A morphogram for silica‐witherite biomorphs and its application to microfossil identification in the early earth rock record

Abstract Archean hydrothermal environments formed a likely site for the origin and early evolution of life. These are also the settings, however, were complex abiologic structures can form. Low‐temperature serpentinization of ultramafic crust can generate alkaline, silica‐saturated fluids in which carbonate–silica crystalline aggregates with life‐like morphologies can self‐assemble. These “biomorphs” could have adsorbed hydrocarbons from Fischer–Tropsch type synthesis processes, leading to metamorphosed structures that resemble carbonaceous microfossils. Although this abiogenic process has been extensively cited in the literature and has generated important controversy, so far only one specific biomorph type with a filamentous shape has been discussed for the interpretation of Archean microfossils. It is therefore critical to precisely determine the full distribution in morphology and size of these biomorphs, and to study the range of plausible geochemical conditions under which these microstructures can form. Here, a set of witherite‐silica biomorph synthesis experiments in silica‐saturated solutions is presented, for a range of pH values (from 9 to 11.5) and barium ion concentrations (from 0.6 to 40 mmol/L BaCl2). Under these varying conditions, a wide range of life‐like structures is found, from fractal dendrites to complex shapes with continuous curvature. The size, spatial concentration, and morphology of the biomorphs are strongly controlled by environmental parameters, among which pH is the most important. This potentially limits the diversity of environments in which the growth of biomorphs could have occurred on Early Earth. Given the variety of the observed biomorph morphologies, our results show that the morphology of an individual microstructure is a poor criterion for biogenicity. However, biomorphs may be distinguished from actual populations of cellular microfossils by their wide, unimodal size distribution. Biomorphs grown by diffusion in silica gel can be differentiated by their continuous gradient in size, spatial density, and morphology along the direction of diffusion.


| INTRODUC TI ON
The search for biosignatures in the Early Archean geological record is challenging, as most sedimentary formations from this time interval have been exposed to hydrothermal fluids, and have undergone at least prehnite-pumpellyite facies to lower greenschist facies metamorphism.
Under these high temperature and high pressure conditions, rocks have recrystallized and organic matter has undergone carbonization. Therefore, any original organic remnant of microbial life preserved within them has been chemically altered and has potentially been deformed. Moreover, there are many non-biological precipitation/crystallization phenomena leading to morphologies resembling primitive fossilized micro-organisms. Examples are exfoliated micas (Wacey, Saunders, Kong, Brasier, & Brasier, 2015), dispersed hematite crystals (Marshall, Emry, & Marshall, 2011;Pinti, Mineau, & Clement, 2009), and migrated hydrocarbons (either biogenic or abiogenic) that filled the pore space between botryoidal quartz grains (Brasier et al., 2005). Most intriguing, however, are self-organized life-like silica-carbonate precipitates (Garcia-Ruiz et al., 2003). These microstructures form spontaneously in the laboratory when alkaline-earth metals are mixed with silica-rich alkaline solutions in the presence of CO 2 (García-Ruiz, 1998). They have also been synthesized by diffusion of alkaline-earth metals through silica gels. Recently, it has been demonstrated that these structures can form in modern serpentinization-derived alkaline spring waters (García-Ruiz, Nakouzi, Kotopoulou, Tamborrino, & Steinbock, 2017).
During hydrothermal serpentinization of seafloor ultramafic rocks, the pH of emanating fluids is largely controlled by temperature. Above 250°C, these fluids are slightly acidic (pH < 5), but with decreasing reaction temperature, the fluids become increasingly alkaline, reaching a pH of 11 at 50°C (Macleod, McKeown, Hall, & Russell, 1994;McCollom & Bach, 2009). This increase in pH is due to low-temperature equilibration with brucite that forms during the serpentinization process (McCollom & Bach, 2009). The temperature of hydrothermal fluids is dependent on the depth of circulation, the average geothermal gradient, and the extent of infiltration of seawater cooling the crust. As a consequence, although the Archean geothermal gradient is believed to be higher than today (Arndt & Nisbet, 2012), fluids that altered ultramafic rocks may have displayed a wide range of temperatures and pH values. Alkaline hydrothermal serpentinization of ultramafic crust-which is observed at modern low-temperature (<250°C) vent sites such as "Lost City" in the Atlantic Ocean (Lang, Butterfield, Schulte, Kelley, & Lilley, 2010;Proskurowski et al., 2008)-likely was an important process in aquatic environments of Hadean and Early Archean age (Russell, Hall, & Martin, 2010;Shibuya, Komiya, Nakamura, Takai, & Maruyama, 2010), when komatiites covered large areas of the ocean floor, which contained more MgO than basaltic rocks today (Arndt & Nisbet, 2012).
Early in Earth history, the concentration of silica in the oceans was much higher than today (Konhauser, Jones, Reysenbach, & Renaut, 2003;Maliva, Knoll, & Simonson, 2005;Siever, 1992), which is attested by ubiquitous sedimentary chert deposits in Archean greenstone belts (Nijman, De Bruijne, & Valkering, 1998; Van den Boorn, Van Bergen, Nijman, & Vroon, 2007;Van Kranendonk & Pirajno, 2004). These cherts formed either by direct precipitation of colloidal silica from silica-rich seawater, or by fluid-induced silica infiltration/replacement (silicification) of preexisting sediments (Stefurak, Lowe, Zentner, & Fischer, 2014;Van den Boorn et al., 2007). In some cases, such as in the Marble Bar chert, Pilbara, Western Australia, soft deformation and remobilization features show that the chert precursor, at least at some point of its history, was a highviscosity gel-like material (McLoughlin, Wilson, & Brasier, 2008;Van Kranendonk, 2006). Debris from micro-organisms living in the upper water column would settle down on the ocean floor, and thus become effectively entombed by silica gel. Upon burial, these amorphous silica deposits (opal-A) would transform to cherts consisting of microcrystalline quartz in which microfossil assemblages could have been preserved. In addition to these clear sedimentary cherts, there is ubiquitous evidence for hydrothermal cherts that formed when silica-rich seawater circulated through the igneous crustal basement. Such hydrothermal effluents, upon cooling and mixing with overlying seawater, would have precipitated silica, directly within the hydrothermal duct or near its vent, thus creating chert dykes and local layered deposits (Van den Boorn et al., 2007).
Barite veins are often found associated with these hydrothermal cherts (Nijman et al., 1998;Van Kranendonk, Hickman, Williams, & Nijman, 2001) indicating that significant amounts of dissolved Ba-ions were present in the precursor hydrothermal fluids. These hydrothermal fluids also caused serpentinization of olivine within the crust, releasing H 2 and causing the metal-catalyzed synthesis of CH 4 and more complex hydrocarbons by Fischer-Tropsch synthesis (McCollom & Seewald, 2006;Milesi et al., 2015). These hydrothermal environments would also have formed an important habitat for thermophilic micro-organisms that are capable of metabolizing reduced gases, such as hydrogen or methane (chemolithoautotrophs; Ueno, Yamada, Yoshida, Maruyama, & Isozaki, 2006). Organic remnants of chemolithoautotrophs could thus be effectively entombed in hydrothermal silica, and could have been preserved as carbonaceous microfossils in Archean chert veins. Finally, chert deposits also form in subaerial hot spring environments. When silica-rich, and often alkaline thermal fluids reach the surface, amorphous silica is precipitated due to evaporation and/or a significant drop in temperature, leading to silica sinters in which remnants of microbial life are superbly preserved (Campbell et al., 2015;Munoz-Saez, Saltiel, Manga, Nguyen, & Gonnermann, 2016;Ruff & Farmer, 2016). Recently, it was shown that such silica sinters with remnant microbial biosignatures (stromatolites, microbial palisade structures, gas bubbles) occurred already as early as 3.5 Ga ago (Djokic, Van Kranendonk, Campbell, Walter, & Ward, 2017).
On a global scale, the CO 2 partial pressure of the Early Archean atmosphere has been interpreted to be higher than today's (Kasting, 2014;Walker, 1985;Wolf & Toon, 2014), leading to significant concentrations of dissolved carbonate species in Archean seawater and mild acidification of the seawater. Three main mechanisms can then be invoked for the formation of biomorphs in the Archean: (i) The diffusion of calcium-rich seawater into gelified silica deposits would result in the formation of monohydrocalcite or aragonite biomorphs, (ii) the diffusion of a barium-rich hydrothermal fluid in gelified orthochemical silica deposits would result in the formation of witherite biomorphs, and (iii) the mixing between a barium-rich hydrothermal fluid and a silica-rich hydrothermal fluid would result in the formation of witherite biomorphs. The potential co-occurrence of early microbial life and mineral-based "biomorphs" in Archean environments must therefore be taken into account in early life research, and the morphological identification of carbonaceous microstructures as ancient microfossils should be carefully assessed. García-Ruiz, Melero-García, and Hyde (2009) have proposed a morphogenetic model describing the growth of silica-carbonate biomorphs. These structures can be formed with barium carbonate (witherite, which is the best studied variety), strontium carbonate (strontianite), or calcium carbonate (aragonite and monohydrocalcite; Bittarello, Roberto Massaro, & Aquilano, 2010;Voinescu et al., 2007;Zhang, 2015;Zhang, Morales, & García-Ruiz, 2017 The orientation of the long axis of the nanorods varies continuously and smoothly with the position of the crystal in the material, a geometrical feature which has been referred to as orientation ordering (García-Ruiz et al., 2002). This generates an overall continuous curvature in the material, characteristic of the second episode in biomorph formation, called the "curvilinear growth regime" .
In this study, we synthesized silica-witherite biomorphs both in alkaline silica-rich solutions and in alkaline silica gels, representing potential precursors for Archean cherts. For experiments realized in alkaline silica-enriched starting solutions, a systematic overview is presented on the variation in morphology-defined as a "morphogram"-of witherite-silica biomorphs that form at the surface (water-air interface), over a range of pH values and barium cation concentrations. To quantify the size distribution of biomorphs, automated measurements in optical images were also performed. In solution, biomorphs tend to aggregate, lowering the quality of these measurements. To avoid this problem, the size distribution was preferentially studied for biomorphs that were grown in silica gel. In this medium, biomorphs are dispersed throughout the gel without touching each other. solution-based experiments and gel-based experiments can be compared because the morphogenetic mechanism underlying biomorph growth in these two media is exactly the same (Kellermeier, Cölfen, & García-Ruiz, 2012). As it is plausible that silica gels could have formed in certain Hadean/Archean aquatic environments, the specific diffusion-related patterns observed in gel experiments are also discussed. The results of both solution-based and gel-based experiments are subsequently used to define criteria for distinction between biomorphs and microfossils, and to make an assessment of the likelihood that assemblages of biomorphs are associated with, or mistaken for, true microfossils in ancient chert deposits.

| Computer simulations of witherite nucleation
Numeric simulations were performed to characterize the effect of our experimental parameters on the crystallization behavior of witherite. According to classical nucleation theory (DeYoreo & Vekilov, 2003;Nývlt, Söhnel, Matuchová, & Broul, 1985), the characteristic waiting time for nucleation T (s) decreases with the saturation index The saturation index of witherite for each individual starting solution was computed using VisualMinteQ (version 3.1) simulations. The partial pressure of CO 2 was fixed at 3.8 × 10 −4 bar, representing ambient atmospheric level. Separate simulations were made for each individual initial barium concentration ([Ba]) in our experiments. The Cl − concentration was fixed at twice the initial [Ba]. To match the experimental values measured, the pH was varied between 9.3 and 11.3, with a step of 0.1 pH units between two simulations. Only the formation of witherite and amorphous silica (gel) was allowed. The activity correction method chosen was based on the theory of Debye-Hückel for non-ideal electrolyte solutions.

| Synthesis of biomorphs in solution
A 15 mmol/L silica solution was prepared by diluting 1 ml of commercial water glass (Sigma-Aldrich, 12.5 wt % of Si) in 350 ml of millipore-filtrated water. To obtain a range of different initial pH values, this mother solution was aliquoted in small volumes, and different volumes of NaOH or HCl solutions (0.1 mol/L) were added, from 1 ml HCl to 1 ml NaOH per 10 ml of the sodium silicate solution. In total, 21 solutions with different initial pH were produced this way.
Several solutions of different BaCl 2 concentration were prepared (giving a range in [Ba] from 1.25 to 40 mmol/L) upon dissolution of solid barium chloride dihydrate in millipore-filtrated water. The solutions were then combined in 24-well ultra-clear dishes to obtain 147 synthesis media with distinct initial conditions. The dishes were covered non-hermetically by a lid, to allow the diffusion of atmospheric CO 2 within the solution while avoiding dust deposition that would decrease the rate of evaporation. This protocol was used twice. The first time, the morphological evolution of biomorphs was specifically tracked. The second time, the pH evolution of a subset of 22 different initial solutions was measured for 24 hr by a Thermo Scientific ROSS Ultra™ semimicro pH electrode.

| Synthesis of biomorphs in a silica gel
Silica gels were prepared by neutralizing a 10 ml silica solution (~0.5 mol/L) using 3.25 ml of an HCl solution (1 mol/L). Once the gelling process was complete, a solution of BaCl 2 (0.25, 0.5 or 1 mol/L) was added on the top of the gel and allowed to diffuse inside. The protocol is described in more detail in Melero-García, Santisteban-Bailón, and García-Ruiz (2009). Under these conditions, large biomorphs appear in a few days in the gel. This protocol was used specifically for the studies of the size distribution, as it produces well-dispersed biomorphs, so that pictures can be easily treated during image analysis.

| Biomorph characterization
Biomorph crystallization (first appearance, growth, and morphology) at the liquid-atmosphere interface was tracked by obtaining optical microscopy pictures of each of the 147 solutions at regular time intervals for 2 days. A petrographic microscope (Leica DM 2500 P; Institut de Physique du Globe de Paris) was used in transmission mode with a 10× objective. Two multifocus long-range microscopes were also used for separate picture acquisition at random intervals (Nikon AZ100; Instituto Andaluz de Ciencias de la Tierra, Granada, Spain).
Optical microscopy pictures were processed using iMageJ software (Abramoff, Magalhaes, & Ram, 2004). After conversion to gray level, a threshold and a binarization were applied to the pictures to separate the crystallized particles from the background. The type of threshold was critical in this aspect, as some types tended to include parts of the background to the biomorphs, whereas other types tended to discard some parts of the biomorphs to the background. A "minimum" threshold was chosen, which was consistent among all pictures and correctly separated the biomorphs from their background. The particles were then detected and analyzed using ImageJ particle analyzer, giving information about the area or the shape of the particles. All data obtained this way, in every picture, for every initial condition and time step, were stored in a five-dimension matrix (using Matlab version R2009b-MATLAB and Statistics Toolbox Release 2012b; The MathWorks, Inc., Natick, MA, USA) for further use.
After the first results had been obtained, specific conditions of synthesis representing different regimes were studied again with the same protocol in 10 ml petri dishes. At different time intervals, a fraction of the structures observed floating at the surface was retrieved, rinsed (successively in 0.01 mol/L NaOH and milli-Q water), placed on conductive tape, and gold-coated to be observed with a Scanning Electron Microscope (Auriga FEG, IPGP). Images were taken in secondary electron mode, either with a chamber detector or with an inlens detector. The working distance was 7 mm, except for a few pictures taken with 10 or 18 mm, and the voltage was between 3 and 10 kV.

| Size distribution studies
Pictures of biomorphs grown in gel were acquired 2 weeks after the onset of the experiment using a direct petrographic microscope (Leica DM 2500 P, IPGP) in transmission mode with a 4× objective. For every field of view, ~30 pictures were taken at regularly increasing focal depths through the gel. These pictures were used for an extended depth-of-field reconstruction using iMageJ (EDF plugin, EPFL), which brought all structures into focus and improved ulterior picture treatment. For comparison with biological data, a culture of cyanobacteria (Synechocystis sp.) from the Pasteur Cyanobacteria Collection (PCC6803) was grown with standard BG-11 media to stationary growth phase. It was subsequently imaged with an Olympus BX-51 microscope under 100× (oil) objective with contrast enhanced using differential interference contrast (DIC) optics. For studies on sizes, pictures were treated in the same way as presented before with iMageJ. When particles tended to connect, they were separated automatically with a watershed algorithm (Beucher & Lantuejoul, 1979) which detects boundaries between areas in grayscale images. The size is given as an equivalent diameter: (2) To quantitatively compare size distributions, their widths are characterized using (average/standard deviation) ratios. These ratios were computed for biomorphs in our experiments, a biological test sample (a picture of a culture of Synechocystis spp.), and size distribution data found in Archean micropaleontology literature (Butterfield & Chandler, 1992;Wacey, Kilburn, Saunders, Cliff, & Brasier, 2011, Supporting Information).

| Numerical simulations
Using numerical simulations described in paragraph 3.1, for each starting solution, the saturation index σ of witherite was calculated.
The results are shown in Figure 1a. Each initial condition is repre-

| Solution experiments
Experiments of nucleation in solution were performed for each of the individual starting conditions shown in Figure 1. Within a few minutes to a few hours (depending on the initial conditions-see Table 1) after reagents had been mixed, biomorphs were observed at the water-air interface. In accordance with Equation 1, Figure 1a and  Our results also illustrate that owing to the increased rate of CO 2 uptake at higher pH values, the pH decreases faster for solutions starting at more alkaline conditions, an observation already made by Eiblmeier, Kellermeier, Rengstl, García-Ruiz, and Kunz (2013). This results in equal equilibration times for all the solutions (around 45 hr). Although the general exponential decrease of the pH in our experiments is in accordance with previous results (Eiblmeier et al., 2013;Kellermeier, Melero-García et al., 2012), the measured rate is two to three times higher. This can be ascribed to differences between the experimental protocols. Our experimental protocol for pH measurement involved frequent opening of the wells, thus accelerating the rate of CO 2 uptake. At the end of the experiments, the precipitate coverage at the water-air interface (given in relative area, %), as a function of initial pH and starting [Ba] is shown on Figure 1c. Overall, the area covered by the precipitates increases with increasing initial pH, while the influence of the initial [Ba] is less conclusive. As the pH value is controlling the carbonate concentration in solution, the extent of biomorph growth is mostly controlled by carbonate availability and not by barium availability.

| Gel experiments
Within a carbonate-rich silica gel, the precipitation of biomorphic witherite is caused by the diffusion of barium through the medium.
The barium concentration, and therefore also the saturation index σ of witherite, decreases spatially away from the diffusion source

| Biomorphs in solution experiments
A wide diversity of carbonate-silica biomorph shapes were observed in the solution experiments (Figures 3-5). These shapes can be clas- The transition from fractal growth to curvilinear growth can be easily observed in some structures, with a core of fractal growth aggregates, surrounded by radially expanding sheets which were formed by curvilinear growth (Figure 5a,b). Instead of twisting, the sheets can also fold onto themselves, forming gutter shapes (5), moth-like shapes (5d), snail-like shapes (5e), or combinations of these (5f,g). In other cases, ring-like structures arise through the curvilinear regime and grow with diverse thickness and to diverse heights to form donut (5h), coral, or urn-like shapes (5i). Lastly, mushroom-like shapes (Figure 5j,k) can emerge from the fractal aggregates. Their formation process is not well understood yet.
Looking at a single experiment, at a given time, only one type of growth process occurs (fractal or curvilinear). However, the morphologies of individual biomorphs vary. For example, circular sheets can grow next to leaf-shaped biomorphs, or spheroids can grow next to framboids.

| Biomorphs in silica gel experiments
The growth of witherite in gels occurs by a counter-diffusion process . A first precipitate of metal carbonate is created at the gel-solution interface at a pH close to 8.5 due to mixing of the acidic metal solution and the alkaline gel. As the acidic metal solution diffuses across the gel, it becomes less concentrated.
Therefore, within a single gel experiment, there is a gradual variation in conditions across the gel, from relatively acidic and metal-rich at the interface to more alkaline and carbonate-rich at the end of the gel. As a consequence, in the gels prepared for this study, the shape of biomorphs changes along the diffusion direction ( Figure 2).

| Influence of pH and [Ba] on biomorph growth in solution experiments
To study the effect of solution properties on the morphological variation in biomorphs, a set of experiments was conducted in which the after mixing of the reagents), and are much more numerous and smaller, around 10-15 μm in size. This is in accordance with previous results presented by (Eiblmeier et al., 2013). After a few hours, at these conditions, new biomorphs appear, with a morphogenetic path very similar to what was described previously for pH 10-10.7.
Based on these observed differences, we can define three general domains for biomorph growth, separated by red lines and numbered as follows in the Figure

| Size distribution of biomorphs
In the case of solution growth, due to the physical effect of the meniscus in the well, biomorphs tend to aggregate in the center of the well, making the accurate size distribution analysis a difficult task.
As a consequence, the size distribution analyses were realized in gel growth experiments. In these experiments, the slow diffusion of the barium solution leads to the formation of larger biomorphs (up to 3-4 mm) than the ones obtained in solution (up to ~200 μm for the same curvilinear growth regime). As discussed previously (sec-  (Table 1) and compared to the same values in other size distributions (see section 3.4).

2− ] diffusion on biomorph growth in solution experiments
During the experiments, pH measurements of the bulk solution show that CO 2 diffusion from the atmosphere progressively acidifies the growth medium (Figure 1b). We hypothesize that during this gradual change, the solution crosses the previously defined pH-dependent crystallization domains, and generates the corresponding biomorph shapes. It is thus expected that biomorphs corresponding to more acidic domains will start growing later than those corresponding to more alkaline domains. This coexistence of different domaincorresponding biomorphs is indeed observed in our experiments ( Figure 9a,b). For the lowest initial pH values of the domain 2, involuted sheets appear first (arrows noted 1 in Figure 9), associated after 3-4 hr to flat sheets (arrow noted 2 in Figure 9). After 1 day, large framboidal biomorphs (arrow noted 3), corresponding to the domain 1, appear in the medium. It therefore appears that the synthesis medium has reached pH values characteristic of domain 1, and the growth regime has switched from a curvilinear to a fractal-type growth process. Similarly, in the whole range of domain 3, the initial development of small framboidal biomorphs is followed by the growth of involuted aggregates and other curvilinear structures corresponding to domain 2. The synthesis medium has reached pH values characteristic of the domain 2. The final pH after equilibration with the atmosphere is the same for all the solutions (approximately at pH = 7-see Figure 1b). Therefore, solutions starting in domain 3 (the highest pH related domain) will cross the conditions related to domains 2 and 1 during their evolution. However, the coexistence of morphologies seems limited. No morphologies corresponding to domain 1 can be observed in the solutions starting in the domain 3 or in the higher pH part of the domain 2. A plausible explanation is that F I G U R E 7 Qualitative morphogram representing the main morphologies appearing through curvilinear growth for each unique initial setting of pH and Ba concentration. The green shade represents aggregates of involuted sheets. The orange shade represents flat sheets and leaf-like biomorphs. The brown shade represents the helical biomorphs (helicoids, braids, and wormlike braids). The gray shade represents coral-like biomorphs. The smaller the rectangle, the later the corresponding morphology appears. Scalebars: (I), (II) 10 μm; (III), (IV) 20 μm [Colour figure can be viewed at wileyonlinelibrary.com] when the solutions reach the conditions of domain 1, the saturation index of witherite is not sufficient anymore to allow further nucleation or growth of biomorphs, and the morphologies corresponding to the domain 1 will not be formed. As was discussed in section 3.1, the rate of pH decrease is higher for higher initial pH. For the whole range in initial pH's of domain 3, the conditions related to domain 2 will be reached while the saturation index of witherite is above the limit to nucleate biomorphs corresponding to domain 2. For solutions starting in domain 2, however, the pH will decrease much slower, and the solutions starting at high pH of this domain will only reach the conditions of domain 1 when the saturation index is under the limit allowing growth of domain 1-related biomorphs. The shapes of the observed biomorphs, their evolution throughout the duration of the experiment, and their association with other biomorph shapes can all be related to crossing by the solution of various growthcontrolling pH and [Ba] domains.

| Morphology of solution-grown biomorphs
Many of the diverse biomorph shapes that we obtained in our solution experiments resemble shapes of modern micro-organisms.  Figure 10f), which can be compared to, for example, the stalks produced by Mariprofundus ferroxydans (Figure 10i, Singer et al., 2011), or a wide range of filamentous bacteria (e.g., Oscillatoria princeps). In the first case, there is an obvious difference in size.
In the latter case, biomorphs can usually be distinguished by their shorter length and coiled internal geometry, although cyanobacteria such as Spirulina sp. display the same internal geometry ( Figure 10g). Helicoidal, and more precisely wormlike biomorphs,  (Sugitani, Mimura, Nagaoka, Lepot, & Takeuchi, 2013;Sugitani et al., 2009Sugitani et al., , 2010 have no morphological equivalents among the biomorphs grown in this study. This confirms the often discussed difficulty of distinguishing actual microbial remnants from abiotic counterparts based on morphological criteria alone (Brasier et al., 2002;Buick, 1990;Garcia-Ruiz et al.,2003;Schopf et al., 2002), especially in ancient metamorphosed rocks.

| Variation of morphologies in populations of solution-grown biomorphs
In contrast to individual morphologies, the variation in shape within a population of microstructures could potentially serve as a criterion to discriminate between an abiotic and biologic origin. As reported in our results (end of section 4.2.1) and as is seen in Figure 9a, for a single constant synthesis condition, biomorphs with a range of smoothly varying morphologies can be observed. For example, at a given time in a single starting solution, biomorphs that were formed through fractal growth can range from dendritic shapes to multiglobular, biglobular, or even spheroidal shapes. This demonstrates the influence of local heterogeneities (such as supersaturation values or impurities) in solutions. Micro-organisms from a single strain, however, exhibit very similar shapes, and a microbial assemblage of several strains displays a discontinuous spectrum of morphologies.
This criterion can be applied to Archean microfossils, for example, carbonaceous microstructures described in the 3,4 Ga Strelley Pool Chert (Sugitani et al., 2013). The structures described therein have spheroidal shapes and sizes (~10 μm) similar to some biomorphs. However, their shape is also remarkably homogeneous across the population. Based on our experimental results, it can be concluded that it is highly unlikely that fractal biomorphs grown from solution could have produced such a homogeneous population of spheroids, which disproves the biomorph hypothesis in this case.

| Size of solution-grown biomorphs
The size range (from a few μm to a few tens of μm) displayed by biomorphs grown in solutions in the upper-pH domains, noted 2 and 3 in Figure 6, lies within the range of prokaryotic sizes. At lower pH values (domain noted 1 in Figure 6), fractal-type biomorphs often grow to several hundreds of micrometers in diameter, which is one or two orders of magnitude larger than individual modern prokaryotes. Only very few strains of modern bacteria reach these sizes.
However, many bacteria tend to associate in colonies, forming for example clusters or filaments, with sizes comparable to the largest biomorphs observed in domain 1. Overall, the absolute size ranges of biomorphs and bacteria (individual or colonial) are similar. Therefore, it is concluded that the absolute size of individual microstructures does not represent a robust criterion for biogenicity of microstructures in the Archean rock record.

| Distribution of sizes in populations of gelgrown biomorphs
In contrast to sizes of individual biomorphs or micro-organisms, the frequency distribution of sizes of biomorph/micro-organism in a sample, a thin section or a picture, is a powerful descriptor of an assemblage. As automated size measurement protocols have been developed (using Elastic Light Scattering or Epifluorescence Microscopy data), the size distribution of single strain unicellular bacterial populations could be studied more effectively than before (Harvey & Marr, 1966;Katz et al., 2003;Uysal, 2001 we also found this kind of distribution (Figure 8b). This is in accordance with early mathematical models which took into account a binary division, a Gaussian distribution of sizes of cells entering division, a Gaussian distribution of sizes of daughter-cells, and a dependency of the growth rate on the cell volume (Koch, 1966).
Therefore, most monospecific unicellular populations can be expected to display this kind of distribution. Natural populations are usually composed of several strains, and their size distributions are thus expected to be plurimodal. However, in the Precambrian micropaleontological record, unimodal distributions are also reported (Butterfield & Chandler, 1992;Sugitani et al., 2013;Wacey et al., 2011). This can be ascribed to three potential factors: (i) micropaleontologists often make size measurements on groups of microstructures that were separated before, based on their morphology; (ii) some groups of organisms can be selectively lost during diagenesis because they are more fragile than others, reducing the resulting diversity in the fossil assemblage; (iii) the plurimodal nature of a distribution can be difficult to detect when the size of the population is small and the distribution of single strains overlap each other.
The width of size distributions is quantitatively compared (see section 3.4) using the Average/Standard deviation ratios (hereafter noted A/SD). This ratio was found to be lower for silicawitherite biomorphs and for abiotic spherulites from the Gwna group (Wacey et al., 2011) than for bacteria (0.8 for the spherulites, between 1.7 and 2.7 for biomorphs, 4.9 for bacteria). In Schopf, Kudryavtsev, Sugitani, and Walter (2010) (Table S1; Butterfield & Chandler, 1992;Wacey et al., 2011)

display high
A/SD values similar to the value of the Synechocystis population (between 4 and 5), which indicates that these populations may represent single strain microbial cells. In contrast, a population of spheroidal cells from the Gunflint formation (Wacey et al., 2011) and a population of spheroids from Agu Bay (Butterfield & Chandler, 1992) display lower A/SD values (between 2 and 3). As their biogenicity is not questioned, these wide distributions may be interpreted as cryptic plurimodal distributions, produced by the assemblage of several strains of bacteria. Alternatively, these wide distributions could be explained by degradational gradients (Knoll & Golubic, 1979).

| Spatial gradients displayed by gelgrown biomorphs
In silica gel experiments, the diffusion process results in a continuous change in size, in density and morphology of biomorphs (see picture 1 and section 3.4) observable on a short spatial scale, a type of spatial gradient which is not observed in biological assemblages. In the geological record, the presence of this kind of gradient within cherts would provide a strong indication that: (i) the structures are abiotic, and (ii) that the precursor of the deposit had a viscosity high enough to allow slow diffusion processes.

| Biomorph growth conditions and Archean paleoenvironments
In the current study we have chosen to perform biomorph synthesis by classical atmospheric CO 2 diffusion into an alkaline, silica-rich, and Ba-rich solution, and to study the full range of morphologies that are formed at variable starting pH. During the Archean, this set of conditions could have been present in shallow-marine hydrothermal vent systems or subaerial geothermal springs. In our experiments, fractal growth can occur over a wide range of conditions, at pH values between 9.5 and 11.3 and [Ba] between 1.25 and 40 mmol/L (see Figure 6), while the curvilinear growth of helicoidal biomorphs is restricted between pH 10.1 and 11.3, and [Ba] between 10 and 40 mmol/L. These barium concentrations are much higher than that of modern seawater ([Ba] = 0.15 μmol/kg, Herzig & Hannington, 2006), and modern hydrothermal fluids ([Ba] = 1.3-54 μmol/kg, (Charlou et al., 2005;Ludwig, Kelley, Butterfield, Nelson, & Früh-Green, 2006;Von Damm, 1995). However, in Archean hydrothermal fluids that leached predominantly ultramafic crust, the barium concentration may have been higher. For instance, komatiites from the Barberton Greenstone Belt, South Africa contain 2-93 ppm barium (Parman, Shimizu, Grove, & Dann, 2003), while typical MORB basalts contain 0.5 ppm barium (Workman & Hart, 2005). The fact that many Archean hydrothermal deposits contain barite (Nijman et al., 1998;Philippot et al., 2007;Van Kranendonk, 2006) suggests that significant amounts of barium were available in these hydrothermal fluids but also shows that, at the time these deposits formed, barium sulfate rather than barium carbonate would precipitate. The solubility product of barium sulfate (K sp = 1.08 10 −10 at T = 25°C) is slightly smaller than that of barium carbonate (K sp = 2.58 10 −9 at T = 25°C; Lide, 1947). This difference in solubility product between the two phases is so small that the formation of either barite or witherite will largely depend on the partial pressure of CO 2 (in the ocean, hydrothermal fluids, or pore fluids), and on pH, which controls the speciation of carbonic acid. An overall high CO 2 pressure and local high pH will create higher supersaturation values for witherite than for barite.
Furthermore, under the reducing conditions of the Hadean and early Archean, in many environments, the concentration of dissolved sulfate would be much lower than today, and witherite instead of barite would form when barium was available. Note that for strontium and calcium, the other alkaline-earth elements that form biomorphs, the solubility product of strontianite (SrCO 3 , K sp = 5.60 10 −10 at 25°C) is almost three orders of magnitude lower than that of celestite (SrSO 4 , K sp = 3.44 10 −7 at 25°C) while the solubility product of aragonite (the CaCO 3 phase forming biomorphs, K sp = 6.0 10 −9 at 25°C) is five order of magnitude lower than the one of gypsum (K sp = 3.14 10 −5 at 25°C; Lide, 1947). Therefore, in silica-rich alkaline solutions, strontium should precipitate in the form of strontianite-silica biomorphs and calcium should precipitate in the form of aragonite-silica biomorphs.
Our experiments allow for the first time to limit the geochemical conditions under which carbonate-silica biomorphs could have formed in surface environments of the early Earth.

| CON CLUS ION
The experimental study of the silica-witherite biomorph system at ambient conditions demonstrates the extensive range of biomimetic morphologies that can be formed in this simple and abiogenic chemical system with only subtle changes in environmental conditions. All the obtained morphologies can be interpreted as different steps of a morphogenetic continuum according to a model previously described . The values of barium concentration and pH, which influences the speciation of dissolved CO 2 and SiO 2 and therefore the mineral saturation indexes, have a strong effect on the final morphologies obtained. They control the number and the size of biomorphs, control a transition from the fractal to the curvilinear growth regime, and affect the twisting during curvilinear growth.
Several paleoenvironmental inferences point to plausible scenarios for the formation of biomorphs during the Archean Eon, either in solution or in gel. However, this study demonstrates that the high barium concentrations and high pH values necessary for biomorph growth to occur in surface environments (influenced by CO 2 diffusion), strongly restrict the number of settings where this growth could have occurred during the Archean. It remains to be determined what limits are imposed on biomorph growth under an extended range of conditions, especially when fluids are warmer (the solubility product of witherite is lowered, but that of silica is increased) or contain more CO 3 2− (the pH of the system is buffered, enabling more time for slow nucleation processes).
Because of their close resemblance to biological shapes and processes-for example, cell division-finding the right criteria to distinguish biomorphs from actual microfossils is crucial for life detection protocols. Based on this study, we can list three criteria to discard the biomorph hypothesis when looking for remnants of prokaryotic life: of cyanobacteria. This is IPGP contribution n° 3912. We are grateful to two anonymous reviewers for their helpful comments.

CO N FLI C T O F I NTE R E S T
The authors declare that there is no conflict of interest regarding the publication of this article.