Possible link between Earth’s rotation rate and oxygenation

The biotic and abiotic controls on major shifts in atmospheric oxygen and the persistence of low-oxygen periods over a majority of Earth’s history remain under debate. Explanations of Earth’s stepwise pattern of oxygenation have mostly neglected the effect of changing diel illumination dynamics linked to daylength, which has increased through geological time due to Earth’s rotational deceleration caused by tidal friction. Here we used microsensor measurements and dynamic modelling of interfacial solute fluxes in cyanobacterial mats to investigate the effect of changing daylength on Precambrian benthic ecosystems. Simulated increases in daylength across Earth’s historical range boosted the diel benthic oxygen export, even when the gross photosynthetic production remained constant. This fundamental relationship between net productivity and daylength emerges from the interaction of diffusive mass transfer and diel illumination dynamics, and is amplified by metabolic regulation and microbial behaviour. We found that the resultant daylength-driven surplus organic carbon burial could have shaped the increase in atmospheric oxygen that occurred during the Great and Neoproterozoic Oxidation Events. Our suggested mechanism, which links the coinciding increases in daylength and atmospheric oxygen via enhanced net productivity, reveals a possible contribution of planetary mechanics to the evolution of Earth’s biology and geochemistry. Rotational deceleration has increased daylength on Earth, potentially linking the increased burial of organic carbon by cyanobacterial mats and planetary oxygenation, according to experiments and modelling of Precambrian benthic ecosystems.

T he rise of free oxygen (O 2 ) in the Earth's atmosphere and oceans enabled the evolution of aerobic life 1 . Oxygenic photosynthesis (OP) in microbial mats was a substantial source of O 2 for the Great Oxidation Event (GOE) ~2.4 billion years ago (Ga), during the stable low-O 2 conditions that followed and for the Neoproterozoic Oxygenation Event (NOE) ~600 Ma (ref. 2 ). The biological 3,4 , tectonic 5 and geochemical 6,7 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 friction 8,9 . 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 O 2 export, changes the balance between aerobic and anaerobic remineralization, and thus enhances the diel organic carbon (C org ) burial. We then investigated the remarkable similarity between the timing and pattern of increase in atmospheric O 2 ( pO 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 O 2 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 C org burial, is the result of this GPP and the rate of C org 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 O 2 . Our modelling framework 12 formulates benthic ecosystems as diffusive-reactive systems with OP, anoxygenic photosynthesis (AP), aerobic respiration (R aero ), sulfate reduction (anaerobic respiration (R anaero )) and abiotic sulfide oxidation (SOX) (Extended Data Fig. 1 and Supplementary Video 1). Starting with a simple in silico mat with only OP and R aero , simulations with the same rate of GPP showed that longer days yield higher export fluxes, that is, an increase in O 2 escape to the overlying water ( Fig. 1a,b). The mechanism behind this relationship is apparent in the duration between the maxima of gross O 2 production and export (Fig. 1a), which illustrates how mass transfer resistance delays the O 2 escape. The export-limiting delay represents a smaller fraction of the day for longer daylengths. Longer days build up steeper O 2 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 signals 13  The biotic and abiotic controls on major shifts in atmospheric oxygen and the persistence of low-oxygen periods over a majority of Earth's history remain under debate. Explanations of Earth's stepwise pattern of oxygenation have mostly neglected the effect of changing diel illumination dynamics linked to daylength, which has increased through geological time due to Earth's rotational deceleration caused by tidal friction. Here we used microsensor measurements and dynamic modelling of interfacial solute fluxes in cyanobacterial mats to investigate the effect of changing daylength on Precambrian benthic ecosystems. Simulated increases in daylength across Earth's historical range boosted the diel benthic oxygen export, even when the gross photosynthetic production remained constant. This fundamental relationship between net productivity and daylength emerges from the interaction of diffusive mass transfer and diel illumination dynamics, and is amplified by metabolic regulation and microbial behaviour. We found that the resultant daylength-driven surplus organic carbon burial could have shaped the increase in atmospheric oxygen that occurred during the Great and Neoproterozoic Oxidation Events. Our suggested mechanism, which links the coinciding increases in daylength and atmospheric oxygen via enhanced net productivity, reveals a possible contribution of planetary mechanics to the evolution of Earth's biology and geochemistry.
C org that escapes R aero 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) C org excess, and possibly the long-term C org burial rate, a crucial determinant for the state of global pO 2 (refs 1,14 ). Overall, although GPP rates are unaffected by changes in daylength, C org burial is modulated through the physics of molecular diffusion.

Daylength increases O 2 export more than reductant export
A more realistic scenario includes R anaero as an additional sink of C org , 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 reduction 15 and because sulfide was transiently abundant in Precambrian coastal habitats 16 . We first chose a mat scenario with the R anaero rate fixed to a constant value, to isolate the effect of daylength on diffusion-driven dynamics of sulfide export (Fig. 1c). Like O 2 fluxes, the reductant export fluxes are shaped by molecular diffusion and rates of production and consumption within the mat (R anaero and SOX). The latter is an additional sink of O 2 and is thus competitive with R aero . Consequently, the C org that escapes both anaerobic and aerobic remineralization can be represented as the difference between the O 2 and H 2 S 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  s export, and diel averages for C org respiration and burial compared for 12 h versus 24 h daylengths. a, Depth-integrated gross OP (∫ z OP, grey fill) in a pure OP system ('OP no H 2 S') under a water column with 25 µM O 2 (pO 2 = 0.1) is identical for the two daylengths with the time of day viewed as a fraction of the diel period. However, the diel fraction during which export is tempered by mass transfer, illustrated by the duration between the maxima of photosynthesis (black dotted line) and export (blue and orange dotted lines), is sensitive to daylength. b, As longer days export more O 2 , less O 2 is available for aerobic respiration (∫ z R aero ) in the mat, and therefore the burial of C org increases with daylength. c, In the presence of anaerobic respiration by sulfur-reducing bacteria, both O 2 and H 2 S export fluxes are modulated by daylength, even though the gross photosynthesis and sulfide production by anaerobic respiration are independent of the illumination dynamics in this simulation ('OP SRB constant'). d, The diel C org burial flux is defined here as the photosynthetically produced C org that escapes both aerobic and anaerobic respiration (∫ z OP - ∫ z R aero - ∫ z R anaero ) and equals the difference between the export budgets of O 2 and H 2 S (shown in C org equivalents). The decrease of ∫ z R aero compared with the diel budget in b is due to abiotic sulfide oxidation (SOX), an alternative sink of O 2 . As ∫ z R anaero is set to be constant, the overall effect remains: mats export more O 2 and retain more C org in longer days. effect of SOX, R aero is less sensitive to daylength than it is in a reductant-free scenario. The effect of an increased O 2 export on the diel C org burial rate is therefore counteracted, but not overwhelmed, by concomitant increases in H 2 S export (Fig. 1d). To further explore if the increase of diel C org burial is maintained when R anaero is affected by local solute dynamics, we implemented sulfate-reducing bacteria (SRB) that are inhibited by O 2 and H 2 S, as observed in modern mats [17][18][19] . Across a range of inhibition strengths, diel C org 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 C org burial to reductant and O 2 availability in the water column. Diel O 2 export and C org burial fluxes increased with daylength across all O 2 boundary conditions (Fig. 2). Increasing O 2 in the water column had a strong enhancing effect on R aero and negative effect on O 2 export fluxes. For the diel C org burial rate, determined by both R aero and R anaero , the effect of O 2 levels in the water column was variable (Extended Data Fig. 3). Depending on the inhibition strength of O 2 on R anaero , C org burial either increases or decreases with the O 2 boundary conditions. Given that R anaero is O 2 sensitive, the negative impact of pO 2 is overwhelmed by the positive effect of daylength enhancing diel benthic C org burial over Earth's history.
To explore the interactions between reductant availability and C org burial with daylength, we also included AP using H 2 S as an electron donor that competes with OP for the contribution to GPP based on mat-intrinsic reductant and light levels 20 (Extended Data Fig. 4). With AP present in mats, the fraction of the day that exports O 2 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 O 2 is produced decreases markedly with daylength. Concomitantly, R anaero decreases with daylength due to the increasing inhibition by O 2 . Although counterintuitive, R aero decreases with daylength because SOX becomes more competitive for O 2 due to the increasing fractions of the day with O 2 production. Consequently, across a range of sulfide and O 2 levels in the overlying water, we found that the C org 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 C org 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 C org burial.
Overall, we show that the net productivity, that is, the short-term C org burial of benthic ecosystems, and thus a crucial determinant of the source strength for global pO 2 , can increase with daylength over Earth's age without assuming a decrease in the global O 2 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 production 21 , redox and phosphate oscillations related to weathering during the 'boring billion' years 6 , continental reconfiguration 22 , long-term changes in insolation 23 or even daylength-related changes in ocean circulation and nutrient supply by upwelling 24 . We therefore evaluated the sensitivity of daylength-driven increases in benthic O 2 export to the rates of GPP. As expected, O 2 export displays a steep dependency on GPP, but daylength-driven changes in C org 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 O 2 export in cyanobacterial mats from the Middle Island Sinkhole (MIS), an extant analogue of Proterozoic mats under low-O 2 conditions 25 . Net O 2 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 photosynthesis 26 . The cyanobacteria exclusively performed AP, and thereby b, Owing to the O 2 export flux modulation, the diel C org burial also consistently increases with daylength despite the counteracting effect of an increasing H 2 S export for scenarios with R anaero (Fig. 1). Fluxes are shown relative to the values of each scenario at 18 h, which corresponds to daylength before the GOE. Metabolic scenarios explored were: purely aerobic systems with only OP and no R anaero ('OP no H 2 S'), systems with constant R anaero that is not affected by changing diel illumination dynamics ('OP SRB constant'), systems with metabolically complex R anaero that responds to local changes in O 2 and sulfide, which are governed by illumination dynamics ('OP SRB') and mat systems with both AP and OP ('OP SRB + AP'). Systems with sulfide-inhibited OP exhibited a steepness of daylength dependency out of scale, and are shown in Extended Data Fig. 8. For the R anaero scenario with a modest inhibition by O 2 and H 2 S ('OP SRB'), we additionally explored a wide range of plausible GPP levels ('OP SRB net production'). Notably, the effect of variations in GPP on burial is less pronounced than that on O 2 export.
depleted the sulfide underneath the SOB layer (Fig. 3b,c). The sudden onset of O 2 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 O 2 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 O 2 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 resultant delay in net O 2 production was consistently observed in four separate mat samples exposed to similar water-column conditions, and throughout seven additional mat samples exposed to a wide range of sulfide and O 2 levels in the water column (Extended Data Fig. 6). The magnitude of the fluxes and the duration of the delays were dependent on the specific sample and on the water-column redox conditions. f, The momentary export flux across the benthic interface was measured over 12-24 h simulated daylengths in one mat sample exposed to 1 µM O 2 from the water column in the absence of sulfide (Extended Data Fig. 7). The resultant diel O 2 export is shown in the key and increased with daylength.
The chemosynthetic SOB modulated the locally availability of light for cyanobacteria and caused delayed O 2 production, which implies a strong effect of daylength on the net O 2 export from mats that host competitive photosynthetic and chemosynthetic communities. We assessed this prediction by measuring the net O 2 production in these mats during different daylengths simulated in the laboratory under low O 2 conditions (Figs. 2a and 3f, and Extended Data Fig. 7). For daylengths of <12 hours, no O 2 was produced and the mats were a net sink for O 2 . For a daylength of 16 hours (that is, late Archean) and longer, a net diel O 2 export occurred, with 21 hour (late Proterozoic) and 24 hour daylengths exporting two and three times, respectively, more O 2 than 16 hour one.
Although similar competitive effects have been observed in other extant mat systems 26 , the applicability of these analogues to Precambrian mats is uncertain. However, several other mechanisms also result in a delayed O 2 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 processes 20,[27][28][29] . Similar to the MIS mat, the implementation of a delayed recovery of OP after exposure to sulfide 27 in our modelled mat showed that GPP and C org 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 O 2 export and C org burial on increasing daylength (Fig. 2).
The regulation of C org burial by daylength and by the corresponding diel O 2 dynamics is conceptually consistent with empirical observations in modern sediments, in which the long-term burial efficiency decreases with the exposure time to O 2 (ref. 14 ). As longer days export more O 2 , the ratio between R aero and R anaero decreases (Extended Data Fig. 3), the average diel O 2 penetration depth decreases (Extended Data Fig. 2b) and the non-photosynthetic layers of mats are exposed to O 2 for a shorter fraction of the day (Extended Data Fig. 2c). This suggests that daylength also promotes long-term C org 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 C org in the oxic zone. Modern mats reach stunning accretion rates 30 (for example, 0.5-5 mm yr −1 ), similar to estimates from ancient microbialites 31 (0.5-15 mm yr −1 ). Given that longer days decreased the diel local O 2 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 C org to O 2 , 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.  10,35,37,59 , illustrate that daylength might have been nearly constant in the Proterozoic. This coincides with the boring billion 6 , and the Earth escaped the 'resonance lock' in the timeframe of the NOE. b, Estimates of the quasi-steady states of the global reservoir of pO 2 as a response to changes in coastal benthic and terrestrial C org burial fluxes driven by changes in daylength. The proposed daylength effect on microbial mat fluxes was calculated based on the Earth rotation model by Bartlett and Stevenson 10 (solid line in a). daylength can account for a substantial portion of the pO 2 changes associated with the GOE and NOE, which lead up to the POE. The oxygenation scheme (grey area) is shown for comparison and is adapted from Alcott et al. 6 . Fluxes are derived from our modelled scenarios, which represent systems that include R aero and R anaero and either exclusive oxygenic or partitioned OP and AP (scenarios 'OP SRB' and 'OP SRB + AP'). Scenarios with metabolic delay mechanisms or a steep dependency on the burial of O 2 were excluded because these yielded oscillations of pO 2 between 0 and 1 even in the boring billion years. Shaded areas represent the range of daylength-driven pO 2 change based on a 1.5-3.7% coverage of the modern oceanic area by benthic coastal mats (which corresponds to 20-50% of the global marine C org burial during the mid-Proterozoic) and a coverage of 5% of the continental area by terrestrial mats. The corresponding global O 2 sinks were parameterized for a reference pO 2 of 0.1 and 0.01 in the mid-Proterozoic 60 . For terrestrial mats we assumed a direct interaction of 95% of their buried C org with pO 2 by erosional weathering, which represents a negative feedback effect of daylength-driven C org burial on pO 2 .

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 C org burial along with Earth's rotation rate, which decreased over Earth's history as inferred from geological proxies 33,34 and models 10,35 . A precise reconstruction of the rotation rate is currently beyond reach owing to uncertainties in the strengths of tidal friction, which includes effects from oceanic 33,36 , atmospheric 10,37 and solid Earth tides 35 . 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 evidence 36 . 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-Proterozoic 33 . Another long-standing hypothesis even predicts a period with a stable rotation rate in the Proterozoic due to a resonant atmospheric thermal tide 10,37 . The dissipation of oceanic and solid Earth tides cause rotational deceleration that is counteracted by atmospheric thermal tides, which depend on daylength 37 . This hypothesized period of stability and the subsequent marked increase in daylength coincide with the boring billion years of O 2 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 C org burial to global scales over Earth's history. Considerations of C org 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 pO 2 . To quantitatively implement Earth's rotational deceleration, we used a recent model 10 , 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 pO 2 , we considered that daylength-driven changes in global C org burial and solute export fluxes interacted with sinks of O 2 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 C org burial are highly uncertain 38-42 , 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 Precambrian 43 . As we expect long-term burial rates to be substantially lower than the diel C org burial 14 , we implemented a weathering-based negative feedback effect between pO 2 and terrestrial diel, and implicitly on long-term, C org burial (Extended Data Figs. 1 and 9). This analysis showed that daylength-driven changes in C org burial could account for the offset between pre-and post-GOE O 2 levels without having to assume any changes in atmospheric reductant fluxes or GPP (Fig. 4b). Mat scenarios with no net C org burial in the pre-GOE Archean (18 h daylength) support 50% of the global marine C org 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 pO 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 C org burial, caused by increasing GPP or decreasing remineralization efficiency [46][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 mats [49][50][51] . Yet, the daylength-driven enhancement of O 2 export and C org 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 pO 2 . Increased weathering would have further boosted the global primary production 7,52 -but probably only transiently as a pulse, followed by a return to the previous quasi-steady state pO 2 (refs 3,6 ) for a given daylength. Although nutrient supply and the corresponding GPP determine the absolute range of pO 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 pO 2 budget, such as plate tectonics (including supercontinent formation) 5,53-55 or new prospects for productivity in the oceans and on land 4,45,56 . 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 O 2 can cause relatively abrupt shifts in pO 2 , such as those due to H 2 escape, insolation, continental phosphorus supply, continental growth or volcanic reductant input 6,23,47,57,58 . 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 O 2 sinks, other than daylength-related increases in terrestrial C org weathering. Yet, the peculiarity of daylength-driven increases in benthic net productivity is that no such changes are required to produce substantial changes in pO 2 . Thus, the dynamics of the Earth-Moon system possibly had major impacts on global O 2 levels during critical turning points of Earth's biogeochemical evolution towards a profusely oxic world.

Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41561-021-00784-3.

Methods
Modelling microbenthic O 2 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 software 12 . 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. O 2 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. R aero 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 (O 2 and H 2 S) were composed from the reaction terms that accounted for sediment porosity and were solved with finite-volume numerical approximations 62 .
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 O 2 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 OP 63 . 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 O 2 production, which is with light availability. Two microbial processes were considered: OP performed by cyanobacteria and R aero . The parameters for the biotic reactions were re-expressed as a biomass-specific maximal yield (Q max ). A fundamental assumption is that the photosynthesis rate is strictly correlated to the instantaneous photon flux: where sat is a Michaelis-Menten function with K PAR = 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 O 2 is OP, and the sinks are aerobic (sedimentary) respiration (R aero ). For the production and consumption rates of C org , we assumed a stoichiometry of: with respect to O 2 cycling rates, where CH 2 O refers to one C org equivalent. Assuming that C org is predominantly particulate, with negligible diffusional transport, diel C org burial was thus calculated as: where ∫OP and ∫R aero are the diel depth-integrated rates of O 2 production and consumption and are equivalent to C org production and consumption according to equation (2). Thus, diel burial can also be represented through the export flux of O 2 at the top and bottom interfaces of the sedimentary domain: 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 O 2 productivity for unitless PAR intensities, we determined the Q max that caused a maximum O 2 export that corresponded to the median maximal flux from illuminated benthic photosynthetic systems 13 . A Q max 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 year 59 . 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 Feulner 23 , or changes in the solar spectrum related to atmospheric composition 64 .
Next, we explored the effect of R anaero 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 R anaero rate was either defined as a constant rate process for the scenario 'OP SRB constant' as: (5) or as an O 2 -and H 2 S-sensitive process as: where inhibition is a function of the local H 2 S and O 2 concentration (x) of the form: when x < K max and 0 when x ≥ K max. Inhibition factors chosen for both scenarios with O 2 -and H 2 S-sensitive SRB ('OP SRB' and 'OP SRB inhibited') were 3 mM for K max,H2S , 0.5 mM for K half,H2S and 1 µM for K half,O2 . K max,O2 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: where k = 351 l mol −1 h −1 (ref. 65 ). For R anaero we assumed the stoichiometry: and therefore calculated diel burial as: where ∫R anaero is the depth-integrated rate of sulfide production by SRB. The export flux of O 2 is shaped by mat-intrinsic rates of R aero , OP and SOX according to: where ∫SOX is the depth-integrated rate of O 2 consumption by SOX. Assuming the complete oxidation of H 2 S to sulfate, H 2 S export can be formulated as: According to equations (10)- (12), diel burial can thus be represented as: Corg buried = O2 export − 2 × H2S export (13) This illustrates that the control of diel burial is related to the export of O 2 and the reduced product of R anaero (such as H 2 S), as the former is an equivalent source and the latter an equivalent sink of C org within the mat. This means that an increase in O 2 export would not result in an increase of burial if H 2 S export increased proportionally in terms of C org equivalents.
To calibrate the productivity for SRB scenarios, we determined values of Q max 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 O 2 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 O 2 concentration in the water column (0-250 µM) for all three SRB scenarios. For the least O 2 -sensitive scenario ('OP SRB'), we also tested sensitivity of burial to gross productivity by varying the maximal photosynthetic yield Q max over the range 0.5-10 mmol g −1 h −1 . Note that the variation in Q max 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 OP [66][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 them 69 . 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 AP 20 . In this 'OP SRB + AP' scenario, the modelled cyanobacteria produced O 2 according to: where normsat is a normalized Michaelis-Menten function with a value of 1 for H 2 S ≥ H 2 S thr , where H 2 S thr is the threshold sulfide level. Conversely, The metabolic behavior is such that OP occurs only below H 2 S thr , 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 R anaero , R aero , SOX and other processes work as in previous scenarios. The interplay of illumination, mat processes and the resultant depth-resolved dynamics of O 2 and H 2 S under this scenario can be seen in the Supplementary Video 1. Assuming sulfate as the product of AP according to: diel burial in this scenario was calculated as where ∫AP is the depth-integrated rate of CO 2 fixation by AP. As in the other scenarios, diel burial can alternatively be calculated according to equation (13). Values of Q max for OP and R anaero were adjusted to produce the same maximum O 2 export flux at 24 h (O 2 boundary at 250 µM) and diel C org flux at 21 h (25 µM O 2 boundary) as in 'OP SRB' . This allowed us to establish directly comparable upscaling calculations for global pO2 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 O 2 and H 2 S as electron donors from the water column on the scenario with AP. Water column O 2 levels from 0 to 250 µM and H 2 S 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 level 27 .
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 O 2 and sulfide concentrations were adjusted in this separate reservoir of bottom water using N 2 , air and neutralized Na 2 S 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 Cline 70 . 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). O 2 , pH and H 2 S microsensors with a tip diameter of 10-50 µm and a response time of <1 s were built, calibrated and employed as previously described [71][72][73] . The microsensor tips were always separated by <500 µm during simultaneous O 2 , pH and H 2 S measurements.
The volumetric rates of gross OP were estimated based on the dynamics of O 2 concentration after a light-dark shift, as described previously 74 . Analogously, the volumetric rates of gross AP were calculated from the increase of H 2 S concentration and pH directly after a light-dark transition (that is, light-driven S tot consumption rates), as previously described 26,27,75 . Net rates and fluxes were calculated from profiles based on Fick's laws using diffusion coefficients for O 2 and sulfide corrected for temperature and salinity.
From diel export to global oxygenation. We considered that changes in diel O 2 and H 2 S export rates, the difference of which is equivalent to diel benthic C org 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 weathering 60 . Although we assumed a constant flux of reductant (vR) available for atmospheric reduction, weathering is dependent on pO2 and thus strongly tempers the accumulation of O 2 in the atmosphere. As a recent computational Earth rotation model 10 predicts a stabilized daylength in the mid-Proterozoic, we started our global calculations by assuming a pO2 of 0.01-0.1 at the predicted stable 21 h. This pO2 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, COPSE 60,76 ) of the global O 2 budget. Considering an evolution of steady states of pO2 throughout Earth's history, we described the pO2 evolution at a given age as: which provides the steady state pO2 as: 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 C org reservoir and a weathering constant 60 . Changes in any of the global fluxes would therefore result in new steady state pO2. For the total marine burial (pelagic pB and coastal benthic mB -tB) we assumed modern values throughout the Precambrian 60 . Beyond the marine realm, we considered the possible existence of terrestrial mats 43 , which would have further boosted global GPP and C org 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 R anaero , 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 pO2 levels assuming the values for uB from Daines et al. 60 .
The Earth rotation rate model 10 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 daylength 10 . Starting at 21 h at 2 Gyr, we estimated the effect of the daylength-driven change in the C org burial from benthic and terrestrial mats, the output of our diel mat model, on pO2 levels both backwards and forwards in time. The modulation of pO2 naturally depends on the steepness of the dependence of mat C org 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 pO2 beyond PAL even due to the minimal variations in daylength within the resonant-locked phase in the mid-Proterozoic 10 and therefore had to be excluded from analysis of pO2 evolution. We additionally included negative feedback effects of increasing pO2 on the mat C org burial by dynamically adjusting the O 2 boundary conditions in each time step according to the pO2 calculated from the previous step. To then calculate the quasisteady-state pO2 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 forms [39][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 lifestyle 21,66,77 . Alternatively, burial of the C org produced by pelagic cyanobacteria might have been hindered by the small cell sizes, low sinking rates and resultant efficient remineralization within the water column 42,78 . The preservation of C org 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 pO2. This implicitly describes a substantial loss in translation of the diel C org 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 C org 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 C org 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 C org , as we expected a negligible effect of molecular diffusion and thus daylength on these fluxes.

Data availability
The datasets generated and analysed are available at https://doi.org/10.17617/3.66, and in the supplementary files with this paper. Source data are provided with this paper. The daylength-driven changes in C org burial from benthic or terrestrial mats (mB; flux arrows not to scale) cause quasi steady-state transitions of global atmospheric pO 2 . Offsets in pO 2 between such steady states are conceptualized here as aO. The diel mat processes (inset box) produce C org burial fluxes (mB), which along with burial from the pelagic domain (pB) comprise the global O 2 source. Both O 2 (mO) and reductant (mR) export from mats are controlled by the interaction between mass transfer and mat-intrinsic process rates (oxygenic photosynthesis, OP; anoxygenic photosynthesis, AP; aerobic respiration, R aero ; sulfate reduction, R anaero ; aerobic H 2 S oxidation, SOX), and hence are sensitive to daylength changes. For the global O 2 sinks, we considered that some of the surplus O 2 released from the terrestrial or marine realm was consumed directly in the atmosphere (atmR) by volcanism-and metamorphism-derived gases (vR) 60 . Surplus reductant released from mats (mR in (a)) will increase atmR. Surplus reductant consumed by mats (mR in (b)) will decrease atmR, and add to source strength mB. Thus, mat C org burial mB is the sum of O 2 export mO and reductant import mR, and also sensitive to daylength. Note that volcanic reductant fluxes (vR) are equal to pelagic C org burial (pB) and the equivalent pelagic O 2 export (pO) to illustrate that reductant uptake by mats influence the global availability of reductant. This influences the consumed fraction of pO by atmR. As a result, mB is equal to wO, that is the O 2 that escapes reduction by atmR. The sink for wO is erosional weathering (WEATH), and the emergent pO 2 for a reference weathering level is (wO/ (0.95 × tB + uB)) 2 76,80 . uB, which implicitly describes the size of the global C org reservoir, uplift forcing and a weathering constant, was chosen based on a mid-Proterozoic pO 2 of 0.01 or 0.1 and was set constant over Earth age. To account for the direct erosion of terrestrial mats, WEATH was set to interact with 95% of terrestrial C org burial rates (tB; a fraction of total mat burial mB). While this makes WEATH also sensitive to daylength and produces a buffering effect through increased weathering strength, atmospheric oxygenation aO still increases with daylength (Fig. 4).   Extended Data Fig. 4 | rates of cyanobacterial OP and AP depend on sulfide concentration and irradiance. (Irradiance as percent of zenith value) For conversion of CO 2 fixation rates into rates of photosynthetic O 2 production and sulfide consumption, we assumed that OP follows 2 H 2 O + CO 2 → O 2 + C org and AP follows H 2 S + 2 CO 2 → SO 4 2− + 2 C org , respectively. Partitioning between OP (green lines) and AP (blue lines) in these cyanobacteria is regulated through light-dependent sulfide threshold levels 20 . Below the threshold level, OP and AP occur in concert such that their combined rate (OP + AP) is conserved. Above the threshold level, only AP occurs representing a higher affinity for AP. This type of partitioning represents a metabolic competition between OP and AP within the cyanobacteria. Notably, based on local light levels, AP would have to occur at a sufficiently high rate to deplete the local sulfide concentration below the threshold for OP to occur and produce O 2 . Instead, simultaneous depth profiling with an H 2 S microsensor showed that migration only occurred if sulfide in the SOB layer was entirely depleted, such as after a sufficient duration of AP activity. Incident irradiance levels of 59 and 82 µmol photons m −2 s −1 were sufficiently high to allow for entire depletion of sulfide (solid and dashed lines in a) by AP in the cyanobacterial layer and to thereby limit sulfide supply to the SOB layer at the mat surface. The migration lag (~2.5 hours) after depletion of sulfide is indicated by the gray shaded area. Note that the duration of the lag is independent of light intensity. Light intensity of 51 µmol photons m −2 s −1 was insufficient for sulfide depletion (dotted lines) and consequently migration did not occurr. Thus, even though light had no direct effect on migration behavior, sufficient light intensity to sustain high rates of AP was necessary to deplete sulfide in order to trigger migration. b, The duration of the lag phase was monitored using an O 2 and H 2 S microsensor under diverse water column conditions in two distinct mat samples. Irradiance during measurements was 73 and 103 µmol photons m −2 s −1 in mat 1 and mat 2, respectively. Data result from continuous profiling and involve an uncertainty of ~15-20 min due to the acquisition time of the profiles. Error bars and values in parenthesis in the legend represent the standard deviation of O 2 and H 2 S concentration, respectively, averaged over three depths and 5-32 timepoints during the time series experiment (n=15-96 dependent on delay duration). Considering that increased sulfide supply from the water column extended the migration lag, migration might be induced via electron donor starvation of the SOB. Extended Data Fig. 8 | simulations of benthic systems with activity delay mechanisms. a-b, For sulfide-inhibited OP as observed in cyanobacteria isolated from Little Salt Spring, that only activate OP with a fixed delay of 30 min after local depletion of sulfide by AP 27 , the temporal evolution over a 12 h and 24 h diel period illustrates that this no-photosynthesis-phase between sulfide being depleted below 1 µM and OP being activated completely suppresses OP in days shorter than 20 h (panel e). The penalty on O 2 export is high enough that cyanobacterial mats, despite the potential for OP, remain net sinks of O 2 during illuminated periods. c, The delay introduces a steep dependency of diel export fluxes and burial on daylength. Note that negative burial fluxes arise because model parameters were tuned such that burial at 21 h is comparable to the scenario without AP (OP SRB in Extended data figure 2) and the AP scenario without delay (Extended data figure 5). d-k, The penalty of the lag on induction of OP is only overcome during longer days and in the presence of O 2 in the water column ([O 2 ] top ). Mats can only net accumulate C org , if OP is active. As the fraction of day during which OP can occur is strongly dependent on daylength, this scenario exhibits the steepest dependency of burial on daylength compared to all other scenarios. Fig. 9 | Weathering and C org burial rates over time and corresponding examples for proxies in the geological record. Values for the total organic carbon (TOC) content in organic-rich sediments, the normalized seawater 87 Sr/ 86 Sr, and the average δ 34 S of sulfate were adapted from Och et al 2 , with permission from Elsevier. Increases in the latter two parameters indicate enhanced weathering fluxes. All rates were derived from our modeled scenario that include aerobic and anaerobic respiration and exclusive oxygenic photosynthesis. Shaded areas represent the range of rates dependent on 1.5-3.7% modern oceanic coverage by benthic coastal mats (corresponding to 20-50% of global marine C org burial during the mid-Proterozoic) and a continental coverage of 5% by terrestrial mats. Changes in global coastal benthic and terrestrial C org burial fluxes are driven by changes in daylength and are shaped by feedback effects of increasing pO 2 (Fig. 4) on aerobic respiration. Pelagic burial, atmospheric reduction by volcanism-and metamorphism-derived gases and weathering were parameterized for a reference pO 2 of 0.1 in the mid-Proterozoic 60 . The rate of atmospheric reduction was assumed to be constant and determined by the flux of reduced gases. In contrast, the rate of erosional weathering increases with daylength as it depends on pO 2 and C org burial by terrestrial mats.