Jihua Hao
email: haojihua@gmail.com

Fang Huang Andrew H Knoll

Juergen Schieber

Robert M Hazen

Isabelle Daniel

Fang Huang

Cycling phosphorus on the Archean Earth: Part II. Phosphorus limitation on primary production in Archean ecosystems

Keywords: vivianite, phosphorus recycling, burial diagenesis, apatite nodules, primary production, oxygenation of atmosphere. (6/6 keywords)

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

How productive were Archean oceans? All recent estimates of Archean primary production are low [START_REF] Bjerrum | Ocean productivity before about 1.9 Gyr ago limited by phosphorus adsorption onto iron oxides[END_REF][START_REF] Canfield | Early anaerobic metabolisms[END_REF][START_REF] Kharecha | A coupled atmosphere-ecosystem model of the early Archean earth[END_REF][START_REF] Laakso | Limitations on Limitation[END_REF][START_REF] Ward | Primary Productivity Was Limited by Electron Donors Prior to the Advent of Oxygenic Photosynthesis[END_REF], but there is no consensus just how low they were, nor on the principal factors that limited photosynthesis in early ecosystems. Some commentators posit that prior to the evolution of oxygenic (cyanobacterial) photosynthesis, the global availability of electron donors would have constrained rates of primary production to low levels. For example, [START_REF] Canfield | Early anaerobic metabolisms[END_REF] estimated the abundances of non-water electron donors in Archean oceans, concluding that the most abundant species, Fe 2+ , would have supported primary production at levels up to 10% of the modern. In contrast, [START_REF] Ward | Primary Productivity Was Limited by Electron Donors Prior to the Advent of Oxygenic Photosynthesis[END_REF] argued that H2 and, to a lesser extent, Fe 2+ together fueled early photoautotrophy at rates well below one percent of modern levels. And recently, [START_REF] Tosca | Products of the iron cycle on the early Earth[END_REF] concluded that photoautotrophy of ferrous iron could have made only a negligible contribution to productivity in early oceans. In contrast, some analyses point to nutrient limitation in early oceans, specifically suggesting that relatively low phosphate availability could have limited primary production, even at low ferrous iron availability [START_REF] Kipp | Biomass recycling and Earth's early phosphorus cycle[END_REF]; others propose that P was relatively bioavailable, especially as phosphite [START_REF] Herschy | Archean phosphorus liberation induced by iron redox geochemistry[END_REF].

Of particular interest is the role that oxygenic photoautotrophs may have played prior to the Great Oxygenation Event (GOE) ca. 2.4 billion years ago. It has been proposed that the GOE simply reflects the evolution of oxygenic photosynthesis (e.g., [START_REF] Fischer | Evolution of Oxygenic Photosynthesis[END_REF][START_REF] Kopp | The Paleoproterozoic snowball Earth: A climate disaster triggered by the evolution of oxygenic photosynthesis[END_REF], but this view is challenged by both an increasing inventory of geochemical evidence for earlier "whiffs of oxygen" [START_REF] Anbar | A whiff of oxygen before the great oxidation event?[END_REF][START_REF] Kaufman | Late archean biospheric oxygenation and atmospheric evolution[END_REF] and molecular clocks that call for the evolution of coupled photosystems capable of extracting electrons from water as early as 3.2 Ga [START_REF] Cardona | Early Archean origin of Photosystem II[END_REF]. Of course, if P availability strictly limited rates of primary production on the Archean Earth, oxygen production may well have been too low to titrate available reductants, even if oxygenic photosynthesis was relatively prominent.

To explore these issues further, we employ kinetic and thermodynamic modeling to estimate P availability in the global scale of seawater through a billion years of recorded Archean history.

Methods

The bioavailability of P in the sunlit ocean primarily reflects two fluxes: continental weathering and P recycling within the ocean. Considering that Archean seawater was weakly acidic [START_REF] Halevy | The geologic history of seawater pH[END_REF][START_REF] Krissansen-Totton | Constraining the climate and ocean pH of the early Earth with a geological carbon cycle model[END_REF] and reducing, seafloor weathering might also have been a significant source of P on the early Earth. In Part I of this series [START_REF] Hao | Cycling Phosphorus on the Archean Earth: Part I. Continental weathering and riverine transport of phosphorus[END_REF], we simulated the input of P to the Archean oceans from continental weathering and erosion, concluding that P fluxes from land were extremely low as the Archean Eon began but increased to values similar to the modern by the time the eon ended.

In this study, we calculate the solubility limits of primary and secondary P-minerals in Archean seawater and porewater environments, simulating seafloor weathering and the precipitation of phosphate minerals in and beneath the Archean ocean. We focus in particular on the precipitation of vivianite, as this precipitation has been argued to be a major sink for phosphate in ferruginous Proterozoic oceans [START_REF] Derry | Causes and consequences of mid-Proterozoic anoxia[END_REF]. With these calculations in hand, we assess P recycling in Archean oceans and estimate the total flux of P for net primary production (NPP). Lastly, we consider the fate of P-precipitates during diagenesis and metamorphism, based on both simulations and geological observation.

Our calculations focus on the global-scale evolution of Archean environments. We understand that the Archean Earth was environmentally heterogeneous, with probable local variations in temperature, Fe(II) concentration between seawater and hydrothermal fluids, redox variation between globally anoxic and locally oxygenated habitats in the late Archean, and variations in the concentration of Fe(II) and S(II) between globally ferruginous seawater and regionally sulfidic seafloor in late Archean oceans. Such heterogeneities are important in considerations of Archean evolution and may influence Archean P cycling, as discussed below. Nonetheless, we argue that our focus on global conditions is most relevant for understanding the P cycle and how it changed through Archean time.

Archean seawater and porewater chemistry

The emergence of land masses in the middle to late Archean Eon [START_REF] Hawkesworth | Earth's Continental Lithosphere Through Time[END_REF], with its consequences for weathering and erosional fluxes, strongly affected marine geochemistry [START_REF] Bindeman | Rapid emergence of subaerial landmasses and onset of a modern hydrologic cycle 2.5 billion years ago[END_REF]. The evolution of seawater pH and major salts (Ca and Mg) has recently been modeled independently by [START_REF] Halevy | The geologic history of seawater pH[END_REF] and [START_REF] Krissansen-Totton | Constraining the climate and ocean pH of the early Earth with a geological carbon cycle model[END_REF], with similar results. In Part I of this series [START_REF] Hao | Cycling Phosphorus on the Archean Earth: Part I. Continental weathering and riverine transport of phosphorus[END_REF], we modified Krissansen-Totton et al.'s (2018) geologic carbon cycle (GCC) model by incorporating continental emergence [START_REF] Flament | The evolution of the87Sr/86Sr of marine carbonates does not constrain continental growth[END_REF][START_REF] Korenaga | Global water cycle and the coevolution of the Earth's interior and surface environment[END_REF] and the weathering kinetics of P, using this modification to simulate the continental flux of P into the oceans (Table 1). The GCC model also outputs major component compositions of the atmosphere (including pCO2,g) and seawater (including pH, Ca 2+ , and CO3 2-), and by linking these factors to continental emergence models and solubilities of P-bearing minerals (Table S2) we can examine seafloor weathering and the precipitation of P in the Archean oceans (Sec. 2.2). In addition, the GCC model allows us to consider the chemistry of porewater, enabling us to explore the post-depositional fate of seafloor P-precipitates (Sec. 2.5).

In addition to the above-mentioned species, our simulations require that we input abundance values for other components of seawater and porewaters. A large, recently compiled dataset of fluid inclusions in Archean quartz from different localities supports the view that the concentration of NaCl in Archean seawater was similar to that of the modern [START_REF] Marty | Salinity of the Archaean oceans from analysis of fluid inclusions in quartz[END_REF]. Accordingly, we assumed that the Cl -concentration of Archean seawater was the same as today's. F -concentration is set to be limited by the solubility of fluorite in Archean seawater and porewater, as it is for modern seawater.

It has been proposed that Fe 2+ in Archean seawater was limited by the solubility of amorphous greenalite, experimentally shown to precipitate readily in equilibrium with Fe(II) and silica in anoxic water [START_REF] Tosca | An authigenic origin for Precambrian greenalite: Implications for iron formation and the chemistry of ancient seawater[END_REF][START_REF] Tosca | Products of the iron cycle on the early Earth[END_REF]. Consistent with these factors, greenalite occurs abundantly in marine sediments, especially in Archean sedimentary successions [START_REF] Isson | Reverse weathering as a long-term stabilizer of marine pH and planetary climate[END_REF][START_REF] Johnson | Low-Fe(III) Greenalite Was a Primary Mineral From Neoarchean Oceans[END_REF]. In comparison to greenalite, siderite precipitation is kinetically sluggish under Archean conditions, occurring only when pCO2,g reaches extreme levels, e.g. > 1 bar [START_REF] Jiang | Fe(II)-carbonate precipitation kinetics and the chemistry of anoxic ferruginous seawater[END_REF]. In the absence of a skeletal silica sink, dissolved silica concentration would presumably have been relatively high, limited by the solubility of amorphous silica [START_REF] Siever | The silica cycle in the Precambrian[END_REF][START_REF] Tréguer | The World Ocean Silica Cycle[END_REF]. Previous workers have also pointed to green rust as a potentially major precipitate from early seawater [START_REF] Halevy | The geologic history of seawater pH[END_REF][START_REF] Tosca | Products of the iron cycle on the early Earth[END_REF], but its precipitation requires either a flux of O2,g or water pH > 8.0 under anoxic conditions, unlike the anoxic and weakly acidic seawater likely during most of the Archean Eon. Moreover, the precipitation of green rust is sensitive to salinity, and the potential effects of elevated Archean SiO2,aq on green rust precipitation remain unknown [START_REF] Tosca | Products of the iron cycle on the early Earth[END_REF]. Given these considerations, we calculated the Fe 2+ concentration in Archean seawater based on the equilibrium constant for amorphous greenalite dissolution derived from recent experiments [START_REF] Tosca | An authigenic origin for Precambrian greenalite: Implications for iron formation and the chemistry of ancient seawater[END_REF] and the assumption that SiO2,aq concentration was equal to the solubility of amorphous silica. Note, however, that siderite could and did form readily by biological reduction of Fe(III) or diagenesis/metamorphism of organic-C in the sediments [START_REF] Vuillemin | Formation of diagenetic siderite in modern ferruginous sediments[END_REF], and so would potentially have been an important mineral product in porewaters beneath Archean oceans (Sec. 4.3).

Thermodynamic models of P-minerals solubilities

We calculated the solubility limits of common primary and secondary phosphate minerals based on equilibrium constants between each mineral and its dominant aqueous species at a given pH in water, e.g. HPO4 2-(pH > 7.2) and H2PO4 -(pH < 7.2) as the dominant phosphate species in this study (Table S1 &S2). Calculations were conducted assuming a warm climate (seawater temperature 25°C), supported by recent climate reconstructions [START_REF] Krissansen-Totton | Constraining the climate and ocean pH of the early Earth with a geological carbon cycle model[END_REF]. Small fluctuation of temperature would be expected to result in only limited changes for reaction constants (e.g. [START_REF] Al-Borno | The temperature dependence of the solubility product constant of vivianite[END_REF]. However, large elevation of temperature would significantly affect reaction constants; therefore, for the calculations in diagenetic and metamorphic environments, we varied temperature to investigate the effect of this variable (see below). Equilibrium constants of the dissolution reactions were calculated by SUPCRT92b [START_REF] Johnson | SUPCRT92: A software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous species, and reactions from 1 to 5000 bar and 0 to 1000[END_REF] (Table S2).

In the modern ocean, the sinking of P is, in general, composed of (co-)precipitation of authigenic minerals (Table S1), burial as organic-P, or adsorption onto metal-hydroxides and carbonate [START_REF] Baturin | Phosphorus cycle in the ocean[END_REF][START_REF] Ruttenberg | The Global Phosphorus Cycle[END_REF]. In iron-rich, low-salinity estuaries along the Baltic Sea, vivianite (Fe3(PO4)2*8H2O) precipitation accounts for as much as 40% of P removal from ambient waters [START_REF] Lenstra | Large variations in iron input to an oligotrophic Baltic Sea estuary: impact on sedimentary phosphorus burial[END_REF], and [START_REF] Derry | Causes and consequences of mid-Proterozoic anoxia[END_REF] has proposed that this mineral formed an important sink for P in the ferruginous, low-sulfate seawater of mid-Proterozoic oceans. Derry's hypothesis may apply, as well, to the Archean, but this possibility needs to be tested for the distinct and evolving conditions of Archean seawater (pH, Fe, S, and silica). The solubility constant of vivianite is adopted from a previous experimental study [START_REF] Al-Borno | The temperature dependence of the solubility product constant of vivianite[END_REF].

Fe3(PO4)2•8H2O,s 3Fe 2+ + 2PO4 3-+ 8H2O

(1) At pH < 7, PO4

We can obtain the equilibrium constant of the following reaction by combining the reaction constants of reactions (1-3):

Fe3(PO4)2•8H2O,s + 2SiO2,am Fe3Si2O5(OH)4,am + 2H2PO4 -+ 2H + + 3H2O (4)
In similar fashion, we compiled the reported equilibrium constants of the dissolution reactions of other common secondary P-minerals and calculated their solubility limits in the Archean seawater and porewater (Table S2).

Crystallization and precipitation kinetics of vivianite

We employed the crystal growth kinetics of vivianite reported previously [START_REF] Madsen | Kinetics of crystal growth of vivianite, Fe3(PO4)2•8H2O, from solution at 25, 35 and 45[END_REF][START_REF] Madsen | Influence of calcium and aluminum on crystallization of vivianite, Fe3(PO4)2•8H2O[END_REF]. Vivianite crystals have shown to follow spiral growth mechanism at low supersaturation states [START_REF] Madsen | Kinetics of crystal growth of vivianite, Fe3(PO4)2•8H2O, from solution at 25, 35 and 45[END_REF] with the rate expression:

Rs = b(cFe -cFe,eq)lnΩ (5) b (nm/s/M) is

Diagenetic and metamorphic transformation of vivianite: modeling

In this study, we simulated the stability and solubility of various phosphate minerals and other diagenetic minerals in porewater environments (Fig. S1-2; 25 °C), thereby mimicking the early diagenesis of P in the Archean marine sediment.

In addition, we simulated the reaction of vivianite + calcite (+ fluorite as a source of F -) to form apatite + siderite (+ release of water) at elevated temperatures, mimicking the fate of vivianite during burial diagenesis and metamorphism. The equilibrium constants of the reaction were calculated by SUPCRT92b, with thermodynamic properties of vivianite from [START_REF] Al-Borno | The temperature dependence of the solubility product constant of vivianite[END_REF].

Results

Limitations on seafloor weathering of apatite

In continental rocks, apatite is the primary P-hosting mineral for chemical weathering, and detrital P, mainly as apatite, is the predominant component of continental P input to the ocean system (Compton et al., 2000;[START_REF] Ruttenberg | The Global Phosphorus Cycle[END_REF]. In oceanic crust, apatite is unlikely to be a major host mineral for P due to high saturation concentrations; rather P is expected to exist either as trace impurities in silicate minerals -including olivine, clinopyroxene, and plagioclase -or in basaltic glass [START_REF] Brunet | Partitioning of phosphorus between olivine, clinopyroxene and silicate glass in an spinel lherzolite xenolith from Yemen[END_REF]. However, trace amounts of apatite are common in basalts and gabbros (e.g., [START_REF] Anderson | Phosphorus fractionation diagram as a quantitative indicator of crystallization differentiation of basaltic liquids[END_REF][START_REF] Coogan | Whole-rock geochemistry of gabbros from the Southwest Indian Ridge: Constraints on geochemical fractionations between the upper and lower oceanic crust and magma chamber processes at (very) slow-spreading ridges[END_REF][START_REF] Meurer | Apatite compositions from oceanic cumulates with implications for the evolution of mid-ocean ridge magmatic systems[END_REF], and apatite may precipitate locally due to the P gradient near a growing crystal [START_REF] Green | Crystallization of apatite in natural magmas under high pressure, hydrous conditions, with particular reference to "Orogenic" rock series[END_REF].

If the concentration of dissolved P in the weathering fluid reaches the solubility limit of apatite, apatite as the reactant will have no reaction affinity to dissolve further [START_REF] Brantley | Reaction Kinetics of Primary Rock-Forming Minerals under Ambient Conditions[END_REF]. Salinity and pH are the two most important environmental determinants of apatite solubility. Seawater pH is primarily buffered by the riverine transport of alkalinity, seafloor weathering of silicates, and hydrothermal fluids. Although the Archean atmosphere had high pCO2,g, simulated pH of Archean seawater ranges from 6.5 to 7.0 [START_REF] Halevy | The geologic history of seawater pH[END_REF][START_REF] Krissansen-Totton | Constraining the climate and ocean pH of the early Earth with a geological carbon cycle model[END_REF], unlike the more acidic rainwater that drove continental weathering [START_REF] Hao | Mobility of nutrients and trace metals during weathering in the late Archean[END_REF]. Ca 2+ level is another important factor in determining the solubility of P. It has been proposed that Archean seawater was more enriched in Ca 2+ than the modern oceans because of enhanced hydrothermal alteration of the seafloor [START_REF] Halevy | The geologic history of seawater pH[END_REF][START_REF] Jones | Iron oxides, divalent cations, silica, and the early earth phosphorus crisis[END_REF][START_REF] Krissansen-Totton | Constraining the climate and ocean pH of the early Earth with a geological carbon cycle model[END_REF].

Based on these considerations, and applying our additional assumptions for Archean seawater composition (Methods), we calculated the solubility limits for three common types of apatite: Cl-apatite, F-apatite, and OH-apatite. Fig. 1 shows that all three minerals had limited solubility (< 0.1 µM; predominantly as H2PO4 -at pH < 7) in Archean seawater;

results are consistent whether one assumes rapid or slow continental emergence on the late Archean Earth. The low solubility of apatite minerals in Archean seawater contrasts markedly with their high solubilities in contemporaneous continental weathering fluids [START_REF] Hao | Mobility of nutrients and trace metals during weathering in the late Archean[END_REF], a difference primarily ascribed to the higher pH and higher concentrations of Ca 2+ and halogens in Archean seawater, relative to rain or river water [START_REF] Hao | Cycling Phosphorus on the Archean Earth: Part I. Continental weathering and riverine transport of phosphorus[END_REF]. In addition, the log dissolution rate of apatite minerals decreases linearly with increasing pH in acidic water [START_REF] Brantley | Reaction Kinetics of Primary Rock-Forming Minerals under Ambient Conditions[END_REF][START_REF] Guidry | Experimental study of igneous and sedimentary apatite dissolution[END_REF]. Thus, in Archean oceans, the weathering of apatite was both thermodynamically and kinetically less favorable than continental weathering. Indeed, the direct implication of Fig. 1 is that seafloor weathering of apatite minerals could have contributed little if any P to early marine life. Consistent with these simulation results, we observed detrital apatite as the major P-phase in Archean black shales, with tiny overgrowths of secondary apatite (Bothaville Formation, South Africa; ca.

2700 Ma) (Fig. 7a &b). Bothaville sediments reflect rapid uplift and erosion of a crustal bloc to the west [START_REF] Schneiderhan | Sedimentary provenance of the neoarchean ventersdorp supergroup, Southern Africa: Shedding light on the evolution of the kaapvaal craton during the neoarchean[END_REF], resulting in large input of P with a major proportion being detrital apatite minerals [START_REF] Hao | Cycling Phosphorus on the Archean Earth: Part I. Continental weathering and riverine transport of phosphorus[END_REF]. In addition, as discussed in Sec. 4.1, we think that seafloor weathering of basalt would contribute little P to early oceans.

Solubility and precipitation of secondary phosphates in the Archean seawater

On the modern Earth, seafloor weathering serves as a net sink for P that balances continental input [START_REF] Compton | Variations in the Global Phosphorus Cycle[END_REF], with P removal occurring mainly as organic-P, various authigenic/biogenic phosphate minerals (CFA, HAP, and other phosphates), and surface adsorption onto or co-precipitation with Fe(III)-(hydr)oxide and carbonate [START_REF] Ruttenberg | The Global Phosphorus Cycle[END_REF]. In anoxic Archean seawater, Fe(II) oxidation could and did occur via photo-and/or bio-oxidation of Fe(II), or the cooling of hydrothermal fluids, as documented by ferric iron in Archean banded iron formations. Several investigators analyzed the P content in BIFs in order to reconstruct paleo-concentrations of P, assuming that adsorption onto Fe-(hydr)oxide was the major sink for P [START_REF] Jones | Iron oxides, divalent cations, silica, and the early earth phosphorus crisis[END_REF][START_REF] Konhauser | Was there really an Archean phosphate crisis?[END_REF][START_REF] Planavsky | The evolution of the marine phosphate reservoir[END_REF].

In addition to surface adsorption, however, our simulations suggest that vivianite would have a much lower solubility in Archean seawater than other secondary P-minerals (e.g. octacalcium phosphate, or OCP) (Table S1 and Fig. 2). Assuming a moderate supersaturation state of vivianite, Ω = 100 or 1000, our calculations indicate that phosphate solubility in Archean oceans would have been similar to that estimated by [START_REF] Jones | Iron oxides, divalent cations, silica, and the early earth phosphorus crisis[END_REF], 0.1 to 0.3 µM dissolved phosphate depending on Ω and age (Fig. 2). This estimate depends heavily on the feasibility of vivianite precipitation, experimentally shown to be sluggish at low supersaturation but potentially facilitated by microbial reduction and mineral adsorption in natural systems (Sec. 4.2). Regardless, in the low-P Archean seawater, octacalcium phosphate (OCP) as the precursor phase of marine apatite [START_REF] Van Cappellen | The formation of marine apatite: A kinetic study[END_REF] has no thermodynamic affinity to precipitate. Undersaturation of OCP in the Archean seawater further indicates that, precipitation of apatite minerals, although thermodynamically favorable given their extremely low solubilities (Fig. 1), was not kinetically feasible [START_REF] Gunnars | Inorganic formation of apatite in brackish seawater from the Baltic Sea: An experimental approach[END_REF].

Using the reported crystallization kinetics of vivianite [START_REF] Madsen | Kinetics of crystal growth of vivianite, Fe3(PO4)2•8H2O, from solution at 25, 35 and 45[END_REF][START_REF] Madsen | Influence of calcium and aluminum on crystallization of vivianite, Fe3(PO4)2•8H2O[END_REF] and assuming the presence of mineral seed, we estimated 46-695 µm crystal growth for 1 year at supersaturation states of 100-1000 in the Archean seawater (Fig. 3a; assuming 0.1 to 1 mM Fe 2+ ), this falling into the size range of vivianite nodules found in natural sediments at low supersaturation states [START_REF] Rothe | The occurrence, identification and environmental relevance of vivianite in waterlogged soils and aquatic sediments[END_REF]. Following the method proposed by [START_REF] Derry | Causes and consequences of mid-Proterozoic anoxia[END_REF], we calculated the precipitation rate of vivianite from water column to sediment, showing that the depositional flux of P as vivianite in the Archean oceans could easily have reached levels comparable to the modern sinking flux for P at Ω > 10 (i.e., solubility of P = 0.03 µM) (Fig. 3b). Derry's model assumes ready vivianite precipitation even at low supersaturation states, but the actual precipitation flux should depend heavily on precipitation kinetics of vivianite, which is known to be affected by a number of factors (Sec. 4.2).

Post-depositional transformation of vivianite

As discussed above, vivianite precipitation could be an important P sink in Archean oceans. The fate of vivianite during diagenesis and metamorphism, however, requires consideration.

Assuming that siderite and greenalite precipitation could reach in equilibrium, our simulations show that in the porewater environment siderite solubility is 2 to 4 orders of magnitude lower than greenalite (Fig. 4a &S3a). Therefore, if siderite precipitation becomes kinetically feasible during burial diagenesis (Sec. 4.3), it should limit the solubility of Fe(II) to low values, as argued for Archean porewaters [START_REF] Tosca | Products of the iron cycle on the early Earth[END_REF]. Under these conditions, vivianite becomes much more soluble than other secondary phosphate minerals, e.g. octacalcium phosphate (OCP) and carbonate fluorapatite (francolite) (Fig. 4b &S3b). OCP is thought to be the precursor phase of marine apatite minerals [START_REF] Eanes | The maturation of crystalline calcium phosphates in aqueous suspensions at physiologic pH[END_REF][START_REF] Van Cappellen | The formation of marine apatite: A kinetic study[END_REF]. In the modern marine sediments, precipitation of P as apatite minerals is thought to one major P sink in the long run [START_REF] Ruttenberg | The Global Phosphorus Cycle[END_REF][START_REF] Van Cappellen | The formation of marine apatite: A kinetic study[END_REF]. Our simulations show that in the Archean porewaters, the solubilities of apatite minerals are expected to be extremely low (at least 1-3 orders of magnitude lower than OCP and 5-9 orders of magnitude lower than vivianite; Fig. 4c), implying strong thermodynamic affinity for the transformation from vivianite to OCP and apatite minerals (Sec 4.3).

In addition, we calculated the reaction constant for the transformation of vivianite + calcite (+ fluorite; with a fluorine level similar to the seawater) to F-apatite + siderite (with release of water) at elevated temperatures, mimicking the burial diagenesis and low-grade metamorphism of vivianite. The result suggests that log (reaction constant) is >> 1, and its value increases with temperature (Fig. 5), suggesting that the transformation becomes thermodynamically more and more favorable. Therefore, it can be reasonably expected that at the elevated temperatures of burial diagenesis and metamorphism (> 100 °C, where the precipitation kinetics of apatite and siderite are feasible), vivianite would inevitably transform to apatite.

Total phosphorus for Archean primary production

Fig. 6 shows the proportional contribution of continental weathering to the total P requirement for NPP as a function of recycling efficiency. In line with the hypothesis by [START_REF] Laakso | Limitations on Limitation[END_REF], the figure indicates that on the Archean Earth, continental weathering would provide the major source of P for life in photic zone, unlike today. Based on our estimate of continental P flux (Table 1) and a recycling efficiency of 0.78 (Sec. 4.4),

we calculate the recycling flux of organic P by the end of the Archean Eon to have been 14-120 × 10 10 moles P/yr (Table 1). Note that the flux of recycling P, which represents an optimistic estimate in this study, depends heavily on the recycling efficiency (and thus burial efficiency) of organic matter in the Archean Eon, which is poorly constrained [START_REF] Kipp | Causes and consequences of high burial efficiency in the Archean ocean[END_REF] for marine primary productivity by the end of Archean Eon, 0.5-4% of modern values (Table 1). Because of limited continental emergence and elevation, the continental flux of P and thus the recycling flux of P would have been much smaller on the earlier Archean Earth, perhaps < 0.05 × 10 10 moles P/yr, i.e. 0.001 % of the modern value (Table 1).

Discussion

Seafloor weathering of phosphorus

In the modern ocean, seafloor weathering is widely agreed to be a net sink for P, primarily due to surface adsorption onto Fe(III)-hydroxide or carbonate [START_REF] Wheat | Phosphate removal by oceanic hydrothermal processes: An update of the phosphorus budget in the oceans[END_REF] or (co)precipitation of P-minerals (hydroxylapatite, CAP, REE/Al-phosphates) [START_REF] Ruttenberg | The Global Phosphorus Cycle[END_REF]. Given the reducing and weakly acidic nature of Archean seawater, however, dissolution of basaltic glass has been proposed as a source of P for autotrophs [START_REF] Kakegawa | Establishment of the phosphorous cycle in early Archean oceans[END_REF]. To date, there is limited evidence to support this hypothesis. [START_REF] De Kanel | The chemistry of orthophosphate uptake from seawater on to calcite and aragonite[END_REF][START_REF] Millero | Adsorption and desorption of phosphate on calcite and aragonite in seawater[END_REF][START_REF] Wheat | Phosphate removal by oceanic hydrothermal processes: An update of the phosphorus budget in the oceans[END_REF] or co-precipitation as carbonate apatite [START_REF] Freeman | The adsorption and precipitation of phosphate onto calcite[END_REF]Rubinstein et al., 2012;[START_REF] Xu | Retention of phosphorus on calcite and dolomite: speciation and modeling[END_REF]; both represent a major sink for P in modern carbonate-rich and/or anoxic sediments (e.g. [START_REF] Baturin | Phosphorus cycle in the ocean[END_REF][START_REF] Fourqurean | Phosphorus limitation of primary production in Florida Bay: Evidence from C:N:P ratios of the dominant seagrass Thalassia testudinum[END_REF][START_REF] Kraal | Phosphorus burial in sediments of the sulfidic deep Black Sea: Key roles for adsorption by calcium carbonate and apatite authigenesis[END_REF]. In addition, elevated temperature or presence of divalent cations (e.g. Ca 2+ , Mg 2+ ) would increase uptake of phosphate by carbonate [START_REF] Millero | Adsorption and desorption of phosphate on calcite and aragonite in seawater[END_REF]. In fact, carbonate minerals can capture 2.3 -4.5 * 10 12 mole P/yr in the modern ocean, 2 -4 times the sink provided by hydrothermal iron hydroxides [START_REF] Baturin | Phosphorus cycle in the ocean[END_REF];

carbonates could be expected to form a larger sink in the Archean due to higher pCO2,g and highly weatherable rocks.

In another study, [START_REF] Murakami | Behavior of phosphorus during hydrothermal alteration of basalt under CO2-rich condition[END_REF] investigated the hydrothermal alteration of basalt under CO2-rich condition (+ 30 mmole/kg Ca 2+ ), mimicking Archean atmospheric and seawater composition. Their experiments revealed under high CO2 conditions, carbonate was a major alteration product, with higher P-uptake than occurred in a CO2-free run, supporting the hypothesis that carbonate minerals would take up phosphate released from seafloor weathering or via diffusion from seawater. A limited contribution of P from glass weathering is further supported by the observations of modern and Archean glasses altered under anoxic conditions; these showed enrichment or no loss of P [START_REF] Alt | Alteration of the upper oceanic crust, DSDP site 417: mineralogy and chemistry[END_REF]Rubinstein et al., 2012;[START_REF] Staudigel | 3.5 billion years of glass bioalteration: Volcanic rocks as a basis for microbial life?[END_REF]. In addition to uptake by carbonates, there are other substantial sinks of P during seafloor weathering, including the precipitation of Al/REE phosphates [START_REF] Byrne | Rare earth precipitation and coprecipitation behavior: The limiting role of PO43-on dissolved rare earth concentrations in seawater[END_REF][START_REF] Rasmussen | The impact of early-diagenetic aluminophosphate precipitation on the oceanic phosphorus budget[END_REF] and vivianite (this study; [START_REF] Derry | Causes and consequences of mid-Proterozoic anoxia[END_REF]. Based on the above considerations, we argue that seafloor weathering should be a negligible source and possibly a large sink in the Archean P cycle.

Vivianite precipitation kinetics

Direct precipitation of vivianite from Fe(II)-PO4 solution has been experimentally

shown to be kinetically inhibited at low saturation states under ambient conditions [START_REF] Walpersdorf | Does vivianite control phosphate solubility in anoxic meadow soils?[END_REF]. In addition, at low supersaturation states, vivianite precipitation has been shown to follow spiral growth mechanism, at rates slower than surface-nucleation growth at high supersaturation states [START_REF] Madsen | Kinetics of crystal growth of vivianite, Fe3(PO4)2•8H2O, from solution at 25, 35 and 45[END_REF][START_REF] Madsen | Influence of calcium and aluminum on crystallization of vivianite, Fe3(PO4)2•8H2O[END_REF] [START_REF] Hansen | Interaction of synthetic sulphate green rust with phosphate and the crystallization of vivianite[END_REF][START_REF] Xiong | Phosphorus cycling under different redox conditions[END_REF]. The presence of mineral seeds (e.g. quartz) could also facilitate the crystallization of vivianite and lower the supersaturation demand [START_REF] Liu | Recovery of phosphate from aqueous solutions via vivianite crystallization: Thermodynamics and influence of pH[END_REF]. These mechanisms may explain the precipitation of vivianite at low to moderate supersaturation states in modern anoxic waters (Ω = 40 for lake Pavin; [START_REF] Cosmidis | Biomineralization of iron-phosphates in the water column of Lake Pavin (Massif Central, France)[END_REF] and sediments (Ω < 1 for Baltic Sea porewater; [START_REF] Jilbert | Iron and manganese shuttles control the formation of authigenic phosphorus minerals in the euxinic basins of the Baltic Sea[END_REF]; Ω < 1000 for Lake Groß-Glienicke and Lake Arendsee porewaters, although Lake Spitzingsee porewater vivianite is absent at Ω > 10000; [START_REF] Rothe | The occurrence, identification and environmental relevance of vivianite in waterlogged soils and aquatic sediments[END_REF], which might also have been true for Archean oceans.

Given these uncertainties, we cannot provide a quantitative estimate for the sedimentation flux of phosphate as vivianite in Archean oceans and thus evaluate the importance of vivianite precipitation as a P sink. Global vivianite fluxes would be greatly affected by poorly constrained concentrations and fluxes of phosphate and ferrous iron in Archean seawater. Moreover, the precipitation kinetics of vivianite are strongly influenced by temperature [START_REF] Madsen | Kinetics of crystal growth of vivianite, Fe3(PO4)2•8H2O, from solution at 25, 35 and 45[END_REF], microbial activity (Borch & Fendorf, 2008), and mineral surface [START_REF] Hansen | Interaction of synthetic sulphate green rust with phosphate and the crystallization of vivianite[END_REF][START_REF] Liu | Recovery of phosphate from aqueous solutions via vivianite crystallization: Thermodynamics and influence of pH[END_REF][START_REF] Xiong | Phosphorus cycling under different redox conditions[END_REF]. Additionally, adsorption onto Fe-(hydr)oxide [START_REF] Bjerrum | Ocean productivity before about 1.9 Gyr ago limited by phosphorus adsorption onto iron oxides[END_REF][START_REF] Jones | Iron oxides, divalent cations, silica, and the early earth phosphorus crisis[END_REF] or green rust [START_REF] Zegeye | Green rust formation controls nutrient availability in a ferruginous water column[END_REF] and/or co-precipitation as Fe(III)-phosphate would have competed for P with vivianite precipitation in surface seawater, and these processes cannot be quantified on the basis of available information. Nevertheless, we support the qualitative argument that the global flux of P precipitated by vivianite was important in the Archean P cycle, limited largely by the input of P from continental weathering and riverine transport (Table 1).

Burial of P in the Archean marine sediments

Within sediments, precipitation of siderite could become kinetically feasible during diagenesis through bioreduction of Fe(III) in the presence of organic matter [START_REF] Vuillemin | Formation of diagenetic siderite in modern ferruginous sediments[END_REF] or via burial heating. Our simulations suggest that siderite precipitation would minimize the solubility of Fe(II) (Fig. 4a); as a result, sedimentary vivianite would have higher solubility than calcium phosphates (Fig. 4b &4c). Under these circumstances, vivianite becomes unstable with respect to calcium phosphates, and the dissolution of vivianite could result in higher P than OCP and francolite solubility in porewater [START_REF] Thinnappan | A combined experimental study of vivianite and As (V) reactivity in the pH range 2-11[END_REF], inducing OCP or francolite precipitation. OCP has been suggested as essential precursor phase for apatite precipitation [START_REF] Gunnars | Inorganic formation of apatite in brackish seawater from the Baltic Sea: An experimental approach[END_REF][START_REF] Van Cappellen | The formation of marine apatite: A kinetic study[END_REF] and the presence of OCP could facilitate the precipitation of apatite, which would continue until P levels declined to values lower than OCP solubility [START_REF] Nancollas | The Nucleation and Growth of Phosphate Minerals[END_REF][START_REF] Van Cappellen | The formation of marine apatite: A kinetic study[END_REF]. Given the much lower solubility of apatite minerals than vivianite and OCP (Fig. 4c), precipitation of apatite should be a significant P-sink, maintaining low levels of P in Archean porewater (< 1 µM as the solubility of OCP in Fig. 4b).

Other forms of deposited P, including Fe(III)/Al-hydroxide or carbonate bound-and organic-P, might also transform into calcium phosphates, along with the reduction of Fe(III)

and breakdown of organic matter in porewater environments. Indeed, transformation of Al/Fe(III)-bound P to OCP has been observed in modern nearshore sediments and shown to be facilitated by increasing pH and/or decreasing Eh [START_REF] Oxmann | Authigenic apatite and octacalcium phosphate formation due to adsorption-precipitation switching across estuarine salinity gradients[END_REF]. In modern anoxic sediment, it has been observed that organic-P could transform progressively into calcium phosphate with the aid of CaCO3 during burial diagenesis [START_REF] Kraal | Phosphorus burial in sediments of the sulfidic deep Black Sea: Key roles for adsorption by calcium carbonate and apatite authigenesis[END_REF].

Archean porewaters were probably enriched in Ca (Fig. S1-2) and enhanced seafloor weathering at high pCO2,g would induce widespread precipitation of CaCO3 in sediments [START_REF] Sleep | Carbon dioxide cycling and implications for climate on ancient Earth[END_REF]. Thus, as argued for vivianite, organic-P would also transform into calcium phosphates during burial diagenesis, depending on the relative concentrations of Ca 2+ and Fe 2+ and ambient pH in sediments. Recently, [START_REF] Johnson | Phosphorus burial in ferruginous SiO2-rich Mesoproterozoic sediments[END_REF] reported carbonate fluorapatite as the major phosphate in a Mesoproterozoic ferruginous sediment, probably transformed from Fe(III)-bound or organic P during burial diagenesis, supporting the hypothesis that precipitation of calcium phosphates as the dominant long-term P-sink.

We also note that the present day mineralogy of iron formations is thought to bear the strong imprint of diagenesis, including supergene enrichment [START_REF] Rasmussen | Dust to dust: Evidence for the formation of "primary" hematite dust in banded iron formations via oxidation of iron silicate nanoparticles[END_REF].

Therefore, the current Fe and P mineralogy of Archean BIFs may not provide a strong test of our or any other low-temperature environmental hypotheses. Ca-rich carbonate would be a major product of seafloor weathering under a high pCO2,g Archean atmosphere [START_REF] Sleep | Carbon dioxide cycling and implications for climate on ancient Earth[END_REF], its solubility increasing with rising burial pressure. CaCO3 dissolution has been shown to aid long-term sequestration of P in the sediments of modern anoxic basins by facilitating the precipitation of Ca-P minerals [START_REF] Kraal | Phosphorus burial in sediments of the sulfidic deep Black Sea: Key roles for adsorption by calcium carbonate and apatite authigenesis[END_REF][START_REF] Krajewski | Biological processes and apatite formation in sedimentary environments[END_REF].

Therefore, in the long term, progressive burial might have converted vivianite to less soluble apatite.

Consistent with these considerations, tiny spheroids of apatite (Fig. 7) have been observed in Archean and Proterozoic carbonaceous shales (several % TOC) from multiple and widely separated localities. These spheroids typically measure 2 to 5 micrometers in diameter and may form solid spheres as well as thick-or thin-walled shells (Fig. 7). The illustrated Archean example (Bothaville Formation, South Africa; ca. 2700 Ma) shows predominantly detrital grains with small later diagenetic overgrowths (Fig. 7a-b). In essence, this coexistence suggests that apatite was originally deposited as a detrital component from continental erosion; in places where P concentrations reached saturation for apatite overgrowth, diagenetic overgrowths started to fill in adjacent pore space. In contrast to the Archean samples, common to all of the Proterozoic precipitates are micron-sized spheres or shells that consist of radiating apatite crystals that in places may extend beyond the apparent original sphere or shell margin outline (Fig. 7c-f). Thin-walled shells commonly show variable degrees of deformation, suggesting that apatite nucleated on partially degraded cell walls or extracellular envelopes. In places, multiple spheres are joined together to form a single mineralized entity [START_REF] Schieber | Benthic microbial mats in black shale units from the Vindhyan Supergroup, Middle Proterozoic of India: the challenges of recognizing the genuine article[END_REF]. The clustering of spheroids (Fig. 7c,d,e), the apparent progression from mineralized membranes, to thick-walled shells and solid spheres (Fig. 7f), and the commonly observed association with organic matter are suggestive of an organic origin, possibly as mineralized microbes that were associated with decaying organic matter [START_REF] Schieber | Benthic microbial mats in black shale units from the Vindhyan Supergroup, Middle Proterozoic of India: the challenges of recognizing the genuine article[END_REF].

The microspheres are consistent with P liberation during organic remineralization, followed by vivianite/OCP precipitation and, later, eventually transformation to apatite during diagenesis, although we cannot reject the alternate possibility that phosphorus precipitated originally as apatite. In either case, however, P liberated by organic remineralization did not return to the water column, but rather was immobilized by mineral precipitation.

In recent experiments, [START_REF] Herschy | Archean phosphorus liberation induced by iron redox geochemistry[END_REF] documented the partial reduction of orthophosphate (PO4 3-) into phosphite (PO3 3-) by Fe(II) at 180 °C, mimicking burial diagenesis. This mechanism is possible, but it has little influence on our conclusions, as even under favorable conditions only about 5% of precipitated phosphate would be reduced to phosphite [START_REF] Herschy | Archean phosphorus liberation induced by iron redox geochemistry[END_REF]. We note as well that the research in question did not include Ca (either aqueous species or carbonate) in the experimental system. Ca would significantly favor the stability of apatite Ca5(PO3)3(OH,F,Cl) against reduction of orthophosphate at the elevated temperatures and pressures associated with diagenesis and low-grade metamorphism (Fig. 5). This inference is consistent with evidence that apatite is the dominant P-mineral in ancient sedimentary rocks [START_REF] Friend | Seawater-like trace element signatures (REE + Y) of Eoarchaean chemical sedimentary rocks from southern West Greenland, and their corruption during high-grade metamorphism[END_REF][START_REF] Lepland | Apatite in early Archean Isua supracrustal rocks, southern West Greenland: Its origin, association with graphite and potential as a biomarker[END_REF].

Recycling of P in the Archean ocean

In the modern ocean, continental input of bioavailable P accounts for less than 1% of the P requirement for net primary production (NPP) (Table 1; [START_REF] Schlesinger | Biogeochemistry: an analysis of global change[END_REF]; the recycling of biological phosphate within the ocean overwhelmingly dominates P supply to the photic zone. On the Archean Earth, however, when the atmosphere and oceans were largely reducing, a lack of oxidants would have suppressed the recycling efficiency of biological P [START_REF] Kipp | Biomass recycling and Earth's early phosphorus cycle[END_REF]. And, as already introduced, our simulation shows that precipitation of secondary phosphates as vivianite or Ca-phosphates might also maintain low concentrations of dissolved P in Archean seawater and porewater, impeding the recycling of phosphate freed via organic matter remineralization. Therefore, the recycling of biological P was very likely much weaker in Archean oceans and, accordingly, NPP must have been much lower.

The recycling efficiency of organic matter is inversely proportional to the burial efficiency of NPP, which depends on the availability of oxygen [START_REF] Hedges | Sedimentary organic matter preservation: A test for selective degradation under oxic conditions[END_REF] and other oxidants, as well as bioturbation [START_REF] Zonneveld | Selective preservation of organic matter in marine environments; Processes and impact on the sedimentary record[END_REF]. Indeed, burial efficiency has an inverse relationship with exposure of oxygen (as well as other oxidants), and extrapolation of the correlation to zero oxygen exposure results in 40-50% burial efficiency [START_REF] Hartnett | Influence of oxygen exposure time on organic carbon preservation in continental margin sediments[END_REF]. Moreover, it has been estimated that burial efficiency can be as high as 22-32% in modern ferruginous lakes [START_REF] Crowe | The methane cycle in ferruginous Lake Matano[END_REF][START_REF] Katsev | Organic carbon burial efficiencies in sediments: The power law of mineralization revisited[END_REF][START_REF] Kuntz | Modeling the carbon cycle in Lake Matano[END_REF], although transferring this estimate to the entire ocean needs further investigation. In contrast, the burial efficiency of oceanic NPP is about 0.1% in modern oceans [START_REF] Hedges | Sedimentary organic matter preservation: an assessment and speculative synthesis[END_REF] Modern lakes certainly have greater inventories of oxidants (O2, SO4 2-, NO3 -) than Archean seawater. Input of sulfate would also undermine the burial P as vivianite by lowering the solubility of Fe(II) in anoxic waters and sediments [START_REF] Rothe | Sedimentary sulphur:iron ratio indicates vivianite occurrence: A study from two contrasting freshwater systems[END_REF]; however, the Archean seawater was depleted in sulfate [START_REF] Lyons | Ancient Sulfur Cycling and Oxygenation of the Early Biosphere[END_REF]. Such considerations suggest that the recycling efficiency of biological P would have been even lower in Archean oceans than in modern ferruginous lakes, i.e. Rrecycling < 0.68-0.78 in the Archean (Fig. 6). As noted above, an independent approach by [START_REF] Ward | Primary Productivity Was Limited by Electron Donors Prior to the Advent of Oxygenic Photosynthesis[END_REF] resulted in similar estimate for the flux of recycled P toward the end of the Archean, supporting a lower recycling efficiency of P than the modern value (~0.997).

Recently, Kipp & Stueken (2017) compiled the availability of oxidants for recycling P through Earth history and used these to argue that rates of P recycling in Archean seawater were 100 times lower than the modern, i.e., a recycling efficiency < 0.01. Kipp & Stueken's estimate should represent a lower limit of recycling efficiency, considering the preferential release of P during organic decomposition [START_REF] Clark | Marine phosphorus is selectively remineralized[END_REF] and photo-oxidation of organics in surface seawater (see below). Moreover the absence of zooplankton and fecal pellets in the Archean ocean might have led to less efficient deposition of particulate organic carbon [START_REF] Logan | Terminal Proterozoic reorganization of biogeochemical cycles[END_REF] and, consequently, burial of organic matter in the Archean ocean.

It is also important to ask whether the recycling efficiency of nutrients might have evolved through Archean time as a function of the redox state of surface environments [START_REF] Hao | Redox states of Archean surficial environments: The importance of H2,g instead of O2,g for weathering reactions[END_REF] and continental emergence (thus, shelf area for upwelling; see [START_REF] Olson | Oceanographic Constraints on Exoplanet Life[END_REF].

In the early Archean, when surface environments were more reducing and emergent continents were minimal, recycling of organic matter would be severely depressed due to oxidant limitation and limited shelf area for upwelling. However, in the middle to late Archean, oxidant inventories increased (Stueken et al., 2012) and continental lands increasingly emerged above sea level [START_REF] Flament | The evolution of the87Sr/86Sr of marine carbonates does not constrain continental growth[END_REF][START_REF] Korenaga | Global water cycle and the coevolution of the Earth's interior and surface environment[END_REF]. Back reduction of river-transported sulfate might have depleted dissolved seawater Fe(II) regionally, even generating euxinic areas in the late Archean ocean [START_REF] Reinhard | A Late Archean Sulfidic Sea Stimulated by Early Oxidative Weathering of the Continents[END_REF].

The solubility of vivianite would increase significantly in regionally euxinic zones, engendering a simultaneous increase of P solubility. As a consequence, the recycling efficiency of nutrients would be expected to increase.

In modern surface seawater, dissolved organic P (DOP) can reach significant levels, sometimes even higher than dissolved inorganic P [START_REF] Ruttenberg | The Global Phosphorus Cycle[END_REF]. Due to the high stability of biomolecules under reducing conditions, organic P might have also been important in the Archean seawater. However, experimental studies have suggested that the lifetime of organic-P under UV radiation would be short [START_REF] Francko | Functionally distinct classes of complex phosphorus compounds in lake water[END_REF]. Thus, high UV radiation, due to the lack of an Archean ozone shield, might efficiently destroy organic P in the surface layers of Archean seawater. Therefore, dissolved organic P might have played a relatively minor role for the Archean life in photic zone.

Electron vs. phosphorus limitation on Archean primary production?

How do the simulations presented here inform the debate about nutrient versus electron donor limitation on net primary production (NPP) in Archean oceans? Total fluxes of electron donors on the Archean Earth have been proposed in several studies [START_REF] Canfield | Early anaerobic metabolisms[END_REF][START_REF] Kharecha | A coupled atmosphere-ecosystem model of the early Archean earth[END_REF][START_REF] Ward | Primary Productivity Was Limited by Electron Donors Prior to the Advent of Oxygenic Photosynthesis[END_REF], but estimated values vary markedly (Fig. 8). By comparison, fluxes of nutrients have been less commonly investigated [START_REF] Laakso | Limitations on Limitation[END_REF][START_REF] Ward | Primary Productivity Was Limited by Electron Donors Prior to the Advent of Oxygenic Photosynthesis[END_REF], particularly for phosphorus, thought to be the most probable limiting nutrient. [It has been proposed that nitrogen limits global primary production on geologic time scales [START_REF] Falkowski | Evolution of the nitrogen cycle and its influence on the biological sequestration of CO2 in the ocean[END_REF]), but at the low levels for Archean NPP advocated here, nitrogen demand could have been met by modest rates of biological nitrogen fixation, and, especially during the early Archean, might have been sustained in most times and in many places by abiotic N-fixation [START_REF] Chameides | Rates of fixation by lightning of carbon and nitrogen in possible primitive atmospheres[END_REF][START_REF] Ward | Primary Productivity Was Limited by Electron Donors Prior to the Advent of Oxygenic Photosynthesis[END_REF][START_REF] Wong | Nitrogen Oxides in Early Earth's Atmosphere as Electron Acceptors for Life's Emergence[END_REF].]

Various lines of evidence support the concept of a more or less low-P Archean ocean [START_REF] Bjerrum | Ocean productivity before about 1.9 Gyr ago limited by phosphorus adsorption onto iron oxides[END_REF][START_REF] Jones | Iron oxides, divalent cations, silica, and the early earth phosphorus crisis[END_REF][START_REF] Planavsky | The evolution of the marine phosphate reservoir[END_REF][START_REF] Reinhard | Evolution of the global phosphorus cycle[END_REF].

Here, we estimate that the total flux of P could have reached 18-154 × 10 10 moles P/yr by the end of the Archean Eon. Assuming a standard Redfield C:P of 106:1, this is equivalent to a NPP of 19-163 × 10 12 moles C/yr, or 0.5-4% of the modern value (ca. 4000 × 10 12 moles C/yr; [START_REF] Field | Primary production of the biosphere: Integrating terrestrial and oceanic components[END_REF]. In the modern ocean, Redfield ratios of individual populations vary within limits set by the fundamental biochemical composition of their constituent cells [START_REF] Geider | Redfield revisited: Variability of C:N:P in marine microalgae and its biochemical basis[END_REF]. If, following [START_REF] Laakso | Limitations on Limitation[END_REF], we accept that mean C:P could have reached values as high at 195:1, the total flux of P could have supported up to 7% of the modern NPP by the end of the Archean Eon. This level of NPP is higher than the estimate by [START_REF] Ward | Primary Productivity Was Limited by Electron Donors Prior to the Advent of Oxygenic Photosynthesis[END_REF], i.e. < 0.1% for the late Archean time limited by the availability of electron donors and the efficiency of anoxygenic photosynthesis.

We stress, however, that our estimated P flux varies markedly through a billion years of recorded Archean history [START_REF] Hao | Cycling Phosphorus on the Archean Earth: Part I. Continental weathering and riverine transport of phosphorus[END_REF]; Figure 8). Early in the Archean, when continental weathering of P was severely limited by continental exposure and elevation, the weathering and erosional flux of P from continents would have been extremely low (Table 1).

Because of this factor and limitations on recycling efficiency from both low oxidant supply and the probability of P capture by vivianite, P supplied by recycling would also have been extremely low (Table 1). Moreover, the limited area of emergent continents and, thus, coastal continental margin shelf could result in relatively weak upwelling, and in consequence, reduced nutrient recycling [START_REF] Olson | Oceanographic Constraints on Exoplanet Life[END_REF]. P, then, could have limited NPP to less than 0.05 × 10 12 moles C/yr, a factor of eight lower than Ward et al.'s estimate for an Archean biosphere fueled by anoxygenic photosynthesis and far lower than the value estimated by [START_REF] Canfield | Early anaerobic metabolisms[END_REF]. Altogether, these results might indicate transition from a P-limited biosphere in the early Archean to an electron donor-limited biosphere as continents emerged toward the end of Archean (Fig. 8).

Questions of NPP limitation by P or electron donors are straightforward only in a world without oxygenic photosynthesis. Once bacteria evolved the capacity to split water, the supply of electron donors became essentially unlimited and primary production would, forever after, be limited by nutrient availability, primarily phosphorus [START_REF] Tyrrell | The relative influences of nitrogen and phosphorus on oceanic primary production[END_REF].

Despite continuing debate about when oxygenic photosynthesis first evolved, there is a consensus that the oxygenation of atmosphere at 2.4 Ga required oxygenic photosynthesis. [START_REF] Ward | Timescales of Oxygenation Following the Evolution of Oxygenic Photosynthesis[END_REF] simulated the oxygenation time of the Archean atmosphere under a series of settings (primary production, burial fraction, and methanogenic fraction) and suggested that with a primary production of 10 14 moles C/yr, irreversible oxygenation of atmosphere would happen within ~ 100 kyr. This level of primary production falls into the range of NPP supported by our estimation of total P in the end of Archean Eon (Table 1). Therefore, increasing emergence of continents and riverine transport of phosphorus would lead to higher primary productivity and once oxygenic autotrophs attained ecological prominence, rapid oxygenation of atmosphere as the Proterozoic Eon began.

Conclusions

The total flux of P for marine ecosystems predominantly reflects input from continental weathering and the recycling of P within the ocean. Archean seawater was anoxic, with a limited supply of oxidants, suppressing P recycling and so linking primary production more closely to continental weathering. Although Archean seawater was weakly acidic, apatite solubility would have been very low due to high levels of Ca and halogens; for this reason, seafloor weathering of P should not have been a major source of P for Archean marine ecosystems. In addition, the solubility of vivianite is predicted to have remained very low (0.1 to 0.3 µM) at moderate supersaturation states (Q/K = 100 to 1000) in Archean ferruginous seawater. Under these conditions, the precipitation flux of vivianite could have reached a level comparable to or higher than the modern sinking flux for P; therefore, it might have been a major sink in the Archean P cycle, with precipitation kinetically facilitated by microbial metabolism and mineral adsorption. Although potentially delivered to accumulating sediments, vivianite would not have been stable during burial diagenesis and metamorphism, reacting readily with calcium carbonate to form more stably calcium phosphates, particularly apatite.

Together with continental input of P, our current estimate of recycling P in the Archean ocean would, under the most favorable circumstances, have allowed up to 7% of modern NPP by the end of the Archean Eon. However, during the early and middle Archean, inputs of continental weathering and P recycling would have been considerably weaker, and the fluxes of electron donors higher. Therefore, NPP of the Archean marine ecosystems may well have been limited by the availability of P instead of electron donors during most of the Archean Eon. Indeed, on the early Archean Earth, NPP may well have been too low to oxygenate the atmosphere and surface ocean, even if oxygenic photoautotrophs were widely distributed in marine and fresh waters. Therefore, rapid oxygenation of the atmosphere might only have become possible as increasing P fluxes from weathering and erosion increased near the end of Archean Eon. Figure 8. Upper limits of net primary production (NPP) in the ocean through the Archean Eon relative to the modern level. Blue lines show the previously reported constraints (upper limit or range) of NPP by the supply of P [START_REF] Bjerrum | Ocean productivity before about 1.9 Gyr ago limited by phosphorus adsorption onto iron oxides[END_REF][START_REF] Laakso | Limitations on Limitation[END_REF]. Green lines display the previously reported constraints (upper limits) of NPP by the supply of electron donors (Canfield et al., 2005;[START_REF] Kharecha | A coupled atmosphere-ecosystem model of the early Archean earth[END_REF][START_REF] Ward | Primary Productivity Was Limited by Electron Donors Prior to the Advent of Oxygenic Photosynthesis[END_REF] and efficiency of early metabolisms [START_REF] Ward | Primary Productivity Was Limited by Electron Donors Prior to the Advent of Oxygenic Photosynthesis[END_REF]. Red curves present our reconstructed evolution (upper limits) of NPP limited by the supply of P assuming: (1) slow emergence of land in the late Archean [START_REF] Flament | The evolution of the87Sr/86Sr of marine carbonates does not constrain continental growth[END_REF]; (2) rapid emergence of land in the late Archean [START_REF] Korenaga | Global water cycle and the coevolution of the Earth's interior and surface environment[END_REF].

Figure 1 .

 1 Figure 1. Limited solubilities of apatite minerals in the Archean seawater conditioned by the

Figure 2 .

 2 Figure 2. Solubilities of various secondary-P minerals in the Archean seawater conditioned

Figure 3 .

 3 Figure 3. Precipitation of vivianite in Archean seawater: a. spiral growth (µm/yr) and b.

Figure 4 .

 4 Figure 4. Solubility of siderite and greenalite (a), secondary phosphate minerals (b), and

Figure 5 .

 5 Figure 5. Transformation of vivianite into apatite during diagenesis and metamorphism:

Figure 6 .

 6 Figure 6. Proportional contribution of continental weathering flux to the total P requirement

Figure 7 .

 7 Figure 7. Contrasting appearance of apatite grains from Archean and Mesoproterozoic

Fig. 9 .

 9 Fig. 9. Reconstructed phosphorus cycle in the early/middle Archean (a) and late Archean (b)

  represents source and minus sign (-) sink. a Reactive P = Dissolved inorganic P + Dissolved organic P + Particulate organic P + Ironbound particulate P + Reactive aeolian P (Compton et al., 2010); b Hao et al. (2020); c Schlesiner & Bernhardt (2013); d Optimisitic estimate calculated with equation (6-8) assuming Rrecycling = 0.78 (Sec. 3.3 in main text); e Seafloor weathering (-) = hydrothermal deposition (-) + seafloor sedimentation (-) = continental input (+) + extraterrestrial input (+); f Paytan & McLaughlin (2007); g Tsukamoto et al. (2018); h NPP(P) = continental input + recycling of organic P + extraterrestrial

  and might have evolved through time(Sec. 4.4). Assuming deep water P concentrations equivalent to 10% of the modern value and a typical vertical mixing rate (3 m/yr),[START_REF] Ward | Primary Productivity Was Limited by Electron Donors Prior to the Advent of Oxygenic Photosynthesis[END_REF] recently estimated Archean P recycling to have been 40 × 10 10 moles P/yr, within the range of our values. Regardless of uncertainties, these estimates agree that the recycling flux of P in late Archean oceans was 1-2 orders of magnitude lower than

today's (about 3710 × 10 10 moles P/yr;

[START_REF] Schlesinger | Biogeochemistry: an analysis of global change[END_REF]

. Together with our estimated continental input of P, up to 18-154 × 10 10 moles P/yr would have been available

  [START_REF] Syverson | Anoxic weathering of mafic oceanic crust promotes atmospheric oxygenation[END_REF] recently observed slight P release during alteration of basalt at 25 °C under anoxic conditions, whereas alteration experiments under oxic condition did not show any P release. These observations seemingly support seafloor weathering as a potential source of P in the anoxic Archean ocean(s). However, Syverson et al. used a simulated seawater solution without any inorganic C, which diverges markedly from realistic estimates of Archean seawater chemistry (high CO2,aq and (bi)carbonate species;[START_REF] Halevy | The geologic history of seawater pH[END_REF][START_REF] Krissansen-Totton | Constraining the climate and ocean pH of the early Earth with a geological carbon cycle model[END_REF]. Under these more realistic conditions, seafloor weathering would precipitate abundant carbonate minerals, a major sink in the Archean carbon cycle[START_REF] Krissansen-Totton | Constraining the climate and ocean pH of the early Earth with a geological carbon cycle model[END_REF] as well as a known mineral product in modern seafloor weathering. Carbonate minerals have a strong affinity to phosphate and could limit soluble P by either surface adsorption (de Kanel

Table 1 .

 1 Fluxes of bioavailable or biological P in the modern and early Earth (in 10 10 moles/yr).

	P fluxes *	Pre-industrial	Early Archean Earth Late Archean Earth
		Earth
	Continental input a	10-15 a (+)	~0 (+)	4-34 b (+)
	Recycling of organic P	~3710 c (+)	< 0.04 (+)	14-120 (+) d
	Seafloor weathering e	10-36 f (-)	(-)	>4 (-)
	Extraterrestrial	(+)	< 0.01 g (+)	< 0.01 (+)
	Total P for net primary
	production h

Acknowledgements

We thank Dimitri A. Sverjensky, Cin-Ty Lee, Nicolas Coltice, Ciaran Harman, Mathew Pasek, Michael Kipp, David Catling, Lu Pan, Chao Liu, Liyan Tian, Ming Tang, Joshua Krissansen-Totton, Dustin Trail, and Paul Falkowski for helpful discussions. We also appreciate constructive comments by three anonymous reviewers, Nicolas Tosca, and Jeffrey Catalano. JHH & ID thank French National Research Agency (#ANR-15-CE31-0010), JHH & RMH thank NASA's Astrobiology Institute grant (80NSSC18M0093), and JHH, AHK, FH, and RMH thank W.M. Keck Foundation for financial support. RMH thanks the Templeton Foundation for financial support. JS thanks the sponsors of the Indiana University Shale Research Consortium (Anadarko, Chevron, ConocoPhillips, ExxonMobil, Shell, Equinor, Marathon, Whiting, and Wintershall) for support of the IU Shale Research Lab.

Research Data Thermodynamic properties of chemical reactions are provided in supplementary file. The continental weathering and seawater chemistry models are calculated using the codes shared online by Krissansen-Totton (https://github.com/joshuakt/early-earthcarbon-cycle) with additional modifications on continental emergence (see main text).

Author contributions JHH and AHK conceived of the project. JHH and FH performed the simulations; JHH and AHK analyzed the results. JS and AHK collected and investigated the textural mode of apatite grains in Archean and Proterozoic shales. All authors discussed the results and wrote the manuscript.


Tristan Gauthier
email: tristan.gauthier@chu-limoges.fr.

Aymeline Lacorre

Camille Sallee

Antoine Tardieu

Frédéric Guyon

François Margueritte

Sébastien Gouy

Impact de l'étude LACC. Une enquête de la SFOG. Impact of the LACC study. A SFOG survey

Keywords: LACC, cancer du col, coelioscopie, robot, manipulateur utérin, laparotomie LACC, cervical cancer, laparoscopy, uterine manipulator, open surgery

Introduction : L'étude LACC (Laparoscopic Approach to Cervical Cancer Trial), parue en 2018 a décrit des résultats oncologiques en faveur de la laparotomie comparativement à la voie mini-invasive dans la prise en charge des cancers du col localisés. Notre but était d'évaluer l'impact de cette étude sur les pratiques chirurgicales en France. Méthodologie : Questionnaire en ligne, composé de treize questions, adressé aux chirurgiens membres de la société française d'oncologie gynécologique (SFOG). Résultats : Quarante questionnaires ont été recueillis. Le nombre médian annuel d'hystérectomie élargie était de cinq (0-20). Avant la parution de l'étude, en cas de cancer du col inférieur à quatre centimètres, 92,5 % réalisaient une hystérectomie élargie par chirurgie miniinvasive. En cas de coelioscopie ou de robot, le manipulateur utérin était utilisé dans 67,6 % et l'ouverture vaginale était réalisée par voie intra-abdominale (78,4 %). Après l'étude LACC, 60 % des chirurgiens ont modifié leur pratique. La laparotomie était privilégiée par 75 % de ceux ayant modifié leur pratique. Parmi ceux continuant à réaliser des chirurgies mini-invasives, le manipulateur et l'ouverture vaginale coelioscopique étaient abandonnés. Un tiers des praticiens ont modifié parallèlement leur pratique chirurgicale en cas de cancer de l'endomètre. Conclusion : Les résultats de l'étude LACC ont conduit à une modification des pratiques chirurgicales avec une augmentation des laparotomies et un arrêt de l'utilisation du manipulateur utérin et de l'ouverture vaginale coelioscopique dans la prise en charge chirurgicale des cancers précoces du col utérin.

La chirurgie mini-invasive est la voie d'abord recommandée en chirurgie gynécologique bénigne [1]. En oncologie, la chirurgie mini-invasive (CMI) a été également promue dans l'objectif d'améliorer le confort des patientes. Dans le cancer du col utérin, il était admis une absence d'infériorité carcinologique comparativement à la laparotomie en cas d'hystérectomie élargie. Cependant, les données reposaient sur des études de faible niveau de preuve [2]. En novembre 2018, l'étude LACC (Laparoscopic Approach to Cervical Cancer Trial), une étude randomisée et multicentrique, a été publiée dans le New England Journal of Medicine (NEJM) [3]. Les paramètres de survie étaient tous en faveur de la laparotomie. La survie sans récidive à quatre ans et demi était réduite de dix pour cent dans le groupe mini-invasif. La survie globale était également impactée. La totalité des récidives pelviennes étaient retrouvées dans le groupe mini-invasif, posant la question d'un moins bon contrôle local et d'un risque de dissémination tumorale local accru par la chirurgie coelioscopique ou robotique [3]. Parmi les explications potentielles aux résultats défavorables de la voie mini-invasive, étaient évoqués l'ouverture vaginale coelioscopique avec l'effet promoteur potentiel du dioxyde de carbone sur la diffusion tumorale et l'utilisation du manipulateur utérin. Les résultats ont remis en cause de façon surprenante les pratiques des chirurgiens oncologues. D'autres études de cohorte, de niveau de preuve moins élevé, ont confirmé ces données [4][5][START_REF] Paik | Comparison of laparoscopic and abdominal radical hysterectomy in early stage cervical cancer patients without adjuvant treatment: Ancillary analysis of a Korean Gynecologic Oncology Group Study (KGOG 1028)[END_REF] aboutissant au retrait de la coelioscopie comme voie d'abord standard en cas de cancer du col utérin localisé, au sein des sociétés savantes comme l'ESGO (European Society of Gynaecological Oncology) et le NCCN (National Comprehensive Cancer Network).

L'objectif de notre étude était d'évaluer l'impact de l'étude LACC sur les pratiques des chirurgiens oncologues français.

Matériel et méthodes

Il s'agissait d'une enquête diffusée sous forme d'un e-questionnaire adressé aux chirurgiens oncologues membres de la Société Française d'Oncologie Gynécologique (SFOG).

Parmi les treize questions, les questions neuf et deux concernaient respectivement le cancer du col utérin et le cancer de l'endomètre.