Marine Phosphate Level During the Archean Constrained by the Global Redox Budget

Understanding the oceanic phosphate concentration is critical for understanding marine productivity and oxygen evolution throughout Earth history. During the Archean, estimates of marine phosphate levels range from scarce to enriched conditions. However, biogeochemical conditions required for sustaining high phosphate concentrations while retaining an anoxic atmosphere during the Archean remain ambiguous. Here, we employ a biogeochemical model of the marine phosphate cycle to determine the conditions under which oceanic phosphate levels could have been higher than present‐day values during the Archean after the emergence of oxygenic photoautotrophs (OP). We show that, under the presence of OP, phosphate‐rich oceans require the limitation by factors other than phosphate, or a high outgassing rate of reducing gases. If these conditions were not met, the occurrence of oceanic phosphate levels higher than present‐day values during the Archean would require the absence of OP.

The suppression of nutrient (i.e., phosphorus; P) availability in the ocean has been proposed as one plausible reason for sustained anoxic conditions throughout the Archean.Phosphorus, a bioessential element for life on Earth, is considered to be an ultimate limiting nutrient (Tyrrell, 1999), which controls the global productivity of marine ecosystems on geological timescales.Geochemical analyses of Fe and P abundances in Archean iron formations (IF) indicate a low P availability (Bjerrum & Canfield, 2002;Jones et al., 2015;Rego et al., 2023), although the estimated phosphate concentrations would be affected by uncertainties in the concentrations of Earth after the evolution of oxygenic photosynthesis are estimated using a theoretical model • Phosphate-rich oceans cause atmospheric oxygenation under reasonable outgassing rates of reducing gases • Without suitable conditions, absence of oxygenic photosynthesis would be required for the phosphate-rich oceans during the Archean

Supporting Information:
Supporting Information may be found in the online version of this article.cations such as Si 2+ , Mg 2+ , and Ca 2+ (Jones et al., 2015;Konhauser et al., 2007).Records of P abundance in shales also support a condition of P scarcity during the Archean (Planavsky et al., 2014;Reinhard et al., 2017).The P scarcity is also supported by biogeochemical models (Kipp & Stüeken, 2017;Reinhard et al., 2017;Watanabe et al., 2023b).
However, in contrast to those studies, some studies suggest the possibility that oceanic phosphate levels during the Archean were comparable to or higher than today (Crockford & Halevy, 2022;Ingalls et al., 2022;Konhauser et al., 2007;Planavsky et al., 2010;Rasmussen et al., 2021Rasmussen et al., , 2023)).Records of P/Ca ratios in shallow marine carbonate minerals (carbonate-associated phosphate, CAP) at ∼2.8-2.5 Ga suggest phosphate-rich oceans with 4-12 times higher phosphate concentrations compared with the present day (Ingalls et al., 2022).Maximum phosphate concentrations of 10-100 μM are inferred from records of apatite nanoparticles with greenalite in deepwater banded IF deposited between 3.46 and 2.46 Ga (Rasmussen et al., 2021).Records of the co-precipitation of Ca-phosphate and ferrous silicate infer a P concentration several orders of magnitude higher than that in the present-day photic zone at 2.46-2.40Ga (Rasmussen et al., 2023).These contradicting views of phosphate levels in the Archean oceans highlight a lack of quantitative understanding of the P cycle in the geological past.In this study, we examine the possibility that oceanic phosphate levels were higher than today during the Archean after the emergence of OP using a biogeochemical model of marine P cycle together with a global Fe and redox (O 2 ) budget.

Materials and Methods
We constructed a conceptual biogeochemical box model that simulates the global P cycle considering the global Fe and O 2 budgets (Figure 1).In this framework, the condition for low atmospheric pO 2 can be represented by the principle of the global redox budget (Claire et al., 2006;Watanabe et al., 2023a).The K oxy value is used to measure the condition for the oxygenation of the atmosphere: where, F bg is the burial flux of organic carbon (OC), F red represents the volcanic outgassing rate of reducing gasses (in terms of Tmol H 2 eq.yr 1 ), and F oxfe is the deposition rate of Fe(III) hydroxides.Note that the weighting factor scales the effect of the burial of OC and Fe(III) in terms of the reducing power of H 2 .When K oxy is below unity, the rapid sink terms of O 2 outweigh the source of O 2 , hindering the build-up of O 2 in the atmosphere (Claire et al., 2006;Watanabe et al., 2023a).We note here that oxidative weathering of continental crust and hydrogen escape do not appear in Equation 1 because these terms would be very small at the boundary of the abrupt rise of pO 2 (Claire et al., 2006;Kasting, 2013;Watanabe et al., 2023a).When K oxy reaches unity, the oxygenation of the atmosphere (i.e., the GOE) occurs.In other words, the conditions for achieving an oxic atmosphere can be represented as follows: F bg = 1 4 (F oxfe + 2F red ). (2) Note that, in the above equations, we do not consider the effect of pyrite burial for the purpose of obtaining upper estimates of marine phosphate concentrations because pyrite burial promotes oxygenation of the atmosphere.The P deposition as vivianite is also ignored for the purpose of obtaining a maximum estimate of marine phosphate concentrations.With these assumptions, the external supply rate of Fe(II) (F ext,fe ) is equal to F oxfe : For marine P cycling, we constructed a biogeochemical model with three ocean boxes (Figure 1b).The model is composed of the low-latitude surface ocean box (s), high-latitude surface ocean box (h), and deep ocean box (d) (Archer et al., 2000).The marine P budget in the whole ocean is represented as follows: where F ext,p denotes the external input flux of P to the ocean, F bg,p is the burial rate of phosphorus in marine sediments, and F scav,p represents the P removal flux via scavenging by Fe minerals from the ocean (Berner, 1973;Bjerrum & Canfield, 2002;Bocher et al., 2004;Cosmidis et al., 2014;Jones et al., 2015;Krom & Berner, 1980;Reinhard et al., 2017;Zegeye et al., 2012).The export production of organic P (F po,p ) and organic C (F po ) is determined by the phosphate concentration in the euphotic zone, [PO 4 3 ] i (Ozaki, Reinhard, & Tajika, 2019;Watanabe et al., 2023b;Yamanaka & Tajika, 1996): where V pz denotes the volume of the photic zone of the surface water boxes; C bio :P bio represents the C:P ratio of the marine organic matter; γ p is the half-saturation constant for the export production (γ p = 1.0 × 10 6 mol L 1 ) (Yamanaka & Tajika, 1996); and ε is the efficiency factor for phosphorus uptake (ε s and ε h are 3.0 and 0.8 yr 1 , respectively), which is tuned to reproduce the present oceanic P concentration (Figure S1 in Supporting Information S1).The burial rates of organic C and P (F bg and F bg,p , respectively) are represented as follows: where α d is the ratio between burial rate of OC and export production rate, and C org :P reac represents the C org : reactive P (originating from organic P) ratio of buried sediments.The value of α d is set to 20%, so that the burial rate of OC relative to the primary production rate is the same as the modern value of the Black Sea (2%) (Betts & Holland, 1991) where the bottom water is anoxic and sulfidic.It should be noted that the ratio of export production rate from the surface ocean and the primary production rate of 10% is assumed following the previous study (α d = 0.02/0.10= 0.20) (Ozaki, Reinhard, & Tajika, 2019;Watanabe et al., 2023b).In the Archean ocean, this value is highly uncertain (Kipp & Stüeken, 2017;Kipp et al., 2020;Kuntz et al., 2015;Laakso & Schrag, 2018;Ozaki et al., 2018) because it may be much higher than this value owing to the lack of sulfate ions (Kuntz et al., 2015;Laakso & Schrag, 2018).Nevertheless, our lower value allows us to obtain the maximum estimate of the marine phosphate concentrations that can be achieved on early Earth.C org :P reac is treated as a constant (the standard value is assumed to be 200) (Algeo & Ingall, 2007), and the impact of its uncertainty on the results is examined in sensitivity experiments.We note here that the Ca-bound P burial, the primary P removal pathway in the present ocean, is not explicitly considered but its effect is represented by the factor C org :P reac assuming that the Ca-bound P originates from the buried organic P.

10.1029/2023GL108077
To get the steady-state solution with the constraint of K oxy of 1, the model is run with the following external P supply rate: where F bg,p,steady is the burial rate of phosphorus in marine sediments at a steady state calculated using Equations 1 and 8.The marine phosphate concentration converges into a steady state that achieves K oxy = 1.We estimated the response of the marine P concentration to the oceanic overturning rate and other parameters that potentially affect the result (Table S1 in Supporting Information S1).The values of the standard parameters are summarized in Table S2 in Supporting Information S1, which reproduces the present oceanic P concentrations (Figure S1 in Supporting Information S1).

Constraints From Low Atmospheric pO 2 During the Archean
The relationship between the K oxy value, F  2d).When K oxy exceeds 1, an abrupt increase of atmospheric pO 2 corresponding to GOE must occur (Claire et al., 2006;Kasting, 2013;Watanabe et al., 2023aWatanabe et al., , 2023b)).At this boundary, [PO 4 3 ] d is ∼0.1 μM (∼5% of the present oceanic level; POL) when F ext,fe is zero (Figure 2c).This value is an upper limit of the [PO As F ext,fe increases, the threshold value of F bg required for the inception of the GOE increases because the oxygenation of Fe(II) prevents the oxygenation of the atmosphere.
The estimated maximum [PO 4 3 ] d (corresponding to a value for K oxy = 1) is summarized in a parameter space of F ext,fe and F red in Figure 3a.The relationship between the Fe(II) influx and F bg,p at the boundary of the oxygenation of the atmosphere (i.e., K oxy = 1) with different F red values is shown in Figure 3b.The required F bg,p for the GOE becomes higher for larger values of F red and F ext,fe .When F red is small (<∼10 Tmol H 2 eq.yr 1 ), the [PO 4 3 ] d value is still more than one order of magnitude smaller than the present condition.With an F red of 1 Tmol H 2 eq.yr 1 , for example, [PO 4 3 ] d is less than 1 μΜ (approximately 40% POL) even under extremely high F ext,fe (1,000 Tmol Fe yr 1 ).This range is consistent with the estimates of a P-scarce ocean (Jones et al., 2015;Kipp & Stüeken, 2017;Rego et al., 2023;Reinhard & Planavsky, 2022;Watanabe et al., 2023b) (Figure S2C in Supporting Information S1) and it also allows the plausible range of estimates from CAP records (Crockford & Halevy, 2022;Ingalls et al., 2022), but the maximum value is still much lower than other estimates of P-rich conditions (Planavsky et al., 2010;Rasmussen et al., 2021Rasmussen et al., , 2023)).To achieve such P-rich oceans (>100% POL), the outgassing rate of reducing gases must be very high (Figure 3a).Specifically, when the outgassing rate of F red is very high (>300 Tmol H 2 yr 1 ), [PO 4 3 ] d higher than the present value could be achieved while maintaining an anoxic atmosphere.These results demonstrate that if the activity of OP is limited by P availability, an extremely elevated outgassing rate of reducing gases is required for deep-ocean P concentrations to be similar to, or more enriched than, those of the present ocean while keeping the ocean-atmosphere system anoxic.

Constraints From the Influx of Reducing Gases
The conditions for the oxygenation of the atmosphere are shown in a diagram of the marine phosphate concentration and influx of reducing power to the ocean-atmosphere system (F red + 0.5 F ext,fe ) (Figure 4).The pinkhatched region represents the maximum outgassing rate from serpentinization of the oceanic crust (∼50 Tmol H 2 eq.yr 1 ) (Krissansen-Totton et al., 2018) (see their Figure 6).When F red is extremely high, way beyond the maximum value, the present marine phosphate concentration could be achieved while keeping the atmosphere anoxic, implying that phosphate-rich conditions require an unrealistically high influx of reducing power.To confirm the robustness of this result, the effects of uncertainties in other model parameters were also examined  (Bjerrum & Canfield, 2002;Ozaki, Thompson, et al., 2019;Watanabe et al., 2023b).In contrast, the sensitivity experiment with respect to the oceanic overturning rate (Figures 3d-3f and Figure S3b in Supporting Information S1), demonstrates that stagnant ocean circulation could allow a higher [PO 4 3 ] d .Specifically, when the oceanic overturning rate is <∼25% of the standard value, [PO 4 3 ] d of >1 μM is permissible assuming the maximum F red .In such stagnant ocean conditions, however, [PO 4 3 ] values in the surface ocean boxes do not increase strongly (Figure S3b in Supporting Information S1), which would not be a suitable condition for explaining the reconstructions of the values in the surface ocean by CAP records.In addition, the range of the influx of reducing gases required for sustaining the present marine P concentration is rather limited (Figure 3d).This result demonstrates that marine P concentrations higher than the present condition cannot be achieved without extremely high influxes of reducing power.
The condition for achieving high marine P would even become more severe with a higher value for the burial efficiency of OC in the ocean (Figures 3g-3i and Figure S4 in Supporting Information S1).We assumed a burial efficiency of the Black Sea as a lower limit for the Archean ocean, but existing literature indicates a higher burial efficiency (Kuntz et al., 2015;Laakso & Schrag, 2018).With a higher burial efficiency of OC, the F red value required for [PO 4 3 ] d of >100% POL becomes even higher.For the case with the burial efficiency of OC of 10%, [PO 4 3 ] d of 100% POL cannot be achieved even with F red of 1,000 Tmol H 2 .eq. yr 1 (Figure S4 in Supporting Information S1).These results indicate the difficulty of achieving high marine P concentrations under the existence of OP.

Discussion
Our results demonstrate that marine phosphate concentrations >100% POL are limited to the condition of an unrealistically high influx of reduced gases larger than the maximum value for serpentinization of the oceanic crust (Krissansen-Totton et al., 2018).This flux would be difficult to achieve on the early Earth even considering other sources of reducing gases; for example, the rate of H 2 release from the mantle is estimated at ∼2.2 Tmol H 2 eq.yr 1 (Catling & Kasting, 2017;Holland, 1984) and this value may be even smaller considering the uncertainty regarding fluxes of H 2 O and CO 2 (Catling & Kasting, 2017).Reconstructions of the H 2 outgassing rate from Precambrian continental lithosphere give values of ∼0.036-0.227Tmol H 2 yr 1 (Lollar et al., 2014).These estimates are two or three orders of magnitude lower than the H 2 outgassing rate required for hypothetical P-rich oceans during the Archean.This clearly indicates that a high marine P concentration would be difficult to sustain during the Archean after the emergence of OP, if OP global activity is limited by P availability.It should be noted that if the oxygen fugacity in the Archean mantle was lower, a higher outgassing flux of reducing gases may be possible (Kadoya et al., 2020;Kipp et al., 2020;Krissansen-Totton et al., 2021;N. F. Wogan & Catling, 2020;N. Wogan et al., 2020).Nevertheless, the condition for high P concentration is rather limited as shown in Figure 3a.This may suggest that high marine P during the mid-late Archean indicates the absence of OP (Ingalls et al., 2022).Although phylogenetic analyses of cyanobacteria and O 2 -utilizing and -producing enzymes infer the early emergence of OP (Garcia-Pichel et al., 2019;  S1 in Supporting Information S1).The gray, black, orange, and light blue lines represent the results with F ext,fe of 0, 1, 10, and 100 Tmol Fe yr 1 .The blue-hatched region represents the condition for the oxic atmosphere (K oxy ≥ 1).Jabłońska & Tawfik, 2021;Schirrmeister et al., 2015), other studies suggest that the emergence of OP occurred immediately before the oxygenation of the atmosphere during the Paleoproterozoic (Kopp et al., 2005).If the latter is the case, O 2 was not generated during much of the Archean.Assuming that the activity of the anaerobic biosphere is limited by the supply rate of electron donors (e.g., H 2 , CO, H 2 S, Fe(II), etc.), the primary productivity would be ∼1% or less of the present productivity (Canfield et al., 2006;Kharecha et al., 2005;Ozaki et al., 2018).Because the amount of P required to sustain such a low activity level is small, high P concentrations could be achieved under an anoxic atmosphere in the absence of OP.
During the late Archean, geological records of transient oxygenation infer the presence of OP (Anbar et al., 2007;Crowe et al., 2013;Czaja et al., 2012;Garvin et al., 2009;Koehler et al., 2018;Ossa Ossa et al., 2016, 2018;Planavsky et al., 2014;Stüeken, Buick, Bekker, et al., 2015).If this is the case, high marine P during the Archean would require the limitation of primary productivity by other factors, for example, nitrogen, N. Before the evolution of nitrogenase-a N-fixing enzyme that allows N fixation-the availability of bioavailable N species in the ocean-atmosphere system would have been limited.If biospheric activity was limited by the availability of N  S1 in Supporting Information S1) (a-c), the ocean circulation rate relative to the present condition and F red (ExpCircFred in Table S1 in Supporting Information S1) (d-f), and the burial efficiency of organic carbon and F red (ExpBurFred in Table S1 in Supporting Information S1) (g-i).The cyan bars represent the range below the maximum value of F red in Krissansen-Totton et al. (2018).The orange lines in (a, d, and g) represent the condition for the present marine P concentration.Calculations are conducted under the condition of K oxy of 1. (Kasting & Siefert, 2001;Navarro-González et al., 2001), P would have accumulated to higher levels than those estimated under the assumption of a P-limited ecosystem.Indeed, a previous modeling study that implicitly assumes a limitation of primary productivity by the availability of N near the continental shelf indicates a marine P over 100% POL under a reasonable influx of reducing power (Alcott et al., 2019).We note that their model is based on the phosphorus cycle model of the present ocean (Slomp & Van Cappellen, 2007), which assumes a linear relationship between P concentrations and the primary production in the proximal coastal ocean obtained for a condition with a N:P ratio of ∼10 (lower than the Redfield's ratio (N:P ratio of 16) and thus N limitation) (Slomp & Van Cappellen, 2004).This supports the feasibility of high P conditions under N-limited conditions.However, it has been proposed that the age of origin of nitrogenase was ∼3.2 Ga (Stüeken, Buick, Guy, & Koehler, 2015), which may suggest that P-rich reconstructions during the Archean require the absence of OP or limitations of primary productivity by other unconsidered factors.One of the other factors that may limit the primary productivity of OP is the competition of P between the anoxygenic photoautotrophs, which can survive with weaker sunlight at a deeper part of the euphotic zone and thus has a priority in utilizing P upwelling from deep oceans (Ozaki, Thompson, et al., 2019).This limitation would require an Fe/P ratio in the deep ocean higher than ∼424, which is obtained by multiplying the reduction rate of C relative to Fe(II) oxidation rate by Fe-using anoxygenic photoautotrophs ratio (4) and the C:P ratio of marine biomass (Ozaki, Thompson, et al., 2019).Assuming the present phosphate concentration in the deep ocean, the marine Fe(II) concentration on an order of ∼1 mM would be required for the limitation by anoxygenic photoautotrophs, which is higher than the values estimated by biogeochemical models (Halevy et al., 2017;Laakso & Schrag, 2014;Watanabe et al., 2023b).Further investigation using a biogeochemical model with Fe and P dynamics would be a fruitful topic (Laakso & Schrag, 2014;Watanabe et al., 2023b).

Conclusion
The biogeochemical conditions required for P-rich oceans during the Archean were examined.Our biogeochemical model revealed that oceanic phosphate concentrations higher than today would have been difficult to achieve during the Archean if OP had already evolved and their activity was limited by phosphate availability.Under such conditions, P-rich oceans would have given rise to the oxygenation of the atmosphere unless the input flux of reducing gases was unrealistically high.The P-rich oceans during the Archean would require the absence of OP or limitations of productivity by other factors (e.g., bioessential elements other than P).Further constraints on marine phosphate concentrations and behaviors of P in anoxic oceans would be beneficial for understanding marine biogeochemical cycles during the Archean.S1 in Supporting Information S1).The gray, black, red, orange, yellow, light blue, blue, navy, and purple lines represent sets of results with outgassing rates of reduced gases of 0, 1, 3, 10, 30, 50, 100, 300, and 1,000 Tmol H 2 eq.yr 1 , respectively.The pink-hatched region is the condition that requires influxes of reducing gases greater than the maximum value for serpentinization of the oceanic crust.The estimates of the Archean marine P are summarized in Crockford and Halevy (2022).The range of the values for Ingalls et al. ( 2022) is shown as a preferred value following Crockford and Halevy (2022).

Figure 1 .
Figure 1.Schematic illustration of the global redox budget during the Archean (a) and an illustration of the biogeochemical box model used in this study (b).
4 3 ] d value under a given F ext,fe when the atmospheric pO 2 is low as in the Archean atmosphere.This maximum [PO 4 3 ] d value becomes even lower when F ext,fe increases.The concentrations in the surface ocean boxes are smaller than in the deep ocean, so we regard [PO 4 3 ] d to be the possible maximum value for the surface ocean.For this reason, we compare the simulated [PO 4 3 ] d to the phosphate levels estimated for the surface ocean based on the CAP records.

Figure 2 .
Figure 2. Relationships between K oxy , external P supply rate (a), marine P concentration in the surface ocean boxes (b) and deep ocean box (c), and the burial flux of organic carbon (d) (ExpKoxy in TableS1in Supporting Information S1).The gray, black, orange, and light blue lines represent the results with F ext,fe of 0, 1, 10, and 100 Tmol Fe yr 1 .The blue-hatched region represents the condition for the oxic atmosphere (K oxy ≥ 1).

Figure 3 .
Figure3.Estimated marine P concentrations (a, d, and g), burial flux of P via deposition of organic matter (Tmol P yr 1 ) (b, e, and h), and scavenging flux of P from the ocean (c, f, and i) shown as a parameter space of the Fe(II) influx (F ext,fe ) and the reducing gas influx (F red ) (ExpFextfeFred in TableS1in Supporting Information S1) (a-c), the ocean circulation rate relative to the present condition and F red (ExpCircFred in TableS1in Supporting Information S1) (d-f), and the burial efficiency of organic carbon and F red (ExpBurFred in TableS1in Supporting Information S1) (g-i).The cyan bars represent the range below the maximum value of F red inKrissansen-Totton et al. (2018).The orange lines in (a, d, and g) represent the condition for the present marine P concentration.Calculations are conducted under the condition of K oxy of 1.

Figure 4 .
Figure 4. Relationships between the marine phosphate concentration calculated under a constraint of K oxy of 1 (ExpFextfe in TableS1in Supporting Information S1).The gray, black, red, orange, yellow, light blue, blue, navy, and purple lines represent sets of results with outgassing rates of reduced gases of 0, 1, 3, 10, 30, 50, 100, 300, and 1,000 Tmol H 2 eq.yr 1 , respectively.The pink-hatched region is the condition that requires influxes of reducing gases greater than the maximum value for serpentinization of the oceanic crust.The estimates of the Archean marine P are summarized inCrockford and Halevy (2022).The range of the values for Ingalls et al. (2022) is shown as a preferred value followingCrockford and Halevy (2022).
ext,p , and [PO 4 3 ] is shown in Figure 2. Different line colors represent the results with different F ext,fe values (0, 1, 10, and 100 Tmol Fe yr 1 ).These calculations are conducted with F red of 10 Tmol H 2 eq.yr 1 .In any F ext,fe value, the estimated [PO 4 3 ] in each ocean box and the required F ext,p increases when K oxy increases because high K oxy values represent a high burial rate of OC (Figures 2b-