Chromium Isotope Systematics in Modern and Ancient Microbialites

Changes in stable chromium isotopes (denoted as δ53Cr) in ancient carbonate sediments are increasingly used to reconstruct the oxygenation history in Earth’s atmosphere and oceans through time. As a significant proportion of marine carbonate older than the Cambrian is microbially-mediated, the utility of δ53Cr values in ancient carbonates hinges on whether these sediments accurately capture the isotope composition of their environment. We report Cr concentrations (Cr) and δ53Cr values of modern marginal marine and non-marine microbial carbonates. These data are supported by stable C and O isotope compositions, as well as rare earth elements and yttrium (REY) concentrations. In addition, we present data on ancient analogs from Precambrian strata. Microbial carbonates from Marion Lake (Australia, δ53Cr ≈ 0.99‰) and Mono Lake (USA, ≈0.78‰) display significantly higher δ53Cr values compared with ancient microbialites from the Andrée Land Group in Greenland (720 Ma, ≈0.36‰) and the Bitter Springs Formation in Australia (800 Ma, ≈−0.12‰). The δ53Cr values are homogenous within microbialite specimens and within individual study sites. This indicates that biological parameters, such as vital effects, causing highly variable δ53Cr values in skeletal carbonates, do not induce variability in δ53Cr values in microbialites. Together with stable C and O isotope compositions and REY patterns, δ53Cr values in microbialites seem to be driven by environmental parameters such as background lithology and salinity. In support, our Cr and δ53Cr results of ancient microbial carbonates agree well with data of abiotically precipitated carbonates of the Proterozoic. If detrital contamination is carefully assessed, microbialites have the potential to record the δ53Cr values of the waters from which they precipitated. However, it remains unclear if these δ53Cr values record (paleo-) redox conditions or rather result from other physico-chemical parameters.


Introduction
Sedimentary carbonates are increasingly examined for their chromium isotope composition (δ 53 Cr) to investigate the evolution of oxygen in the Earth's atmosphere and oceans (e.g., [1]). Chromium mobilization from igneous rocks is dependent on oxidative weathering (catalyzed by MnO 2 ), and thus, accumulation of Cr in marine sediments requires the presence of oxygen in the atmosphere (0.0003% to 0.003% of present atmospheric levels (PAL) [2]). Changes in the redox state   Table 1). Two specimens from Marion Lake (MRN) were investigated: (a) profile A, (b) profile B. (c) Mono Lake, (d) Andrée Land Group (ALG; bulk sample not indicated), (e) Bitter Springs Formation (BSF). Table 1. Description of microbialite samples. Positions represent inner to outer parts of the microbialite samples (see Figure 1). For water sample sites and geological background, see Figure 2.

Sample Description
Marion Lake is part of a lagoon system situated in a depression on the Yorke Peninsula in South Australia (Australia; Figure 2). Due to late Pleistocene and Holocene transgressions, the depression was flooded multiple times and turned into a shallow strait. Protected by accreted coastal barriers, a marine unit of fossiliferous seagrass carbonate accumulated [40]. Subsequently, the environment evolved into a shallow lake system where gypsum deposited [40]. A proportion of the seagrass carbonate is underlying a unit of porous limestone (boxwork limestone) capped by a thin (10 cm) stromatolitic limestone (3780 ± 110 years) [41]. This stromatolitic limestone contains finely laminated undulatory stromatolites, such as the samples investigated in this study. Today, Marion Lake is a hypersaline [42] gypsum-carbonate lake on a regressive marginal flat with a connection to open marine conditions [43] and a pH of between 7.4 and 7.9 (measured in this study). Within this marginal flat, fine-grained, thinly laminated microbialites form [24,40]. They constitute low-Mg calcite and aragonite with well-preserved relics of microfossils (bacteria) and extracellular polymeric substances (EPS), and generally lack detrital material [24,40]. The lack of detrital particles and the thin micritic laminae with microfossils indicate that these carbonate precipitates were mediated by microbes [24].

Sample Description
Marion Lake is part of a lagoon system situated in a depression on the Yorke Peninsula in South Australia (Australia; Figure 2). Due to late Pleistocene and Holocene transgressions, the depression was flooded multiple times and turned into a shallow strait. Protected by accreted coastal barriers, a marine unit of fossiliferous seagrass carbonate accumulated [40]. Subsequently, the environment evolved into a shallow lake system where gypsum deposited [40]. A proportion of the seagrass carbonate is underlying a unit of porous limestone (boxwork limestone) capped by a thin (10 cm) stromatolitic limestone (3780 ± 110 years) [41]. This stromatolitic limestone contains finely laminated undulatory stromatolites, such as the samples investigated in this study. Today, Marion Lake is a hypersaline [42] gypsum-carbonate lake on a regressive marginal flat with a connection to open marine conditions [43] and a pH of between 7.4 and 7.9 (measured in this study). Within this marginal flat, fine-grained, thinly laminated microbialites form [24,40]. They constitute low-Mg calcite and aragonite with well-preserved relics of microfossils (bacteria) and extracellular polymeric substances (EPS), and generally lack detrital material ( [24,40]. The lack of detrital particles and the thin micritic laminae with microfossils indicate that these carbonate precipitates were mediated by microbes [24]. Mono Lake is located in Central California on the eastern slope of the Sierra Nevada mountain range (USA, Figure 2). Mono Lake is located in a structural basin and surrounded by mainly Cenozoic volcanic rocks [44]. The water level of Mono Lake has been affected severely by anthropogenic influence, as inflow streams were diverted to the Los Angeles Aqueduct [44]. This induced a drop in the water level of more than 12 m, as well as increased concentrations of solutes in the remaining water. Facilitated by the low water level, the annual mixing during winter has occasionally been interrupted (e.g., induced by heavy rainfalls) and lead to meromixis (e.g., [45]). Today, Mono Lake is a closed basin lake with hypersaline conditions (90 g/L), high alkalinity (pH ≥ 9.2), and high dissolved organic carbon (DOC ≈ 6.7 mM) surrounded [44][45][46][47]. Freshwater influx is delivered by streams, groundwater as well as hot springs [44,48]. Bicarbonate-rich lake water mixes Mono Lake is located in Central California on the eastern slope of the Sierra Nevada mountain range (USA, Figure 2). Mono Lake is located in a structural basin and surrounded by mainly Cenozoic volcanic rocks [44]. The water level of Mono Lake has been affected severely by anthropogenic influence, as inflow streams were diverted to the Los Angeles Aqueduct [44]. This induced a drop in the water level of more than 12 m, as well as increased concentrations of solutes in the remaining water. Facilitated by the low water level, the annual mixing during winter has occasionally been interrupted (e.g., induced by heavy rainfalls) and lead to meromixis (e.g., [45]). Today, Mono Lake is a closed basin lake with hypersaline conditions (90 g/L), high alkalinity (pH ≥ 9.2), and high dissolved organic carbon (DOC ≈ 6.7 mM) surrounded [44][45][46][47]. Freshwater influx is delivered by streams, groundwater as well as hot springs [44,48]. Bicarbonate-rich lake water mixes with a Ca-rich groundwater influx, calcite tufa precipitate mediated by microbial activity (Figure 1) [37,[49][50][51]. The precise age of the sample is unknown.
The Andrée Land Group (ALG; NE Greenland) formed approximately 720 Ma on a carbonate ramp [38]. Selected dolomitized stromatolites from ALG serve as ancient marine analogs of microbialites. The well-preserved stromatolites from the Bitter Springs Formation (BSF; Loves Creek, Australia, 800 Ma; Figure 1) belong to a unit of cyclic stromatolitic carbonates. The environmental conditions of the BSF (recently also referred to as Bitter Springs Group) changed from restricted marine to alkaline lacustrine. Our samples belonged to the Johnny Creek Formation and were deposited under non-marine evaporative conditions [39].

Sample Preparation
The microbialites were cut in approximately 1 cm 3 cubes along profiles perpendicular to the lamination or along a core to rim profile (indicated in Figure 1) to capture overall internal variations. For ALG, a larger sample (≈15 cm 3 ) was additionally analyzed and is referred to as "bulk" (ALG-B; Table 1). Microbialite samples were powdered and dissolved in 0.5 mol/L HCl, and aliquots of the dissolved samples were analyzed for major, trace, and REY concentrations as well as Cr isotope ratios. Powders of microbialite samples were additionally analyzed for their δ 18 O and δ 13 C values.

Chromium Isotope Analysis
Powdered microbialite samples containing approximately 300 ng Cr were dissolved in 0.5 mol/L HCl, centrifuged, and the supernatant was collected and filtered through 0.45 µm nylon membrane filters (Advantec MFS) before ion chromatography. The microbialite samples were spiked with an adequate amount of 50 Cr− 54 Cr double spike and evaporated to dryness [3,52,53]. Samples were then re-dissolved in aqua regia to ensure equilibration between sample and spike and dried down again. To separate Cr from microbialite samples, chromatographic Cr separation modified after [54][55][56] was applied. In short, microbialite samples were re-dissolved with 20 mL of a 0.025 mol/L HCl solution containing 0.5 mL of 0.2 mol/L (NH 4 ) 2 S 2 O 8 , capped, and boiled for 1 h to oxidize Cr(III) to Cr(VI). After cooling to room temperature, the samples were subject to an anion column containing pre-cleaned Dowex AG 1 × 8 anion resin. Next, the resin was rinsed with 10 mL 0.2 mol/L HCl, 2 mL 2 mol/L HCl and 5 mL Milli-Q™ water (18.2 MΩ cm, hereafter MQ). Chromium was then reduced and eluted with 2 mol/L HNO 3 and 5% H 2 O 2 . The eluent was evaporated to dryness, re-dissolved in 100 µL concentrated double-distilled HCl on a hotplate for 10 min, and subsequently diluted with 2.3 mL MQ. These solutions were then passed over a pre-cleaned Dowex AG50W-X8 (200-400 mesh) cation exchange resin, and the final eluents were immediately collected in Savillex TM Teflon beakers. Another 8 mL of 0.5 mol/L HCl was used to collect the remaining Cr. The final Cr sample was evaporated to dryness; matrix elements (for example, Mn, Mg, Ca, or Al) were retained in the resin during ion chromatography.
The final Cr samples were loaded onto outgassed Re filaments using 2 µL of a 2:1:0.5 mixture of silica gel, 0.5 mol/L H 3 PO 4 and 0.5 mol/L H 3 BO 3 . Both Cr concentrations and isotope ratios were analyzed using an IsotopX/GV IsoProbe T thermal ionization mass spectrometer (TIMS) equipped with eight Faraday cups at the University of Copenhagen, Denmark. Four Cr beams ( 50 Cr + , 52 Cr + , 53 Cr +, and 54 Cr + ) were analyzed simultaneously with 49 Ti + , 51 V +, and 56 Fe + beams, which were used to monitor interfering ions. Each sample was analyzed at approximately 1100 • C with a 52 Cr ion beam of between 350 and 1000 mV in 1 to 3 runs per loaded sample. Each run consisted of 120 cycles grouped into 24 blocks (5 cycles each) with 10 s integration periods and 20 s baseline measurements at ±0.5 AMU. The raw data were corrected for naturally-and instrumentally-induced isotope fractionation using the double spike routine of [53]. The corrected values are reported in delta notation (% ) with 2SD (Table 2; Equation (1)). To assess the precision of our analyses, a double-spike treated, certified standard reference material (NIST SRM 979) was analyzed two to three times, which resulted in an external reproducibility of 0.00 ± 0.13% and 0.05 ± 0.09% (2SD) for 52 Cr ion beam intensities of 500 mV and 1000 mV, respectively. Repeated analyses of certified carbonate standards (JDo-1, JLs-1) resulted in Cr and δ 53 Cr values within the range of published values [9,14,57,58]. Procedural blanks consistently resulted in Cr of <8 ng for water samples and ≈1 ng for microbialite samples.
The δ 53 Cr values of sediment samples can be corrected for detrital contamination using concentrations of Al or Ti as immobile reference elements as outlined by [54,56,59]. Briefly, detrital Cr (Cr det ) is calculated as Cr det = Al sample /Al det × Cr det . We applied a detrital correction (Equations (2) and (3)) to the results of the microbialite samples using the crustal Cr/Al ratio ((Cr/Al) det ) of [60] together with the δ 53 Cr value of the average crust (δ 53 Cr det = −0.12 ± 0.10% , 2SE; [53]).
The fraction of detritally contributed Cr (f det ) is defined according to Equation (3).

Stable O and C Isotope Analysis
Aliquots of the powdered microbialite samples (0.6-1.0 mg) were placed into 3.5 mL glass vials, sealed with rubber septa, flushed with He and allowed to react with in excess 104% phosphoric acid (H 3 PO 4 ) at 70 • C. After a reaction time of 100 min, they were routinely analysed for their stable C and O isotope values at the Analytical, Environmental and Geo-Chemistry lab at the Vrije Universiteit Brussel, Belgium, using a Nu Perspective isotope ratio mass spectrometry (IRMS) coupled with an automatic gas sampling system (GasPrep from Nu Instruments). The stable C and O isotope values are reported as δ 13 C and δ 18 O, respectively, and given in permille relative to the Vienna Pee Dee Belemnite standard (% VPDB). The reproducibility of replicated standard materials is based on analyses of the certified reference materials IAEA 603 and IAEA CO-8 along with an in-house standard (MAR-2(3)), and is better than 0.12% and 0.21% for C and O isotope values (2σ, n = 48), respectively. All samples were analysed three times; these repeat analyses were used for calculating average values and standard deviation (1SD).

Elemental Concentrations and REY
Aliquots of the dissolved microbialite samples were analysed for major, trace and REY patterns with inductively coupled plasma mass spectrometry (ICP-MS; Bruker Daltonics Aurora Elite) at the University of Copenhagen. The sample aliquots along with certified standard reference materials (limestone: JLs-1; basalt: BHVO-1) were diluted in 2% HNO 3 and analysed along with calibration solutions. The concentrations of REY were normalised ( SN ) to the Post Archean Australian Shale (PAAS; [61]). Anomalies of Y, Eu and Ce were calculated using Y/Ho SN , Eu SN /Eu [62][63][64][65]. Following [66], La concentrations were not used in the calculations as La anomalies caused by e.g., high salinity, can affect Ce SN /Ce* SN . The light REY SN (LREE) include the elements La to Eu, the heavy REY SN (HREE comprise Gd to Lu.

Chromium Concentrations and Isotope Compositions
The microbialite samples show Cr between 0.69 to 1.89 ppm in the case of modern samples, with two outliers of 3.09 and 6.09 ppm (MRN), and between 1.67 and 4.57 ppm for Precambrian samples ( Figure 3). The Cr in the microbialite samples were too low for sub-millimetric Cr isotope analysis and/or the microbialite laminae were too thin to be sampled individually, and thus, multiple laminae were sampled at a time.  Figure 1 and Table 1).

Figure 3. Cr concentrations (a) and isotope compositions (b) of microbialites and the estimated Marion
Lake water samples (dashed grey line). Numbers on y-axis indicate the sample position (see Figure 1 and Table 1). The δ 53 Cr values of all modern microbialite samples lie within a narrow range of 0.71 to 1.07% , with δ 53 Cr variations from 0.93 ± 0.05% (2SD) to 1.07 ± 0.10% for Marion Lake and from 0.71 ± 0.05% to 0.85 ± 0.14% for Mono Lake (Table 2). Ancient microbialites in this study displayed Cr isotope ranges from 0.23 ± 0.07% to 0.43 ± 0.05% and from −0.18 ± 0.06% to −0.14 ± 0.02% , for ALG and BSF, respectively ( Table 2). The samples from Mono Lake and BSF showed low Cr/Al ratios in a range similar to or higher than the reference material and are thus unsuitable for detrital correction. In contrast, detrital Cr only contributed 5 to 24% to most samples from Marion Lake and ALG samples and was thus suitable for detrital correction ( Figure 4; Table 3) [54,67]. However, the detritus-corrected δ 53 Cr values for Marion Lake and ALG samples were within the error of or only slightly higher than the uncorrected δ 53 Cr values (Table 3). Thus, we refer to uncorrected δ 53 Cr values for all samples throughout the manuscript.  Figure 1 and Table 1).

Stable O and C Isotopes
Both Lake Marion and Mono Lake microbialites displayed high δ 13 C values of between +1.97-+8.52% ( Figure 5; Table 2

Stable O and C Isotopes
Both Lake Marion and Mono Lake microbialites displayed high δ 13 C values of between +1.97-+8.52‰ ( Figure 5; Table 2). Oxygen isotope values of Lake Marion carbonate samples are +0.46-+1.73‰, which are high compared with Mono Lake samples with δ 18 O values of −2.47-−1.50‰.
The Precambrian microbialites had relatively low δ 18 O values compared with their modern counterparts. The ALG samples were only slightly lower (approximately −3.20 ± 0.37‰, 2SD) than those from Mono Lake, while the BSF samples had the lowest δ 18 O values (approximately -6.84 ± 0.29‰) of all microbialites analysed in this work. Furthermore, BSF samples had low δ 13 C values in a narrow range of −0.31 ± 0.07 to −0.48 ± 0.16‰ (SD), while ALG samples had high δ 13 C values (+3.85 ± 0.21‰, 2SD) in a similar range as Marion Lake samples.  [53]. Literature values of dolostones and limestones from the Precambrian are published in [67][68][69]. (b) Stable C and O isotope ratios, illustrating the differences in the depositional environments and/or the degree of diagenetic overprinting.

Elemental Concentrations and REY
The concentrations of specific trace (Cr) and REY elements are listed in Table 2 and Table 4, respectively. Patterns of REY are normalised to a standard reference material (Post Archean Australian Shale; [61]. The REY patterns of Marion Lake microbialites co-varied with seawater REY patterns with a near-shore depositional setting (negative Ce anomaly, positive Y anomaly, Y/HoSN ≈ 48, enrichment in heavy REY; [32,70]) ( Figure 6; Table 4). Mono Lake samples deviated from the REY pattern of the basalt standard, showing a positive Ce anomaly and a slight increase in the HREE. The Precambrian microbialites had relatively low δ 18 O values compared with their modern counterparts. The ALG samples were only slightly lower (approximately −3.20 ± 0.37% , 2SD) than those from Mono Lake, while the BSF samples had the lowest δ 18 O values (approximately −6.84 ± 0.29% ) of all microbialites analysed in this work. Furthermore, BSF samples had low δ 13 C values in a narrow range of −0.31 ± 0.07 to −0.48 ± 0.16% (SD), while ALG samples had high δ 13 C values (+3.85 ± 0.21% , 2SD) in a similar range as Marion Lake samples.

Elemental Concentrations and REY
The concentrations of specific trace (Cr) and REY elements are listed in Tables 2 and 4, respectively. Patterns of REY are normalised to a standard reference material (Post Archean Australian Shale; [61]. The REY patterns of Marion Lake microbialites co-varied with seawater REY patterns with a near-shore depositional setting (negative Ce anomaly, positive Y anomaly, Y/Ho SN ≈ 48, enrichment in heavy REY; [32,70]) ( Figure 6; Table 4). Mono Lake samples deviated from the REY pattern of the basalt standard, showing a positive Ce anomaly and a slight increase in the HREE.  The REY patterns of the ancient microbialite samples (BSF and ALG) showed less distinct REY patterns and are rather flat ( Figure 6; Table 4). They differed from typical seawater patterns, containing depleted HREE and no Y anomaly. The slight convexity of REY patterns with peak concentrations of Gd in ALG microbialites closely resembled REY patterns of shallow marine conditions [72], which are in line with the depositional environment of a carbonate ramp in a rift basin. The REY patterns of BSF showed a similar convexity as ALG, and the positive Eu resembled the basalt standard (indicated in Figure 6).

Geochemistry of Modern Microbialites
Due to their abundance in Precambrian strata, microbial carbonates have the potential to record past seawater chemistry. We present the first Cr isotope data of modern microbialites and found homogeneous Cr and δ 53 Cr values in our samples. In both studied locations, δ 53 Cr values displayed a tight range (Marion Lake: 0.99 ± 0.11‰; Mono Lake: 0.78 ± 0.14‰; Figure 3). Apart from two Cr outliers in the nucleus of the Marion Lake microbialites, we did not observe significant internal variation in Cr or δ 53 Cr values (2SD ≤ 0.14‰ per transect; n = 3 and 4, respectively; Figure 3). The outliers in Cr (Marion Lake, position 1:6.06 ppm and the adjacent sample, position 2:3.09 ppm) were sampled from and close to the nucleus of the microbialite, where Cr may have accumulated more efficiently compared with the laminae. This might be because the microbial mat started to grow around a nucleus consisting of a piece of carbonate, which perhaps originates from a different The REY patterns of the ancient microbialite samples (BSF and ALG) showed less distinct REY patterns and are rather flat ( Figure 6; Table 4). They differed from typical seawater patterns, containing depleted HREE and no Y anomaly. The slight convexity of REY patterns with peak concentrations of Gd in ALG microbialites closely resembled REY patterns of shallow marine conditions [72], which are in line with the depositional environment of a carbonate ramp in a rift basin. The REY patterns of BSF showed a similar convexity as ALG, and the positive Eu resembled the basalt standard (indicated in Figure 6).

Geochemistry of Modern Microbialites
Due to their abundance in Precambrian strata, microbial carbonates have the potential to record past seawater chemistry. We present the first Cr isotope data of modern microbialites and found homogeneous Cr and δ 53 Cr values in our samples. In both studied locations, δ 53 Cr values displayed a tight range (Marion Lake: 0.99 ± 0.11% ; Mono Lake: 0.78 ± 0.14% ; Figure 3). Apart from two Cr outliers in the nucleus of the Marion Lake microbialites, we did not observe significant internal variation in Cr or δ 53 Cr values (2SD ≤ 0.14% per transect; n = 3 and 4, respectively; Figure 3). The outliers in Cr (Marion Lake, position 1:6.06 ppm and the adjacent sample, position 2:3.09 ppm) were sampled from and close to the nucleus of the microbialite, where Cr may have accumulated more efficiently compared with the laminae. This might be because the microbial mat started to grow around a nucleus consisting of a piece of carbonate, which perhaps originates from a different depositional and temporal setting. Despite Cr outliers in the nucleus of the Marion Lake microbialites, δ 53 Cr values are consistent across laminae (0.93-1.07% ; Figure 3).
Multiple laminae were combined in individual samples, which may have homogenised sub-millimetric heterogeneity. Thus, Cr in our samples seemed homogeneous, at least on the scale sampled here. Trace elements, such as Fe, Cu, Zn, and As, are known to be heterogeneously distributed between laminae, and this can also be the case for Cr [73,74]. These elements are enriched on a sub-millimetric scale in certain laminae or mineral phases. The enrichment was attributed to passive binding of cations to EPS in the surface of a microbial mat and re-distribution into sulfide-rich laminae upon degradation of EPS during early diagenesis [73,74]. Thus, Cr is likely to show similar small-scale variations. While the methods applied in this study cannot resolve Cr variations in individual laminae, the tight ranges in Cr and δ 53 Cr values measured suggest that intra-lamina variation is minimal. Here, we focused on capturing overall internal variations since we aim to create a framework to reconstruct long-term biogeochemical changes. Similarly to the homogeneous Cr distribution, δ 13 C and δ 18 O values of our modern samples fell into a tight range at both locations ( Figure 5). The homogeneity of these geochemical tools across laminae suggests that these microbialites record relatively stable water column Cr, δ 53 Cr as well as δ 13 C and δ 18 O values.
The contribution of detrital material in Mono Lake microbialites (>57% detrital Cr) was significantly higher than the fractions of <24% determined for Marion Lake samples. This coincided with the δ 53 Cr values of Mono Lake microbialites (≈0.78% ), which were slightly lower than those of Marion Lake samples (≈0.99% ). The calculated high detrital Cr contributions were indicative of the influence of weathering of igneous rocks nearby Mono Lake, presumably carrying a typical detrital δ 53 Cr value of −0.12% . The δ 53 Cr values of Mono Lake microbialites were well above the detrital δ 53 Cr value. Still, we suggest that detrital material can have a significant impact on δ 53 Cr values in samples with high detrital Cr. Especially in samples that were deposited in environments with igneous or Al-rich lithologies and thus high background levels of Cr, detrital contamination should be carefully assessed, even if their Cr isotope compositions are above typical detrital δ 53 Cr values.

Biological Controls on δ 53 Cr Values in Modern Microbialites
The homogeneous Cr distribution and δ 53 Cr values we observed in our microbialites contrast the heterogeneous Cr distribution and highly variable δ 53 Cr values measured in modern skeletal carbonates (e.g., [13][14][15][16][17][18][19]75]). Although the impact of vital effects on δ 53 Cr values is poorly constrained, some of these studies suggest that the large variability in δ 53 Cr values within a single or between several specimen(s) of metazoan species can be caused by vital effects. Microbial carbonate precipitation does not involve higher organisms and thus, the variability in δ 53 Cr values in metazoans caused by vital effects may not apply to microbialites. In microbial mats, several species of microbes are present and perhaps involved in the precipitation of microbial carbonates. In both of our modern samples, the most common microbes found in microbialites, cyanobacteria and sulfate-reducing bacteria, were likely present [24,76]. Despite the diversity of microbes within a microbial mat, Cr and δ 53 Cr values in microbialites are homogeneous on the scale we investigated. This implies that the vital effects that seem to strongly affect the variability in δ 53 Cr values in metazoans do not or insignificantly affect microbial carbonates.
On a cross-plot of Cr and δ 53 Cr values, samples from both locations fell into site-specific groups with some overlap in their δ 53 Cr values ( Figure 5). This sharply contrasts the highly variable δ 53 Cr values found in some metazoans. For example, different species of foraminifera from the West Pacific display δ 53 Cr values between 0.21 and 2.37% [16]. The overlap in δ 53 Cr values in stromatolite and tufa samples is remarkable, considering the differences in their formation, microbial community composition and morphology. For example, stromatolites in Marion Lake form from lithifying microbial mats, where organic substrates such as EPS are replaced by carbonates (e.g., [20,63]). In contrast, tufa in Mono Lake precipitates due to a combination of microbial activity and mixing of bicarbonate-rich lake water with Ca-rich groundwater [37,49,50]. If these differences cause strong and distinct (vital) effects on Cr isotope fractionation, we would expect the two types of microbialites to have vastly different δ 53 Cr values. Instead, despite these differences, their δ 53 Cr values overlapped. This further confirms that Cr isotope fractionation is at least somewhat similar in the investigated types of microbialites. Thus, we found no evidence that differences in formation, microbial community composition and morphology of microbialites drive the variability of δ 53 Cr values. We note that we did not investigate the microbial community compositions or structure and that our approach does not allow analysis of Cr isotope fractionation associated with specific bacterial metabolisms.
Although biological processes seem to have an insignificant effect on δ 53 Cr variability, biological processes (e.g., metabolism of microbes) during incorporation of Cr into microbialites can still influence Cr isotope fractionation. Based on the knowledge on Cr isotope fractionation associated with organics, we propose a basic conceptual model for Cr incorporation and isotope fractionation in microbialites, assuming the presence of common cyanobacteria and sulfate-reducing bacteria. In this model (Figure 7; [55]), Cr(VI) from the fluid in which the microbial mat grows is partially reduced to Cr(III) by organic matter in a first step (1). This process was shown to favour isotopically light Cr (e.g., [6,15]). In organic-rich environments, such as within a microbial mat, the solubility of Cr(III) is increased due to complexation with ligands [77][78][79]. Thus, we suspect that (2) isotopically light Cr(III) is more likely to stay in solution compared with open marine conditions, (3) limiting its availability for precipitating carbonate. As a consequence, (4) isotopically heavy Cr(VI) is more efficiently incorporated into microbial carbonate (and associated organics) compared with skeletal carbonates precipitating under open marine conditions with high Cr(III) availability. The resulting δ 53 Cr value in microbial carbonate is thus expected to show a smaller offset from ambient water compared with skeletal carbonates from open marine conditions. Furthermore, microbial carbonate is more likely to record a false positive, i.e., higher δ 53 Cr values compared to ambient water than a false negative. This potentially also applies to ancient microbialites when extrapolating in the rock record. values overlapped. This further confirms that Cr isotope fractionation is at least somewhat similar in the investigated types of microbialites. Thus, we found no evidence that differences in formation, microbial community composition and morphology of microbialites drive the variability of δ 53 Cr values. We note that we did not investigate the microbial community compositions or structure and that our approach does not allow analysis of Cr isotope fractionation associated with specific bacterial metabolisms. Although biological processes seem to have an insignificant effect on δ 53 Cr variability, biological processes (e.g., metabolism of microbes) during incorporation of Cr into microbialites can still influence Cr isotope fractionation. Based on the knowledge on Cr isotope fractionation associated with organics, we propose a basic conceptual model for Cr incorporation and isotope fractionation in microbialites, assuming the presence of common cyanobacteria and sulfate-reducing bacteria. In this model (Figure 7; [55]), Cr(VI) from the fluid in which the microbial mat grows is partially reduced to Cr(III) by organic matter in a first step (1). This process was shown to favour isotopically light Cr (e.g., [6,15]). In organic-rich environments, such as within a microbial mat, the solubility of Cr(III) is increased due to complexation with ligands [77][78][79]. Thus, we suspect that (2) isotopically light Cr(III) is more likely to stay in solution compared with open marine conditions, (3) limiting its availability for precipitating carbonate. As a consequence, (4) isotopically heavy Cr(VI) is more efficiently incorporated into microbial carbonate (and associated organics) compared with skeletal carbonates precipitating under open marine conditions with high Cr(III) availability. The resulting δ 53 Cr value in microbial carbonate is thus expected to show a smaller offset from ambient water compared with skeletal carbonates from open marine conditions. Furthermore, microbial carbonate is more likely to record a false positive, i.e., higher δ 53 Cr values compared to ambient water than a false negative. This potentially also applies to ancient microbialites when extrapolating in the rock record.

Environmental Controls on δ 53 Cr Values in Modern Microbialites
There is a lack of evidence of biological controls causing Cr isotope variability in microbialites. Hence, we suspect that the differences in δ 53 Cr values observed in microbialites from different locations are predominantly driven by environmental parameters. The main parameter influencing Cr isotope fractionation is redox state change since the reduction of Cr prefers isotopically light Cr (e.g., [3]). However, both of our modern microbialites formed in mostly oxygenated lakes and thus we cannot provide information on the influence of water column redox state on δ 53 Cr values in microbialites. We note that the redox state within a microbial mat changes from oxic at the surface to anoxic with depth, and this can affect δ 53 Cr values. The δ 53 Cr value in the oxic surface of the mat is likely equal to ambient water. However, at depth, where conditions within the mat are reducing, Cr reduction may cause lower δ 53 Cr values than in the surface and thus a larger offset from the δ 53 Cr

Environmental Controls on δ 53 Cr Values in Modern Microbialites
There is a lack of evidence of biological controls causing Cr isotope variability in microbialites. Hence, we suspect that the differences in δ 53 Cr values observed in microbialites from different locations are predominantly driven by environmental parameters. The main parameter influencing Cr isotope fractionation is redox state change since the reduction of Cr prefers isotopically light Cr (e.g., [3]). However, both of our modern microbialites formed in mostly oxygenated lakes and thus we cannot provide information on the influence of water column redox state on δ 53 Cr values in microbialites. We note that the redox state within a microbial mat changes from oxic at the surface to anoxic with depth, and this can affect δ 53 Cr values. The δ 53 Cr value in the oxic surface of the mat is likely equal to ambient water. However, at depth, where conditions within the mat are reducing, Cr reduction may cause lower δ 53 Cr values than in the surface and thus a larger offset from the δ 53 Cr value of ambient water. To decipher the effect of this redox-gradient on δ 53 Cr value, investigations on a micro-scale are required.
Previous studies have shown that Cr isotope fractionation can be dependent on physico-chemical parameters. Here, we focused on pH and salinity [10,83], although other physico-chemical parameters may also be relevant. Laboratory experiments identified small ∆ 53 Cr values (0.06-0.29% ) in a pH range of~8.5-10.4, and ∆ 53 Cr ≈ 0% for pH ≥ 9.4 [9,10]. Two water bodies in the Southern Ocean with different salinities also show distinct δ 53 Cr values, and their mixing leads to gradually changing δ 53 Cr values [83]. Assuming ∆ 53 Cr ≈ 0% for Mono Lake (pH ≥ 9.2 [46]), this agrees with [9,10]. However, also for Marion Lake, the estimated ∆ 53 Cr is ≈0% , whereas the pH range was lower (7.4-7.9; this study). Thus, our observations for natural samples only partially align with laboratory-precipitated carbonate, and pH does not seem to be the dominant influence on Cr isotope fractionation in these modern environments. Both our modern microbialites formed in hypersaline lakes (Marion Lake: >30 mg/L, Mono Lake: 90 g/L; [42,47], although salinity in Mono Lake was not constant over the last century [44]). It is thus possible that high salinity affected δ 53 Cr values in our modern microbialites. Hypersaline conditions are conducive to microbial carbonate formation and can facilitate similar δ 53 Cr and ∆ 53 Cr values at different sites. This supports our assumption that both ∆ 53 Cr values of Marion and Mono Lake microbialites are consistently small.
Stable C and O isotope ratios are commonly thought to reflect environmental conditions without being influenced by microbial metabolism [22,30,31]. Indeed, these data provide geochemical evidence that the modern microbialites were deposited in high-productive evaporative environments. The δ 13 C values in Mono Lake microbialites reached values up to 8.52% . Such high δ 13 C values are typically observed in modern microbial carbonates, reflecting environments with extensive microbial activity. Further, high stable O isotope values of Marion Lake microbialites are indicative of an evaporative setting, such as a lagoon [84]. In contrast, δ 18 O values of Mono Lake tufa can be attributed to geographic location and the influence of precipitation with depleted δ 18 O values [84,85]. Since δ 13 C and δ 18 O values are known to record environmental conditions without being significantly influenced by microbial activity, the same may be true for δ 53 Cr values. We acknowledge that these elements likely respond differently to both environmental and biological processes. However, due to the site-specific distinction in δ 53 Cr values, stable C and O isotopes observed here, we propose that these geochemical tools are predominantly influenced by environmental rather than biological parameters.
The hypothesis that δ 53 Cr values are mainly influenced by environmental conditions distinctive to marine vs. terrestrial settings (e.g., detrital contamination, pH, salinity) is further supported by REY data. Although REY abundance might be enriched during microbial stromatolite formation [65], patterns of REY in Marion and Mono Lake microbialites showed distinct differences that are consistent with their depositional environments [31,70]. Marion Lake microbialites formed in a coastal-influenced lake. Indeed, their typically marine REY patterns indicate that the influx of seawater strongly influences the water chemistry of Marion Lake microbialites ( Figure 6). Samples from Mono Lake co-varied with the rather flat REY pattern of igneous rocks with overall high REY concentrations and a positive Eu anomaly that can also be representative of the hydrothermal environment in which these microbialites formed [86]. This pattern is consistent with the local water chemistry that is controlled by the surrounding mostly volcanic rocks ( Figure 6; Table 4). The Ce anomaly in Mono Lake samples could indicate stratification of the water column or mixing of oxic lake water with anoxic ground water during tufa formation. The HREE of Mono Lake microbialites were slightly higher than LREE, in contrast with the basalt standard that shows a decrease in the concentrations of these elements. The slight enrichment in HREE in Mono Lake samples was consistent with previous observations in microbialites, where HREE can be complexed by organic components associated with microbialites (ligands, biofilms, EPS) and then preferentially incorporated, leading to an enrichment in HREE [70].

Comparison of Cr in Modern Microbialites and Seawater
The δ 53 Cr values in our modern microbialite samples exhibit limited variation. For paleoreconstructions, the δ 53 Cr value within a water body is expected to be stable during the time relevant for microbialite growth. Hence, also the ∆ 53 Cr values (∆ 53 Cr microbialite-water = δ 53 Cr microbialite − δ 53 Cr water ) should not vary significantly. We estimated a δ 53 Cr value of ≈1% for Marion Lake water. This estimation is based on the δ 53 Cr value of seawater from Lady Elliot Island, Australia (0.72-1.01% ; [17]), and average seawater δ 53 Cr values (0.41-1.72% ; for references see [87]). Using this estimated δ 53 Cr value, the ∆ 53 Cr value in Marion Lake is ≈0% , in line with previously reported values [17]. An estimation of a δ 53 Cr value of Mono Lake water is challenging due to both the lack of Cr isotope data in lakes, as well as due to the complexity in evolution of Mono Lake. Anthropogenic influence led to substantial changes in the hydrology of Mono Lake (e.g., water level, concentration of solutes, mixing) [44]. Even though Mono Lake is surrounded by igneous rocks, which are known to carry δ 53 Cr values of around −0.1% (e.g., [53,88]), the water δ 53 Cr value can be well above the typical detrital Cr isotope composition (e.g., [89][90][91]). The range in δ 53 Cr values of river waters draining igneous rock catchments is large (−0.17-1.71% ), but typically higher than 0.1% [89][90][91]. Thus, the δ 53 Cr value of Mono Lake water is likely higher than 0.1% , and the offset between Mono Lake microbialites and ambient waters may approach a similarly small value as in Marion Lake (≈0% ). The estimated water δ 53 Cr values are strongly simplified approximations and the Cr isotope offset between microbialites and water needs to be studied in detail.
The homogeneous δ 53 Cr values in our microbialite samples likely also result in consistent Cr isotope offsets between microbialites and ambient waters. This opposes previous observations of biogenic carbonates, which are up to 0.9% lower than ambient water (corals and foraminifera; e.g., [13][14][15][16][17][18][19]75]). Incorporation of Cr into microbial carbonates seems to induce a consistent and potentially small fractionation effect contrasting the typical fractionation effects observed for metazoans (see Section 4.1.2). Hence, Cr isotope fractionation during incorporation in microbially-mediated carbonates perhaps more closely resembles the observations of abiotic experiments. Laboratory experiments precipitating inorganic calcite found small and positive ∆ 53 Cr values (0.06-0.29% ) for a pH range of~8.5-10.4 [9], and ∆ 53 Cr ≈ 0% at pH > 9.4 [10]. Thus, for the Mono Lake site with a pH of ≥9.2 [46], a ∆ 53 Cr of ≈0% is in line with the results from inorganically-precipitated calcite. Incorporation of Cr with isotope ratios similar to the ones in ambient waters due to a lack of vital effects enhances their reliability to reflecting δ 53 Cr values of ambient waters with a consistent ∆ 53 Cr value. This is in agreement with [17] who suggested microbial carbonates as promising archives for paleo-reconstructions since these authors found δ 53 Cr values in carbonates produced by a coralline red algae identical to ambient seawater.

Diagenetic Alteration of Ancient Microbialites
Chromium can be leached from carbonate sediments during diagenesis, leading to lower Cr and δ 53 Cr values [54]. The ALG samples were dolomitized, but their textures and geochemistry show no severe alteration due to fluid mixing during burial [38]. Still, we cannot exclude that ancient δ 53 Cr values are shifted towards lower values due to fluid mixing during burial [39]. Furthermore, our ancient samples showed slightly higher Cr compared with modern samples as well as a similarly small variability in δ 53 Cr values ( Figure 5). Thus, we infer that they were not significantly affected by Cr loss during diagenesis. However, we propose that the low Cr/Al ratio in the BSF samples indicates significant and potentially post-depositional alteration. This is also supported by BSF δ 13 C and δ 18 O values ( Table 2). The BSF samples showed low δ 13 C values paired with significantly lower δ 18 O values, which points to a non-marine setting and perhaps a stronger degree of post-depositional diagenetic alteration compared to ALG samples. These samples should thus be considered unsuitable for paleo-environmental reconstructions using δ 53 Cr as redox tracer.

Comparison of Modern and Ancient Microbialites
The differences in microbial community composition and structure between various modern, but also between modern and ancient microbialites can be substantial and potentially compromise comparability (reviewed by [92]). The two types of modern microbialites from marginal marine and non-marine environments we studied (stromatolite and tufa, respectively) provide insights into Cr isotope fractionation effects in these types of microbial carbonates. Like the modern samples, the δ 53 Cr values that we measured in ancient microbialites from marginal marine (ALG) and evaporative lacustrine (BSF) environments were homogeneous and distinct (ALG: 0.36 ± 0.14% , BSF: −0.12 ± 0.14% ; Figures 3 and 5). These observations are first indicators that despite the diversity of microbialites in the present and through geological time scales, there are at least some similarities in their Cr isotope systematics. These similarities allow homogeneous incorporation of Cr from a presumably stable water column.

Biological and Environmental Controls on δ 53 Cr Values in Ancient Microbialites
Assuming microbial activity does not significantly affect the behaviour of traditional geochemical tools recorded in microbialites, we propose that microbial activity did also not mask δ 53 Cr values recorded by ancient microbialites, especially ALG samples. Although high δ 13 C values of ALG samples (+3.77 ± 0.10% (2SD); Figure 5; Table 2) can indicate environmental conditions with high microbial activity, they can also be indicative of an evaporative lagoon setting comparable to Marion Lake and the δ 13 C data of modern Marion Lake microbialites. Thus, the δ 53 Cr values of these samples are still thought to reflect environmental conditions. Further, due to presumably lower oxygen levels compared to present day, Cr(III) mobility was possibly increased relative to Cr(VI). As a result, more Cr(III) might have been incorporated in microbialites, leading to lower ∆ 53 Cr values. However, quantifying specific processes that may affect Cr isotope fractionation in the present or past exceeds the scope of this manuscript.
We propose that not only in the modern, but also in the ancient microbialites we investigated, the differences in δ 53 Cr values were strongly affected by the depositional environment [1]. The non-marine samples (Mono Lake and BSF) showed higher Al concentrations compared to the marine samples. Mono Lake and BSF microbialites are surrounded by Al-rich volcanic rocks [44], and by silt-and mudstones [39], respectively. Both of these microbialites show low Cr/Al ratios, indicating that these samples were substantially influenced by detrital material. This is in agreement with the depositional environment, since these microbialites formed in an inland seaway or mud flat spreading over a metamorphic province. This is further supported by the flat REY pattern of the BSF samples, indicating detrital influence. The Eu anomaly was possibly caused by rivers draining igneous rocks and discharging in the lake in which the BSF microbialites precipitated ( Figure 6). Contrasting these observations, no co-variations of Y/Ho SN and Eu SN /Eu* SN or Ce SN /Ce* SN were detected in BSF samples, indicating that detrital contamination was negligible. However, the preservation potential of marine REY patterns in Proterozoic carbonates is limited, for example due to overprinting with meteoric waters or REY-enriched particles [72].
Environmental parameters driving δ 53 Cr values in microbialites include-besides depositional settings-salinity. The δ 53 Cr values in microbialites from the marginal marine environment (ALG) are with ≈0.36% higher compared with the ones from the evaporative lacustrine (BSF) setting (≈−0.12% ), although BSF samples did not show pristine δ 53 Cr values. While Marion Lake and ALG microbialites were deposited under marine-influenced conditions (higher δ 53 Cr values than Mono Lake and BSF, respectively), both Mono Lake and our BSF samples are non-marine (lower δ 53 Cr values than Marion Lake and ALG, respectively). Even though salinity may have some control on Cr isotope variability [83,93], all our samples were deposited under high-salinity conditions (hypersaline for Marion Lake, Mono Lake and BSF, and (evaporative) shallow-water conditions for ALG [38,39]). Thus, salinity is unlikely to explain the observed site-specific δ 53 Cr values in our samples.

Comparison of Abiotic and Microbial Carbonates from the Precambrian
Our Cr data on ancient microbialites compare well with published data on Cr and Cr isotope compositions in Precambrian carbonates ( Figure 5; e.g., [68]). Together with many Precambrian carbonate samples (e.g., [52,54], not illustrated in Figure 5), the BSF microbialites analysed in this study fell in the range of detrital δ 53 Cr values. Typically, such low δ 53 Cr values are attributed to the lack of atmospheric oxygen and immobility of poorly soluble Cr(III) (e.g., [1,52]). However, the BSF record comprises large magnitude δ 13 C excursions, anhydrite-bearing red beds and evaporites, indicating the presence of a locally oxygenated atmosphere [39,94]. Since the presence of atmospheric oxygen induces Cr isotope fractionation, it is unlikely that the δ 53 Cr value in the water from which BSF microbialites precipitated was unfractionated. Hence, in our BSF samples, detrital contamination and diagenesis masked the effect of atmospheric oxygen on Cr isotope fractionation.
In contrast, our ALG samples showed similar Cr and δ 53 Cr values as some limestones and dolostone from the Yangtze Platform (Dengying Formation, 593 Ma; [68]) as well as from the Otavi Group (Namibia, ≈580-770 Ma; [69]), Turukhansk Uplift (Siberia, ≈900-1035 Ma), Angmaat Formation (Canada, ≈1092 Ma) and the Vazante Group (Brasil, ≈1112 Ma) [67]. While the carbonates underlying the Dengying Formation (Doushantuo Formation) have mostly negative δ 53 Cr values [54,68], the Dengying Formation, as well as the ALG samples, showed δ 53 Cr values above the detrital value (ALG: 0.23% or higher). Positively fractionated Cr isotope compositions back to approximately 1100 Ma are interpreted as indication of at least local oxygenation of oceans and atmosphere [1,55,68,69]). The shift to positive values is attributed to Cr isotope fractionation ultimately caused by oxygenation of the atmosphere (e.g., [2,52,95]). Under an at least locally oxygenated atmosphere, Cr(III) in terrestrial rocks is oxidised to Cr(VI) during weathering. Mobile Cr(VI) is transported to the oceans, where it can be reduced and thus fractionated. As a result, locally oxic water bodies carry isotopically heavier δ 53 Cr values compared with anoxic oceans.
Importantly, the δ 53 Cr values in our Proterozoic microbialites are in agreement with previously published data measured on carbonates, which supposedly were deposited abiotically. This finding supports our interpretation that environmental conditions are the main control on δ 53 Cr values in microbialites. Detailed studies on, e.g., diagenetic alteration or dolomitization, are needed to reveal details on Cr isotope fractionation in microbial carbonates.

Implications and Conclusions
Despite the pervasive occurrence of microbialites in the Precambrian, the behaviour of Cr in microbially-precipitated carbonates has not yet been examined. We analyzed Cr and δ 53 Cr values in modern and ancient microbialites from non-marine to marginal marine environments. Our data show homogeneous δ 53 Cr values of sub-samples along profiles throughout all microbialites and site-specific δ 53 Cr values. This observation is remarkable and promising, considering the diversity of microbial community compositions within a single microbialite. Overlapping δ 53 Cr values in the two types of modern microbialites indicate that despite the differences in their formation and morphology, Cr isotope systematics seem to be similar. The lack of variability in δ 53 Cr values due to biological parameters such as vital effects sharply contrasts the variability found in modern skeletal carbonates (such as mollusks or corals). The Cr and δ 53 Cr values in our microbial carbonates from the Proterozoic are in good agreement with published Cr isotope data of presumably abiotic carbonates of similar age. This further supports our interpretation that variations in δ 53 Cr values in microbial carbonates are driven by environmental rather than biological parameters. Due to the lack of evidence of biological processes driving δ 53 Cr variability, we suggest that environmental parameters are the main control on Cr isotope variability in microbialites from different locations. Background lithology and salinity are among the environmental parameters that mostly affect Cr, but the specific processes are not fully resolved. Using stable C and O isotope compositions as well as REY patterns, we observed a strong influence of detrital contamination on Cr in microbialites that formed in environments where igneous rocks constitute the background lithology.
Environmental parameters can affect microbialite δ 53 Cr data along with detrital contamination and (early) diagenetic alteration and have to be investigated in more detail. Still, our new results provide a promising foundation for the use of δ 53 Cr values in microbialites for reconstructing the δ 53 Cr values of the environments in which they formed.