Terrestrial microbialites provide constraints on the mesoproterozoic atmosphere

Palaeoclimate data indicate that Earth surface temperatures have remained largely temperate for the past 3.5 Byr despite significantly lower solar luminosity over this time relative to the present day. There is evidence for episodic early and late Proterozoic glaciation, but little evidence of glaciation in the intervening billion years. A prolonged equable Mesoproterozoic Earth requires elevated greenhouse gas concentrations. Two endmember scenarios have been proposed for maintaining global warmth. These include extremely high pCO2 or more modest pCO2 with higher methane concentrations. This paper reports on the δ13C of organic matter in 1.1 Ga stromatolites from the Copper Harbor Conglomerate (CHC) of the Mesoproterozoic Midcontinent Rift (North America) and δ18O and Δ47 temperatures of inorganic stromatolite carbonate to constrain formation and burial conditions and the magnitude of ancient carbon isotope discrimination. CHC sediments have never been heated above ~125–155°C, providing a novel geochemical archive of the ancient environment. Stromatolite Δ47 data record moderate alteration, and therefore, the occluded organic matter was unlikely to have experienced significant thermal alteration after deposition. The δ13C values of ancient mat organic matter and inorganic carbonate show isotope discrimination (εp) values ~15.5–18.5‰, similar to modern microbial mats formed in equilibrium with low concentrations of dissolved inorganic carbon. In combination, these data are consistent with a temperate climate Mesoproterozoic biosphere supported by relatively modest pCO2. This result agrees with Atmosphere‐Ocean Global Circulation Model reconstructions for Mesoproterozoic climate using 5–10 times present atmospheric levels pCO2 and pCH4 of >28 ppmv. However, given marine modelling constraints of CH4 production that suggest pCH4 was below 10 ppm, this creates a methane paradox. Either an additional source of CH4 (e.g. from terrestrial ecosystems) or another greenhouse gas, such as N2O, would have been necessary to maintain equable conditions in the Mesoproterozoic.


| INTRODUCTION
Constraints on Earth surface temperature and atmospheric composition provide critical insight regarding the evolution of the biosphere (Kasting, 1993). The Mesoproterozoic has long been considered to be part of the 'boring billion' years between the Palaeoproterozoic Huronian and Neoproterozoic 'snowball Earth' events, when there was comparatively little change in Earth surface, greenhouse gas or oceanic conditions (Shields and Veizer, 2002;Lyons et al., 2014; accompanied by relatively steady atmospheric pO 2 . More recently, however, new data indicate complex patterns of oceanic oxygenation and euxinia through time (Planavsky et al., , 2018 and suggest that by the mid-Proterozoic, atmospheric pCO 2 likely dropped to less than one quarter of the Palaeoproterozoic levels Sheldon, 2006Sheldon, , 2013. For example, Kanzaki and Murakami (2015) estimate 23-210 times present atmospheric levels (PAL) at 1.85 Ga based on palaeosol geochemistry, but a number of studies have estimated the pCO 2 of the Mesoproterozoic Bartley and Kah, 2004;Kah and Riding, 2007;Mitchell and Sheldon, 2010) and report widely varying, but generally much lower estimates. For example,  give an estimate of 10-200 PAL pCO 2 at 1.4 Ga based on the carbon isotopic composition of large microfossils, Kah and Riding (2007) give an estimate of ≤10 PAL at 1.2 Ga based on microbialite sheath calcification and a number of palaeosols from the Midcontinent Rift (Mitchell and Sheldon, 2010;Sheldon, 2013) have consistently indicated 4-6 PAL at 1.1 Ga. A fundamental question is whether or not pCO 2 of this range could maintain temperate, non-glacial conditions without an additional greenhouse gas present. Given that a variety of proxies are consistent with low atmospheric pO 2 in the Mesoproterozoic (reviewed in Planavsky et al., 2018), CH 4 would likely have been stable in the atmosphere, and given that it has a warming potential about 25 times that of CO 2 , it has often been proposed as a candidate Proterozoic greenhouse gas (Sheldon, 2013).
However, recent work suggests that anaerobic oxidation of CH 4 coupled with SO 4 2− reduction may have limited the flux of CH 4 from marine systems and potentially limited the buildup of CH 4 in the Proterozoic atmosphere (Olson et al., 2016). If this is correct, higher pCO 2 or elevated amounts of some other additional greenhouse gas would be needed to maintain temperate conditions. Constraints from the rock record (see supplemental table DR1 from Fiorella and Sheldon, 2017) indicate no evidence for glaciation at this time, except at one locality, to at least 60° N and S. New Atmospheric-Ocean Global Circulation Model (AOGCM) results show that the modest (5-10 PAL) concentrations of CO 2 could maintain a largely ice-free globe with a range of pCH 4 from 28 to 280 ppmv (Fiorella and Sheldon, 2017), although a completely ice-free globe is only possible at the highest total greenhouse gas loads. Thus, Zhao et al. (2017) have described the late Mesoproterozoic as a potential methane paradox.
Morphological evidence for microbialite abundance and diversity indicate maxima for both during the Mesoproterozoic (Noffke and Awramik, 2013). Some argue that this is due to the evolution of new carbonate concentration mechanisms in the sheaths of cyanobacteria (Riding, 2011) that could have evolved in response to changing atmospheric conditions. Continental environments might have been even more chemically favourable for habitation than marine environments (Parnell et al., 2015) at this time. A range of evidence supports episodic glaciation during the early and late Proterozoic (Kaufman et al., 1997;Kennedy et al., 1998;Walter et al., 2000;Kendall et al., 2004), but there is little or no evidence of prolonged, widespread glaciation during the Mesoproterozoic (table S1 of Fiorella and Sheldon, 2017). Thus, the inferred increase in microbialite abundance and diversity occurs during a time of clement conditions and of broad potential ecological niches including marine (Kah et al., 1999), transitional (Beghin et al., 2017) and terrestrial environments (Wellman and Strother, 2015). In total, biological and sedimentological evidence suggest a robust biosphere with globally temperate, ice-free conditions during this prolonged interval. If the Mesoproterozoic was a period of general and prolonged warmth, was high CO 2 responsible for the lack of glaciation?
This study presents new clumped and organic isotopic analyses of low thermal maturity stromatolites from Horseshoe Harbor, Michigan, within the Copper Harbor Conglomerate (CHC) of the Mesoproterozoic-aged Midcontinent Rift. Recent work demonstrates that these mats and associated geologic formations are minimally altered and have experienced limited heating in the 1.1 Byr since deposition (Nishioka, 1984;Gallagher et al., 2017). Clumped isotope temperatures provide some constraint on maximum formation temperatures and the potential for burial alteration of the organic isotopes, making it possible to use paired records of organic and inorganic carbon isotopes as a semi-quantitative indicator of atmospheric gas concentration.

| Midcontinent Rift System
The Midcontinent Rift System (MCR; Figure 1) represents a widespread, failed continental rifting event that is characterized by large-scale emplacement of flood basalts that occurred in multiple pulses of volcanism ~1.1 Ga (Davis and Paces, 1990;Hutchinson et al., 1990;Ohr, 1993;Cumming et al., 2013). Rifting and extension are associated with widespread sedimentary deposition during early rift subsidence and record a classic continental rift sequence of alluvial fan sediments that transition to lacustrine and fluvial systems (Elmore et al., 1989;Sheldon, 2009, 2016). These igneous and clastic sedimentary units are collectively referred to as the Keweenaw Supergroup (Morey and Ojakangas, 1982). On the eastern side of the rift, this includes lower volcanic strata through sedimentary strata of the Oronto Group, terminating in overlying sandstone units.
In Michigan (USA), the clastic sediments of the Oronto Group consist of the CHC, Nonesuch and Freda formations, corresponding to the alluvial fan, lacustrine and fluvial deposits that span the rift interval (Elmore, 1984, Elmore et al., 1989.The main stage of the MCR (Figure 1) occurred over a period of less than 50 Myr (Cannon and Hinze, 1992) and rifting was soon followed by regional compression that drove reactivation and reversal of rift-bounding faults (Stein et al., 2015) associated with uplift of rift sediments. The rapid process of rifting and resultant regional compression means that rift sediments ( Figure 1) were shallowly buried and minimally heated in some parts of the rift (<125°C; Mauk and Hieshima, 1992). This is due to the absence of large regional tectonic deformation in the mid-continent and the relatively short duration of rifting (Pratt et al., 1991;Price et al., 1996). The MCR experienced prehnite-pumpellyite grade metamorphism in places close to the basin-bounding faults, but thermal history models of available temperature constraints from the Nonesuch and CHC formations within the MCR indicate both low peak burial temperatures and a relatively short duration of burial before unroofing (Gallagher et al., 2017). Fluid inclusion studies of CHC microbial mats show that isolated inclusions homogenize at temperatures as low as 53-88°C (Nishioka et al., 1984). These low temperatures contrast with fluid inclusion data from carbonates directly associated with copper mineralization that show homogenization temperatures up to 119°C (Livnat, 1983). Thus, Nonesuch and CHC localities that are away from basin-bounding faults typically experienced relatively mild thermal alteration to temperatures well below experimental constraints for abiotic Fischer-Tropsch synthesis of organic compounds (i.e. 250°C, high pressure; McCollom andSeewald, 2006, Taran et al., 2007).

Conditions in the MCR
The MCR extends from Kansas to Ontario and preserves a variety of textural evidence for life (Noffke, 2009;Sheldon, 2012;Noffke and Awramik, 2013;Wilmeth et al., 2014) that support the interpretations of a widely distributed terrestrial biosphere at 1.1 Ga (Figures 2 and 3). This includes a number of fossil-bearing lake (Wellman and Strother, 2015), pond (Elmore, 1983) and floodplain deposits (Sheldon, 2012) that preserve an array of acritarchs, stromatolites and microbially induced sedimentary structures. The stromatolites are found primarily in the CHC at two localities, and are interpreted to have formed in the distal parts of an alluvial fan where braided streams emptied into a large lake system associated with the Nonesuch Formation shale and mudstone deposition ( Figure 2). These sediments display similarities to modern playa mudflats (Nishioka et al., 1984) and preserve evidence of desiccation features in both mudflat/ sandflat and braidplain facies (Fedorchuk et al., 2016). Stromatolitic structures show alternation between detrital and carbonate laminae (Figures 2 and 3), with radial calcite overgrowths in some areas of the laminae (Elmore, 1983), and both abiogenic and biogenic forms have been identified (Fedorchuk et al., 2016). Both within the CHC (Wilmeth et al., 2014) and elsewhere within the MCR (Sheldon, 2012), other domal microbialite features have been noted, including some with preserved organic matter, suggesting a wide array of potential microbial communities and inhabited environmental niches at this time. Previous workers have demonstrated the potential for using the clumped isotope composition of similar microbialites in the geologic record to reconstruct environmental conditions at the time of their formation in lake and lake-margin deposits. These studies show that modern and ancient microbial carbonates reasonably record the temperature of the past surface water conditions, though they may be biased by variations in timing of precipitation or formation depths (Frantz et al., 2014;Petryshyn et al., 2015).

| METHODS
Stromatolites within CHC sediments at Horseshoe Harbor contain both calcitic laminae preserved in fine growth layers and sparite present in in-filled voids and larger, secondary fractures (Elmore, 1983(Elmore, , 1984. Samples were collected from the CHC in 2011, cut using a solvent-cleaned, watercooled rock saw and polished using a diamond grit polish. Thin sections were analysed to identify areas with no or minimal alteration of primary laminae. Samples of pristine carbonate laminae and secondary sparite were drilled at low speed using a Micromill to evaluate potential spatial variability in isotopic data. Drilled areas were specifically chosen to minimize any potential contamination with visible secondary carbonate. This had the effect of limiting the sample size available for analysis. Carbonate powders were reacted with 105% anhydrous phosphoric acid in a common acid bath at the University of Michigan (UM) and analysed for δ 13 C, δ 18 O and Δ 47 on a Thermo Scientific MAT 253 Mass Spectrometer following established extraction and data reduction procedures (Defliese et al., 2015; Methods S1). For organic δ 13 C, carbonate was removed via reaction with weak HCl and analysed at UM on a Costech Elemental Analyzer attached to a Thermo Delta V. The Δ 47 values were corrected for the temperature of acid reaction (Defliese et al., 2015) and normalized relative to the Absolute Reference Frame of Dennis et al. (2011). Stromatolitic material contains a relatively high abundance of organic matter that can pose a challenge to reliable clumped isotope measurements. Analytical methods ensured samples presented had low Δ 48 and Δ 49 values. Isotopic data are included in Tables 1-3. Mean Δ 47 values of UM Carrara after normalization were 0.397 ± 0.007 and 0.406 ± 0.007 during the analytical period. SEs for Δ 47 temperature estimates were ~2.6 to 6°C for unknowns, with the exception of two samples that show considerably higher uncertainty (11.7°C), possibly due to heterogeneity of the carbonate powder as a result of inclusion of trace amounts of secondary, higher temperature sparite during the micro-drilling process. Reproducibility for conventional carbonate δ 13 C and δ 18 O and organic carbon δ 13 C was better than 0.2‰ for all analyses. All of the measured and calculated geochemical data are presented in Tables  1-3 and raw data in Data S1. All data were collected prior to the establishment of current background and 17 O correction procedures (Bernasconi et al., 2018;Peterson et al., 2019), which can result in higher analytical uncertainties than present.

| Carbonate geochemistry results
Thin section analyses of mat carbonates show finely laminated layers ( Figure 3B,C) with organic matter bound, in parts, by coarse-grained, anhedral microsparite that is readily distinguished from laminated carbonate. Stromatolite microfabrics contain light-dark laminae ~20 μm to several millimetres thick and consist of calcite and a mix of detrital material (Elmore, 1983(Elmore, , 1984 (Defliese et al., 2015). These data show a consistent, but small offset between primary and secondary carbonate Δ 47 , indicating infilling of void space by secondary calcite after burial. Secondary carbonate may bias primary carbonate material via infilling of microvoids in the carbonate fabric that may be difficult to separate when sampling. The Δ 47 temperatures are used for two purposes: (a) to provide constraints on potential diagenetic temperatures affecting organic carbon associated with the mats and (b) to provide reasonable bounds to calculate the δ 18 O of fluids in equilibrium with the carbonate using the temperaturedependent fractionation factor (Kim and O'Neil, 1997). Δ 47 temperatures may also provide an upper bound for formation temperature, as secondary processes are unlikely to produce cooler temperatures. The Δ 47 temperatures and δ 18 O carb yield water compositions of −1.7 to −5.4‰ for T°C = 25 and 40°C (Table 3), consistent with a range of fresh meteoric waters at low latitude, although calculated fluid compositions have the potential to be biased by any post-depositional solid-state bond reordering that could have affected clumped isotope temperatures.

| Organic geochemistry results
Copper Harbor Conglomerate stromatolites contain 0.04-0.22 wt% organic carbon within carbonate laminae. In areas with no visible recrystallization, it is assumed that this organic matter reflects primary Mesoproterozoic organics, unmodified by any post-depositional thermal processes (see "Preservation potential of Carbonate Δ 47 During Burial and Sediment Diagenesis"). The δ 13 C org values range from −24.0 to −27.4‰ (Table 2) and are comparable to δ 13 C org from contemporaneous floodplain sedimentary rocks from the MCR (−26 to −29‰; Sheldon, 2012) (Imbus et al., 1992). Imbus et al. (1992) note that consistency between CHC mat carbonate δ 13 C and Nonesuch layered carbonate δ 13 C suggests a common Dissolved Inorganic Carbon (DIC) source for these associated sediments.

| Preservation potential of Carbonate Δ 47 During Burial and Sediment Diagenesis
The Δ 47 data from mat carbonates have the potential to record Mesoproterozoic temperature; however, there are a number of potentially significant uncertainties associated with interpreting Δ 47 data from 1.1 Ga microbial carbonates. This is particularly true when relating measured temperature to environmental conditions at the time of mat formation. Thus, it is suggested that measured Δ 47 temperatures do not necessarily reflect primary formation temperature, but could record a combination of formation temperature plus secondary effects that bias primary signatures. First, a number of authors have identified deviations from the experimental temperature-Δ 47 calibration line for equilibrium precipitation (Ghosh et al., 2006) that may result from kinetic isotope effects (Ghosh et al., 2006;Affek et al., 2008;Tripati et al., 2010;Daëron et al., 2011;Saenger et al., 2012;Eagle et al., 2013). This has the potential to influence interpreted carbonate formation temperature. If mat carbonate forms at or near equilibrium, Δ 47 from CHC mats should yield reliable temperature estimates, barring secondary alteration or solid-state reordering. However, if the carbonates formed via rapid CO 2 degassing (Affek et al., 2008), kinetic effects could decrease recorded Δ 47 values, producing an increase in apparent temperature. Recent work by Petryshyn et al. (2016) shows that modern microbial mats yield Δ 47 temperatures within error of summer water temperature for non-diagenetically altered carbonates. However, ancient mat carbonates from the Eocene Green River Formation (Frantz et al., 2014) are also shown to reproduce surface water temperatures reasonably well. Thus, while the extent of kinetic bias on temperature relationships are at present unknown, microbial carbonate temperatures recorded by carbonate Δ 47 are generally consistent with modern environmental conditions, but represent at best a seasonal maximum. This result is similar to Δ 47 in other lacustrine carbonates that are shown to record warm season temperatures (Hren and Sheldon, 2012). Second, solid-state bond reordering has the potential to alter Δ 47 values over 1.1 Ga and at moderate temperatures (Henkes et al., 2014). This becomes a greater probability with increasing burial temperature and time. Thus, Δ 47 values from Proterozoic carbonates should be viewed cautiously as a record of primary T °C and most likely represents a combination of primary temperatures and an unknown degree of thermal reordering. For CHC stromatolites, potential post-depositional Δ 47 alteration is likely minimized by low burial depths and temperatures. The coolest stromatolitic Δ 47 temperatures measured are <30°C and mean sparite Δ 47 temperatures are all lower than 54°C. Clumped isotope temperatures therefore likely show minor thermal alteration during shallow burial heating since the Mesoproterozoic. Biomarker and clay mineral thermometry support low regional MCR burial temperatures (100-125°C) (Nishioka et al., 1984;Pratt et al., 1991), but far warmer than measured mat Δ 47 values. Regional temperatures from clay and biomarker data are consistent with recent clumped isotope results from the MCR White Pine Mine, that show spatially variable hydrothermal temperatures (49-116°C) in association with zones of copper mineralization, and fluid inclusions show equilibration temperatures of 53-88°C (Nishioka et al., 1984). If the MCR experienced prolonged periods of high temperature (>125°C) for tens of millions of years, this could have the effect of resetting primary Δ 47 results to lower values (higher T °C) (Gallagher et al., 2017). The highest measured Δ 47 temperatures in the MCR are found in areas with obvious alteration of primary carbonate and closest to the major bounding Keweenaw Fault. Results from altered CHC carbonates relatively close to the Keweenaw Fault show the lowest Δ 47 temperatures of the MCR even within the alteration zone (~70°C; Gallagher et al., 2017). The sample location of Horseshoe Harbor, wellremoved from the Keweenaw Fault, suggests that it is within one of the lowest thermal alteration zones of the whole MCR and thus would be expected to have the least thermal impact from either burial or primary ore-related fluids. This is supported by fluid inclusion data that show the lowest closure temperatures are found within mat carbonates at Dan's point, near the sampling locality used for this paper (Nishioka et al., 1984). In the absence of recrystallization, post-depositional alteration is expected to decrease bond ordering (Henkes et al., 2014) and Δ 47 values, resulting in higher calculated temperatures. Bond-reordering experiments predict that the Δ 47 temperatures preserved by stromatolites could in fact reflect primary or early diagenetic crystallization temperature (Henkes et al., 2014;Shenton et al., 2015). Regardless, the low temperatures recorded in mat carbonate Δ 47 suggest minimal temperature effects due to bond reordering.
In addition to the effects of bond reordering, shallow-water carbonate diagenesis can introduce alteration of primary geochemical signatures within ancient carbonates Higgins et al., 2018). In particular, variations in the extent and style of early diagenesis can influence whether the composition of the carbonate mineral is determined by chemistry of the fluid or by the precursor sediment. This results from the fact that the transformation of metastable carbonate minerals to more recalcitrant forms, such as limestone or dolomite, involves exchange between mineral and pore fluids that can translate to fluid-buffered exchange for one element such as O and sediment buffered for another such as C . Indeed, Swart (2008) argues that stratigraphic variations in Neogene marine carbonate δ 13 C could be explained, in part, due to mixing of pelagic and platform C sources with distinct δ 13 C values. Higgins et al. (2018) suggest that observed Neogene carbonate δ 13 C trends could reflect changes in the extent of diagenetic alteration of aragonite to calcite under fluid-buffered conditions. Thus, changes in relative sea level could in fact account for much of the variability in the Neogene marine δ 13 C record.
CHC stromatolites are comprised of primary calcite microlaminae in association with secondary sparite outside the mat. Early diagenetic transformation of metastable carbonate phases to more stable calcite could bias the carbon isotope signature preserved in these samples if the process occurred under fluid-buffered versus sediment-buffered conditions. Carbon is typically assumed to be robust to diagenetic alteration due to sediment buffering of a carbonate-rich system. This contrasts with oxygen, which is more likely to be fluid buffered due to the relative abundance of water during diagenesis. High burial temperatures could result in significant degradation of sedimentary organic matter associated with thermal cracking and shift the DIC pool closer to organicderived carbon sources. Carbonate δ 13 C and δ 18 O values for CHC mat calcite and secondary sparite are similar despite different modes and timescales of genesis, with no consistent relationship between Δ 47 , δ 13 C and δ 18 O data. While one cannot exclude fluid-buffering of the carbon pool during any transformation of metastable mat carbonate to calcite, it is assumed here that mats represent primary or sediment-buffered conditions for carbon and either sediment-buffered or fluid-buffered system for oxygen.
Due to the 1.1 Ga age of the CHC, Δ 47 values of non-recrystallized primary carbonate most likely represent a mixed primary and secondary signature. Processes of non-equilibrium kinetic isotope fractionation and diagenetic alteration of primary carbonate after formation are all expected to yield temperatures higher than conditions during formation, as there is no convincing mechanism for producing colder temperatures via secondary processes after burial. Thus, while other geochemical studies such as magnetic susceptibility  could potentially provide additional constraints on the extent of possible diagenetic alteration of primary carbonate for the CHC mats, it is believed that the low temperatures preserved in stromatolitic carbonate record maximum crystallization temperature at or soon after formation. There is no simple scenario to explain the generation of cooler Δ 47 temperatures due to burial for a billion years and briefly, at temperatures up to 125°C. Thermal history modelling of the MCR indicates that for a carbonate formed at 25°C, temperatures >140°C would be required to alter clumped isotope temperatures by more than +10°C, with no increase in apparent clumped temperature for burial at 125°C (Gallagher et al., 2017). Thus, because the maximum alteration temperatures were at or below that threshold, Δ 47 data could provide a maximum T °C of the palaeoenvironment but no information on whether or not conditions were significantly cooler than this. These data do indicate, however, that the mat carbonates did not experience enough heating to fully reset clumped isotope data.
Despite uncertainty in the absolute temperature of formation, Δ 47 data record a maximum formation temperature of less than 30°C. The low temperatures recorded by stromatolite carbonate within the CHC as well as associated sparite suggests that organic carbon occluded within these same layers also likely did not experience significant thermal degradation or recrystallization associated with higher burial temperatures. Significant alteration of kerogen δ 13 C values only occurs at much higher temperatures (>500°C; Peters et al., 1981;Schoell, 1984), and abiogenic generation of isotopically depleted values requires both high temperature and high pressure (McCollom and Seewald, 2006). Based on this, it is assumed that neither carbonate nor organic matter carbon isotopic compositions are likely to have been altered dramatically from primary compositions.

Carbon isotopes and Implications for Mesoproterozoic pCO 2
A number of authors have used organic δ 13 C data to quantify the concentration of DIC (Eichmann and Schidlowski, 1975;Popp et al., 1989), most commonly with free-floating aquatic organisms that can take up aqueous CO 2 directly from the surrounding water. This approach is founded on the observation that autotrophic photosynthetic carbon fixation involves transport of inorganic carbon to the site of fixation and binding with the C-fixing enzyme (O'Leary, 1981;Farquhar et al., 1982). In aqueous environments and for organisms without active CO 2 transport, the δ 13 C of fixed carbon is controlled by the rate of diffusion of CO 2 to the fixation site and the isotopic composition of the dissolved CO 2(aq) pool. The overall isotope effect can be described by: where ε p equals the isotope effect associated with C fixation, ε t = fractionation associated with CO 2 diffusion (ε tw = −0.7‰ in water), ε f = isotopic fractionation associated with C fixation by the Rubisco enzyme (~−29‰) and p i and p a reflect the internal and ambient pCO 2 (O' Leary, 1981;Farquhar et al., 1982;Popp et al., 1989). Such an approach provides a reasonable estimate of the effect of carbon limitation (i.e. concentration) on isotope discrimination. In an aqueous system, the isotope effect can be described by ε p = ([δ p + 1,000)/(δ d + 1,000]−1) 1,000 where δ p represents organic fixed carbon and δ d the DIC. The δ 13 C aq is recorded by δ 13 C carb , and follows the temperature-dependent fractionation between DIC and calcite (Deines et al., 1974). The δ 13 C org represents δ p and is paired with δ 13 C DIC to quantify carbon isotope discrimination during biosynthetic C fixation. Inorganic carbonate δ 13 C may be related to δ 13 C CO 2aq using the temperature-dependent fractionation between CO 2(g) and CO 2(aq) (Deines et al., 1974).
The CHC microbial mats were formed in a braidplain system (Elmore, 1983(Elmore, , 1984Sheldon, 2012;Wilmeth et al., 2014;Petryshyn et al., 2015;Fedorchuk et al., 2016) and preserve ancient organic carbon, as well as mat-associated carbonate. As a result, these systems record the isotopic composition of fixed organic carbon and the DIC that may have been utilized for C fixation during growth in these systems. Microbial mats present a more complex system with respect to carbon cycling/diffusion than individual free-floating cellular organisms, yet the fundamental principles of carbon discrimination remain unchanged. Mats can be treated effectively as an ecosystem that ultimately is limited by the same factors (carbon, major and minor nutrients, nitrogen and available chemical or light energy) as a single cell. Mat organic carbon and carbonate δ 13 C are used to provide bounds on carbon discrimination during mat formation that can be related to general carbon limitation. For photoautotrophs, this is ultimately limited by the DIC pool, which in many cases is controlled by atmospheric pCO 2 . The δ 13 C calcite is used to constrain δ 13 C aq following Deines et al. (1974) using an assumed temperature of 25 and 40°C. These temperatures are consistent with surface conditions proposed by Fiorella and Sheldon (2017) for these palaeolatitudes under a variety of greenhouse gas scenarios, as a plausible but poorly constrained palaeotemperature. Reconstructed clumped isotope temperatures from the CHC stromatolites of 22-44°C provide some additional support for this range of potential mat environmental conditions. Mean δ 13 C aq values range from −10.8 at 25°C to −9.6‰ at 40°C (Table 3). Combined with mean organic carbon δ 13 C of stromatolite laminae (−25.8‰), these data yield calculated ε p values of 15.4-16.7. If the most depleted organic carbon isotope values represent the primary δ 13 C org , absolute ε p values for CHC mats range from 17.1 to 18.4.
Stromatolite carbon isotopes and ε p can be related to DIC concentrations and ultimately ambient CO 2 if (a) the mechanisms of carbon fixation/mat formation are known and (b) modern isotope systematics show a relationship to ambient HREN aNd SHELdON CO 2 in the environment of formation. A variety of mechanisms drive the formation of carbonate within stromatolitic mats (Dupraz et al., 2009), including uptake of CO 2 during photosynthesis and degassing of CO 2 from waters. Depending on the formation environment, aqueous systems may be in varied states of CO 2 disequilibrium relative to the atmosphere. The CHC mats are draped over large cobbles, formed on conglomeratic lenses and infilled with sands, gravels and silts associated with the alluvial fan of the Mesoproterozoic Rift (Figure 2). Associated with these stromatolites are intact mud-cracks and ripples, some containing gypsum, as well as recognized exposure surfaces (Elmore, 1983(Elmore, , 1984 that indicate a shallow, episodically sub-aerial and variableenergy aqueous system. CHC mats were formed in shallow water, within the photic zone. In addition, acritarchs found in associated sediments (Wellman and Strother, 2015) and carbon isotopes of organic matter within the CHC mats and penecontemporaneous floodplain mats (Sheldon, 2012) strongly suggest phototrophy as a key metabolism. Thus, it is highly probably that CHC mat carbon fixation was underpinned by phototrophic metabolism. Growth waters were likely at least somewhat mixed with respect to the atmosphere. Environments characterized by high shear stress have potential to inhibit microbial mat accumulation; thus, mat structures preserved in the CHC could have formed during intervals of greater quiescence within an otherwise turbid system (Elmore, 1983). Such conditions would be more prone to restriction, with mat accumulation representative of low energy intervals. However, regular intermixing of coarse sand and sediment as well as large cobbles within mat layers indicates that the frequent intervals of turbidity were likely a regular feature of the system ( Figure 2C). Furthermore, direct association of mats with ripples strongly support growth in an environment with moving water that is likely to have greater exchange of dissolved gases between the aqueous environment and the atmosphere.
The second condition that must be met to relate mat carbon isotopes to ambient CO 2 is that modern mats must show a relationship between DIC, pCO 2 and carbon discrimination. Chemostat experiments show that ε p of photosynthetic autotrophs is controlled by dissolved CO 2 , nutrient availability, growth rate and, for single cells, cellular volume to surface F I G U R E 4 Carbon isotope discrimination (ε p ) between mat organic matter and CO 2(aq) for modern microbial mats from alkaline, evaporative marine and hydrothermal systems. For reference, ε p data and predictions for single-celled aquatic organisms as a function of CO 2(aq) are shown. Solid lines represent the empirically derived relationships between C isotope discrimination and CO 2(aq) for single-celled organisms with a volume to surface area (V/S) ratio of 5 and varied growth rates (μ/d) after Laws et al. (1995). Gray shaded area shows the calculated ε p values for CHC mats. The CHC mats yield ε p values compatible with modern mats in waters with low CO 2(aq) , and fall below the empirical relationship for slowgrowing photoautotrophs (μ = 0.2) with moderate to high V/S ratios. The ε p data are compatible with mats formed in waters with CO 2(aq) that is equivalent to less than ~20 PAL, and most consistent with Mesoproterozoic pCO 2 of less than several times PAL

pCO2 (ppm) [CO2(aq)] µM
Modern Mats, Alkaline Pool, British Columbia, Brady et al., 2013Shark Bay, Pages et al., 2014Orakai Hot Springs, DesMarais, 1992Laws et al., 1995McCabe, 1985 Modern Microbial Mats Modern Single-Celled Aquatic Organisms area ratio (V/S) (Popp et al., 1989;Laws et al., 1995;Dupraz et al., 2009) (Figure 4). In a well-mixed water body, the δ 13 C org of individual aquatic photosynthesizers reflects isotopic discrimination associated with diffusion of CO 2 to the site of C fixation and the dissolved CO 2 is proportional to atmospheric pCO 2 . In biogenic stromatolitic mats, fine-scale carbon isotope systematics are highly variable with depth in the mat due to unique assemblages of symbiotic organisms and restrictions on gas diffusion through the mat. Despite these complexities, empirical data show that just as for freefloating aquatic organisms, the amount of dissolved CO 2 in water is generally the first-order C limitation for photoautotrophs within a mat. This limitation is in part recorded in the biomass δ 13 C of mat ecosystems, which integrate material from chemoautotrophs or photoautotrophs and the heterotrophs that feed on them or their exudates. As with singlecelled organisms, modern empirical data show that bulk mat ε p approaches a maxima when pCO 2 or dissolved CO 2 is high in the aqueous environment ( Figure 4). This empirical observation provides an important, if imperfect tool to assess past pCO 2 , particularly when estimates for atmospheric pCO 2 range from several times PAL to >100 PAL.
Studies of carbon isotope fractionation during CO 2 uptake and photosynthetic fixation show a strong dependence on dissolved aqueous CO 2 concentration (Popp et al., 1989). Under conditions of low CO 2aq and pCO 2atm , δ 13 C of organic biomass shows significantly reduced carbon isotope discrimination, while under high CO 2 availability, carbon isotope discrimination approaches a theoretical maximum (Popp et al., 1989). Data from modern microbial mat carbonates formed in marine hypersaline, freshwater alkaline and hydrothermal systems were used to calculate carbonate isotope discrimination () as a function of variable [DIC] using published δ 13 C carbonate , δ 13 C mat and DIC data (Des Marais et al., 1992;Brady et al., 2013;Pagès et al., 2014). The value is calculated after Laws et al. (1995), where ε = (1,000 (δ 13 C org −δ 13 C aq )/ (1,000 + δ 13 C org )). For clarification, the δ 13 C of organic matter was compared relative to δ 13 C aq (not δ 13 C DIC ) to quantify ε. The δ 13 C gas was calculated from the isotopic composition of associated carbonates using the empirical δ 13 C carb /δ 13 C aq fractionation factor determined by Deines et al. (1974). Figure  4 shows measured ε versus CO 2aq for modern microbial mats in alkaline pools in British Columbia (Brady et al., 2013), Orakei Hot Springs (Des Marais et al., 1992 and Shark Bay (Pagès et al., 2014), as well as data for free-floating single cell growth experiments (McCabe, 1985;Laws et al., 1995), and the pCO 2 that would be calculated for an atmosphere in equilibrium with the dissolved CO 2aq . These data provide boundary conditions for examining the isotopic values recorded by CHC mat carbonate and organic matter. The pCO 2 values associated with each ε value for modern mats do not represent true atmospheric pCO 2 , but rather the calculated pCO 2 based on the measured dissolved CO 2 concentration (DIC in μmol/l), water temperature, Henry's constant for CO 2 and assumption of equilibrium between DIC and the atmosphere. Using this approach, the calculated atmospheric pCO 2 for waters associated with carbonate-bearing microbial mats in British Columbia (Brady et al., 2013) ranges from 93 to 413 ppm with a mean of 208 ppm. Modern data for Orakei hot springs have high DIC and high CO 2aq and are not in equilibrium with the atmosphere due to high dissolved CO 2 . These produce a theoretical pCO 2atm value significantly in excess of modern and are included to demonstrate that waters in equilibrium with far higher dissolved CO 2 concentrations than the modern still follow the general patterns of carbon isotope discrimination observed in other mat systems. The modern mat C data shown here are derived from environments with flowing water, lakes and marine systems, with mixed microbial communities. All follow the general relationship between [DIC] and carbon isotope discrimination within the mat.
Modern mats exhibit smaller ε p than plants or singlecelled photoautotrophs for comparable pCO 2 , likely due to diffusion limitation at the water-mat interface, C-limited cellular growth rates and recycling of C within the mat system. The difference is greatest in modern mats in hypersaline or high temperature conditions where ε p values may range from ~1 to 14 for a range of dissolved aqueous CO 2 . Stromatolitic mats today are characterized by complex cycling of carbon that varies as a function of microbial assemblages and aqueous conditions. Thus, it is known that there can be significant variation in CO 2aq and δ 13 C org within a mat and between different mat types (Dupraz et al., 2009). This heterogeneity was likely no different in the deep past. For example, Lepot et al. (2009) show large variability in δ 13 C of organic matter in 2.72 Ga microbial structures, highlighting the role of microbial metabolism in controlling isotope heterogeneity on the micron scale and larger. Despite this, microbial mats are ecosystems comprised of an array of communities assembled into effectively a single structure. All organisms within this system are ultimately limited by one or more nutrients, including carbon. From an ecosystem perspective, modern data provide semi-quantitative boundary conditions for interpreting ancient mat systems, particularly when considering ancient systems for which some suggest pCO 2 was in excess of 30-100 PAL. Modern data demonstrate that for most shallow mat systems within the photic zone with a significant proportion of phototrophs, mats as a whole are sensitive to large changes in CO 2aq , producing a large increase in ε for only modest increases in CO 2aq . A mat within a mixed aquatic system can effectively be thought of as a system with a very large volume to surface area ratio (surface area being the exposed interface between the mat and ambient water), whereas under quieter conditions, effective volume to surface area would be lower. Modern mat isotope data match reasonably well (Figure 4) with CO 2 -carbon isotope sensitivity observed in modern free-floating low volume to surface area microbes with slow growth rate (McCabe, 1985;Laws et al., 1995).
One potential complication to the approach used here to constrain past DIC and ultimately pCO 2 , is if CO 2 was not the primary C source supporting the mat system. For example, Olsen et al. (2016) suggest that marine methanotrophy coupled with sulphate reduction could have been an important component of C and S cycling in the Mesoproterozoic, serving as a limit to buildup of CH 4 in the atmosphere. If the mat ecosystem was dominated by methanotrophy with CH 4 available via sources outside the mat, this would render expected relationships between mat δ 13 C and atmospheric pCO 2 (by virtue of the relationship with DIC) void. Methanotrophs can derive energy via either anaerobic or aerobic pathways. In the modern, mats underpinned by anaerobic methanotrophy are observed in areas of methane and other hydrocarbon seeps and often associated with sulphate reduction (Drake et al., 2015). In benthic mats near seeps, methanotrophy may contribute nearly 50% of total fatty acids in mat organics (Ding and Valentine, 2008). However, CHC mats are located in a relatively shallow ancient braidplain and are associated with mud-cracks and gypsum, indicating at least somewhat oxic conditions and free sulphate at or around the time of mat formation. In addition, anaerobic methanotrophy is known to generate some of the most depleted δ 13 C values in carbonate (−125‰; Drake et al., 2015). While it is impossible to rule out methanotrophy as an important metabolism within CHC mats, fossil evidence of phototrophs and δ 13 C data are consistent with phototrophy.
Carbonate and organic δ 13 C data from CHC stromatolites are coupled with clumped isotope temperatures to provide reasonable boundary conditions for δ 13 C CO 2aq , ε p and CO 2aq . Because mat samples derive from a system with at least intermittently moving water ( Figure 2) and underlain by non-carbonate bedrock, it is assumed that limitation to CO 2 diffusion into or out of the water system is far less than within the mat system. Thus, even in slow or occasionally stagnant water, CO 2 diffusion into the mat is likely the primary limitation to carbon assimilation within the mat as a whole. With these assumptions, modern data provide reasonable, if imprecise limits for interpreting palaeo-ε data with respect to ancient CO 2aq and pCO 2 within the palaeoenvironment. Specifically, carbon discrimination data from modern hot springs are used as an upper limit for ε p -pCO 2 relationships in the ancient. Measured ε p values for the Proterozoic stromatolites range from 15.4 to 18.4 for temperatures of 25-40°C. Modern mat ε p values are all less than 21‰ and mats that record an ε p of less than 18‰ are found in waters in equilibrium with DIC of less than 130 μM, consistent with a pCO 2 effectively less than 1,000 ppm. Modern mat carbon discrimination data generally follow the pattern of ε p versus DIC observed in slow growing cells with moderate to high volume to surface area (Figure 4). The ε p data for CHC mats are equivalent to modern mats grown in waters with DIC and in theoretical equilibrium with pCO 2 of less than ~20 PAL, and most consistent with mat data for waters in equilibrium with pCO 2 of less than several times PAL. While pCO 2 estimates based on δ 13 C org −δ 13 C DIC require accurate measurement of primary δ 13 C p and δ 13 C aq and optimally, equilibrium between the DIC and the atmosphere, these limits are consistent with palaeosol (Sheldon, 2006(Sheldon, , 2013, single organism carbon discrimination  and fossil carbonate-based (Bartley and Kah, 2004;Kah and Riding, 2007) estimates for late Mesoproterozoic pCO 2 ( Figure 5). Thus, CHC stromatolite data are consistent with both temperate palaeoenvironmental conditions and relatively low pCO 2 .

| Comparison of Temperature, pCO 2 and Mesoproterozoic AOGCMs
Reconstructions of the past solar insolation indicate that a 'faint young Sun' paradox exists throughout the Precambrian wherein equable conditions would need to have been maintained in the presence of significantly lower insolation that has increased steadily from less than 70% of the present day value over the past 4.5 Ga (Gough, 1981). Recent work by Fiorella and Sheldon (2017) using 91% total solar insolation (Gough, 1981) shows that an equable Mesoproterozoic climate could have been maintained by increased CH 4 flux from methanogenic bacteria even in the absence of strongly elevated pCO 2 . The AOGCM outputs show that ice-free conditions could be maintained for pCO 2 < 10 PAL with the threshold for regional-scale glaciation occurring with CH 4 at 28 ppmv or pCO 2 below 5 PAL. These results are in agreement with temperatures for ~30° latitude predicted by AOGCM simulations of the Mesoproterozoic using these boundary conditions ( Figure 6). Recent work by Olson et al. (2016) suggests that anaerobic oxidation of CH 4 coupled with SO 4 2− reduction could act as an obstacle to CH 4 accumulation in the atmosphere, limiting pCH 4 to less than 10 ppmv if the only source of CH 4 is marine production, independent of pO 2 . If both the AOGCM results (Fiorella and Sheldon, 2017) and modelled CH 4 fluxes are correct (Daines and Lenton, 2016;Olson et al., 2016), a paradox develops because the apparent CH 4 level would be too low to support the observed equable conditions. There are at least two potential solutions to this paradox. The first is that a marine-only model of CH 4 flux underestimates the total biogenic CH 4 flux. As noted above, there is extensive evidence for a significant lake and floodplain biosphere (Elmore, 1983;Sheldon, 2012;Wellman and Strother, 2015) by the Mesoproterozoic and many stable isotopic values from those systems, especially in palaeo-lake sediments (Imbus et al., 1992), are too negative to have been the result of C derived only from photosynthetic means. Thus, a potentially large terrestrial biogenic CH 4 flux is supported by existing constraints. This idea was recently tested by Zhao et al. (2017) who modelled the potential for a significant terrestrial CH 4 flux to supplement the marine CH 4 flux. They found that if terrestrial cyanobacterial mats covered 8%-10% of the Earth's surface, clement conditions would have been maintained even at the relatively low pCO 2 values indicated by palaeosols (Sheldon, 2013) and, as reported herein, microbialites. Secondly, atmospheric model simulations have typically focused on a narrow range of greenhouse gases that include CO 2 , CH 4 and sometimes H 2 O vapour (cf. Roberson et al., 2011). However, there are a number of other greenhouse gases that have significantly higher climate forcings than CO 2 that are poorly constrained in the geologic record. For example, as Fiorella and Sheldon (2017) noted, one potential way to reconcile differences in CH 4 levels is with N 2 O (e.g. see Roberson et al., 2011). While there are no direct proxies for pN 2 O, a 10-fold increase from the modern value of 0.3 ppm would provide enough additional greenhouse forcing to offset a fivefold lower pCH 4 value. Thus, there are at least two potential solutions to the apparent CH 4 paradox that would bear further investigation. Ultimately, the development of proxies for greenhouse gases beyond CO 2 would substantially enhance our ability to reconcile the challenges presented by the 'faint young Sun' paradox across the whole of the Precambrian. F I G U R E 5 Proterozoic pCO 2 ranges. Gray shaded area shows upper and lower pCO 2 limits for an ice-free (20°C) and glacial (5°C) world based on photochemical model estimates (Kasting, 1987). Calculated pCO 2 estimates (<20 PAL and most likely <5 PAL) agree with (A) cyanobacterial calcification (Kah and Riding, 2007), (B) minimum isotopic , (C) palaeosol mass balance (Sheldon, 2006(Sheldon, , 2013Mitchell and Sheldon, 2010) and (D) carbon reservoir modelling (Bartley and Kah, 2004) estimates. These data support equable Mesoproterozoic temperatures and low pCO 2 . These data indicate that CH 4 or some other greenhouse gas (e.g. N 2 O) likely played a role in regulating global temperature and provided a negative feedback to the buildup of atmospheric oxygen (figure modified from Kah and Riding, 2007)  F I G U R E 6 Calculated zonal mean temperatures for the Mesoproterozoic using boundary conditions of 5 PAL CO 2 (bottom line) and 10 PAL and 140 ppm CH 4 (top line) and Mesoproterozoic palaeogeography (Fiorella and Sheldon, 2017). Upper boundary for Mean Annual Air Temperature (MAAT) for the tropics and/or near tropical regions (<30° latitude) is shown (circle and shaded area) based on stromatolite Δ 47 temperature data that may reflect a combination of primary and/or early diagenetic alteration of original clumped isotope signatures

| CONCLUSIONS
Sedimentary features and organic and inorganic carbon isotope data from 1.1 Ga stromatolites in the CHC indicate formation in waters with relatively low DIC. This most likely results from equilibrium with a relatively low atmospheric pCO 2 (less than 20 PAL; Figures 4 and 5) during a time when solar luminosity was ~9% lower than today. If pCO 2 was indeed lower than this bound, elevated concentrations of other greenhouse gases, such as methane, may have played a role in regulating global temperature. However, current estimates of the potential Mesoproterozoic CH 4 flux from marine environments are relatively low, creating a methane paradox. The paradox is potentially resolvable either through a relatively extensive terrestrial biosphere or through elevated levels of other greenhouse gases such as N 2 O. At present, the means to test between those hypotheses is lacking, but if biologically produced gases such as CH 4 played a key role in regulating global temperature during the Mesoproterozoic, their concentrations may have acted as a negative feedback to the buildup of atmospheric O 2 due to the potential to oxidize readily in the presence of free oxygen as well as providing global climate regulation.