates and fluxes were calculated from profiles based on Fick’s laws using diffusion coefficients for O2 and sulfide corrected for temperature and salinity.

### From diel export to global oxygenation

We considered that changes in diel O2 and H2S export rates, the difference of which is equivalent to diel benthic Corg burial, interact with global redox controls beyond the mat domain (Extended Data Fig. 1). Namely, we considered atmospheric reduction by volcanism- and metamorphism-derived gases (atmR) and weathering60. Although we assumed a constant flux of reductant (vR) available for atmospheric reduction, weathering is dependent on $$p{{\rm{O}}_2}$$ and thus strongly tempers the accumulation of O2 in the atmosphere. As a recent computational Earth rotation model10 predicts a stabilized daylength in the mid-Proterozoic, we started our global calculations by assuming a $$p{{\rm{O}}_2}$$ of 0.01–0.1 at the predicted stable 21 h. This $$p{{\rm{O}}_2}$$ is the result of the interaction of global sources and sinks (illustrated in Extended Data Fig. 1) according to a simplified version of the formulations (for example, COPSE60,76) of the global O2 budget. Considering an evolution of steady states of $$p{{\rm{O}}_2}$$ throughout Earth’s history, we described the $$p{{\rm{O}}_2}$$ evolution at a given age as:

$$\frac{{\mathrm{d}}( {p{{\mathrm{O}}_2}})}{{\mathrm{d}}t} = {\mathrm{pB}} + {\mathrm{mB}}-{\mathrm{vR}}-\left( {0.95 \times {\mathrm{tB}} + {\mathrm{uB}}} \right)\times{p{{\mathrm{O}}_2}}^{0.5},$$
(18)

which provides the steady state $$p{{\rm{O}}_2}$$ as:

$$p{{\rm{O}}_2} = \left( \frac{ {{\mathrm{pB}} + {\mathrm{mB}}-{\mathrm{vR}}}}{{0.95 \times {\mathrm{tB}} + {\mathrm{uB}}} } \right)^2,$$
(19)

where pB is the global burial flux associated with marine pelagic production, mB is total mat burial flux, vR is the flux of volcanic reductant, tB is the burial flux by terrestrial mats, and uB is an aggregate flux term that captures uplift forcing, the global Corg reservoir and a weathering constant60.

Changes in any of the global fluxes would therefore result in new steady state $$p{{\rm{O}}_2}$$. For the total marine burial (pelagic pB and coastal benthic mB – tB) we assumed modern values throughout the Precambrian60. Beyond the marine realm, we considered the possible existence of terrestrial mats43, which would have further boosted global GPP and Corg burial, but would have also been more susceptible to weathering (tB in Extended Data Fig. 1). For these terrestrial mats, we assumed the same regulation mechanisms of export fluxes as those for coastal benthic mats and considered that AP might have been driven by reductant supplied from Ranaero, but we did not explore the effects of external reductant availability for terrestrial mats. Using our diel mat model output for tB at 21 h daylength and for 5% continental coverage, we then calculated vR for the two $$p{{\rm{O}}_2}$$ levels assuming the values for uB from Daines et al.60.

The Earth rotation rate model10 predicts monotonic deceleration before 2.2 Ga followed by a stable daylength of ~21 h due to the atmospheric thermal tide resonance until ~650 Ma, with a subsequent increase towards the modern 24 h daylength10. Starting at 21 h at 2 Gyr, we estimated the effect of the daylength-driven change in the Corg burial from benthic and terrestrial mats, the output of our diel mat model, on $$p{{\rm{O}}_2}$$ levels both backwards and forwards in time. The modulation of $$p{{\rm{O}}_2}$$ naturally depends on the steepness of the dependence of mat Corg burial on daylength (Fig. 2). However, we limited our analysis to the effect of mats with metabolic regulation from the moderately daylength-sensitive scenarios ‘OP SRB’ and ‘OP SRB + AP’. Scenarios with a steeper dependency of burial on daylength yielded oscillations of $$p{{\rm{O}}_2}$$ beyond PAL even due to the minimal variations in daylength within the resonant-locked phase in the mid-Proterozoic10 and therefore had to be excluded from analysis of $$p{{\rm{O}}_2}$$ evolution. We additionally included negative feedback effects of increasing $$p{{\rm{O}}_2}$$ on the mat Corg burial by dynamically adjusting the O2 boundary conditions in each time step according to the $$p{{\rm{O}}_2}$$ calculated from the previous step. To then calculate the quasisteady-state $$p{{\rm{O}}_2}$$ level based on changes in the benthic and terrestrial burial, the actual coverage and thus partitioning between the pelagic and benthic burial have to be considered. Reliable estimates for this partitioning are lacking. The presence of pelagic cyanobacteria has persisted since 1.1 Ga (ref. 38). Yet, cyanobacteria in the palaeontological record are primarily benthic, with sparse evidence for pelagic forms39,40,41. Hypotheses for the limited pelagic productivity during the Proterozoic range from an inaccessible, toxic or damaging photic zone to late evolution of a planktonic lifestyle21,66,77. Alternatively, burial of the Corg produced by pelagic cyanobacteria might have been hindered by the small cell sizes, low sinking rates and resultant efficient remineralization within the water column42,78. The preservation of Corg by benthic microbial mats is as uncertain, especially when eroded—on land or in the oceans. In our calculations we considered the terrestrial erosional weathering explicitly (tB in Extended Data Fig. 1), which introduces a strong negative feedback effect on $$p{{\rm{O}}_2}$$. This implicitly describes a substantial loss in translation of the diel Corg to long-term burial that we, however, did not explicitly account for. For marine benthic mats we argue that a more direct link between the diel and long-term burial of Corg is plausible given that mats can reach substantial thicknesses when undisturbed (for example, in Solar Lake the thickness is >1 m) (ref. 79) and that mats have a similar remineralization fate as pelagic Corg export when eroded. To address these uncertainties, we considered benthic burial as between 20 and 50% of the total marine burial at 21 h daylength. Note that this partitioning must shift during our simulations over Earth history because benthic (and terrestrial) burial is daylength dependent, whereas we took an ‘all is constant’ approach for pelagic burial and the fraction of weathered diel Corg, as we expected a negligible effect of molecular diffusion and thus daylength on these fluxes.