Trapping and binding ’ : A review of the factors controlling the development of fossil agglutinated microbialites and their distribution in space and time

Trapping and binding of allochthonous grains by benthic microbial communities has been considered a fundamental process of microbialite accretion since its discovery in popular shallow-marine modern examples (Bahamas and Shark Bay). However, agglutinated textures are rare in fossil microbialites and, thus, the role of trapping and binding has been debated in the last four decades. Recently, renewed attention on this subject has produced new findings of fossil agglutinated microbialites (those mainly formed by ‘trapping and binding’ and analogous to modern examples), but they are still few and geologically recent (post-Paleozoic) when compared to the 3.5 Gyr long record of microbialites. In order to better understand this discrepancy between modern and fossil examples, an extensive literature review is presented here, providing the first thorough database of agglutinated microbialites, which shows that all of them are formed in shallow-marine environments and most under tidal influence. In addition, a Lower Cretaceous example is described, including very diverse microbialites, each of them formed in a particular paleoenvironment. Some of these microbialites developed in grainy settings, but only those formed in marginal-marine tide-influenced environments accreted mainly by trapping and binding the surrounding grains, being analogous of modern agglutinated microbialites, and matching the environmental pattern observed in the literature database. The combination of the literature review with the case study allows to discuss the factors that control and enhance ‘trapping and binding’: a) occurrence of grains in the microbialite environment; b) frequent currents that mobilize the grains and supply them onto the microbialite surface; c) high concentration and diversity of electrolytes in the water to increase the adhesiveness of the extracellular polymeric substances (EPS) of the microbialite surface; and d) a CaCO⁠ 3 saturation state not high enough to promote early and strong carbonate precipitation within EPS, which would eventually decrease its availability to adhere grains. Therefore, this review shows that the keys to solve the ‘trapping and binding’ debate may be environmental, because the conjuction of these hydrodynamic and hydrochemical parameters is preferentially achieved in shallow-marine settings and especially in those influenced by tides, at least since Mesozoic times. This explains the limited environmental and stratigraphic distribution of microbialites mainly formed by ‘trapping and binding’, and opens new ways to look, geologically and microbiologically, at this process, so often cited and yet


Introduction
Microbialites are organosedimentary deposits formed or influenced by benthic microbial communities since~3500 Ma (Burne and Moore, 1987;Riding et al., 1991a;Riding, 2011a;Dupraz et al., 2009Dupraz et al., , 2011. Many different biotic and abiotic processes are involved in the development of these deposits (e.g. Monty, 1976;Riding, 2000Riding, , 2011aArp et al., 2001aArp et al., , 2012Dupraz et al., 2009Dupraz et al., , 2011Bosak et al., 2013), but the original definition of 'microbialites' highlighted two specific roles of the microbial communities (e.g. microbial mats, biofilms) in their ori tings (e.g. alkaline and/or hypersaline, p. 308). Following that suggestion, this article presents a dual approach aiming to provide new keys for this long-standing debate, through the combination of a thorough literature review (covering modern and fossil microbialites formed in different settings) with a fossil case study. The case study is especially relevant because it presents Lower Cretaceous coastal deposits that show an unusual diversity of microbialites (not only stromatolites, Fig. 2), some formed by trapping and binding of grains and some others not, but with the peculiarity that each of them is associated with a different paleoenvironment, ranging from freshwater to hypersaline and including shallow-marine examples, which allows to link each microbialite type to the specific factors that influenced their accretion processes. The combination of the results of this case study with the literature review shows that a complex interplay of factors is necessary for a microbialite to sustainedly develop mainly through 'trapping and binding' (i.e. agglutinated microbialite), and it also shows that this process seems to have a strong environmental control, being highly influenced by the hydrodynamic and hydrochemical conditions where the microbialite develops. Furthermore, the exhaustive literature review of agglutinated microbialites (conducted here for the first time) suggests that the environmental conditions suitable for grain agglutination are most easily achieved in specific environments, mainly shallow marine, and especially those with tidal influence. Therefore, this study presents an in-depth approach to the four-decade long debate of agglutinated microbialites, not only pinpointing the factors that control the often-cited process of 'trapping and binding', but also opening new ways to discuss and to clarify the debate about its scarceness and its temporal and spatial distribution throughout the geological record.

Terminology
The study field of microbialite research has now more than a century of history (Riding, 2011b) and during that time the discipline has accumulated a significant amount of terminology, which is continuously being discussed, revised and updated (e.g. Hofmann, 1969;Walter, 1972Walter, , 1976Krumbein, 1983;Grey, 1989;Riding, 1999Riding, , 2011aDupraz et al., 2011;Myshrall et al., 2012;Harwood Theisen and Sumner, 2016). Therefore, it is always advisable to clarify the meaning of the terms and methods used. In this article, the characterization of microbialites will follow the traditional multiscale approach (e.g. Preiss, 1976;Grey, 1989;Shapiro, 2000;Vennin et al., 2015), separately describing the macroscopic (i.e. outcrop), mesoscopic (i.e. hand specimen) and microscopic (i.e. thin section) features. The general classification of microbialites (e.g. stromatolite, thrombolite, leiolite) will be based, as commonly done, on their internal structure at mesoscale (e.g. presence/ absence of lamination; Kennard and James, 1986;Braga et al., 1995;Dupraz et al., 2011). More specific classifications within the general categories (e.g. micritic stromatolite, agglutinated thrombolite) are normally carried out according to microscopic features of microbialites (e.g. Riding, 1991Riding, , 2000Riding, , 2011aSchmid, 1996;Dupraz et al., 2011). Here, the term 'microfabric' will be used to refer to the microscopic features of a particular area of a microbialite (e.g. a lamina, a clot), since it is a term traditionally used in carbonate petrology (e.g. Bathurst, 1993, and references therein) that encompasses both textural and structural aspects (Flügel, 2010, p. 177). Thus, the description of the different microfabrics analyzed in this article will emphasize the relationships between the different components observed under the microscope (e.g. grains, matrix, cements; cf. Rezak and Lavoie, 1990;Vennin et al., 2015;Harwood Theisen and Sumner, 2016). A microfabric of particular interest to this study is the 'agglutinated microfabric', and the microbialites dominated by this microfabric will be thus classified as 'agglutinated microbialites'. The term 'agglutinated' was first applied to microbialtes by (Riding et al. 1991a, p. 30) to refer to "stromatolites produced by trapping of particulate sediment" (Riding, 1999, p. 325, changed 'particulate sediment' for 'allochthonous particles' in the definition), and it is preferred here to the term 'coarse-grained' (sensu Awramik and Riding, 1988, and often used as somehow synonymous, cf. Suarez-Gonzalez et al., 2014;Frantz et al., 2015), in order to avoid confusions with the Udden-Wentworth grain-size scale (cf. Folk, 1954). Thus, 'agglutinated' is applied here to microfabrics that are dominated by allochthonous particles that can be confidently interpreted as trapped and bound by the original microbial community that formed the microbialite (see criteria in Frantz et al., 2015). The scarcity of fossil analogues of the modern agglutinated microbialites (e.g. Bahamas and Shark Bay) is the basis of the long-standing debate investigated here (see sections 1 and 4), and therefore it is fundamental for this study that the fossil agglutinated microfabrics are clearly comparable with the modern ones (i.e. rich in allochthonous, silt-and sand-sized material). Some micritic microfabrics within microbialites have been locally interpreted as formed by trapping and binding of allochthonous micrite (e.g. Black, 1933;Rodríguez-Martínez et al., 2012;Tosti and Riding, 2017) and classified as 'fine-grained agglutinated' (sensu Riding et al., 1991a). However, they are not considered here because they are very rarely described, because their interpretation is challenging (Riding, 2000;Tosti and Riding, 2017) and mostly dependent on the presence of clay and silt detrital particles accompanying the micrite (Rodríguez-Martínez et al., 2012), and because they are not analogues of the aforementioned modern marine agglutinated examples.

Material and methods
The literature review presented here covers an extensive database, compiled by the authors, of research studies about microbialites of all ages and environmental settings. From this database, all the microbialite examples showing clear evidence of the accretion process of 'trapping and binding' were selected. Tables 1 and 2 show a compilation of all modern and fossil agglutinated microbialites (i.e. those predominantly formed by 'trapping and binding' of mostly carbonate particles, being analogous of the modern examples of the Bahamas and Shark Bay where that process was first described). Examples of microbialites only partially including agglutinated microfabrics or trapped grains within their microfabrics are not listed in the tables, but are included and discussed in the text.
The results presented from the Cretaceous Leza Formation to complement the literature review are based on detailed studies (see Suarez-Gonzalez et al., 2015), including geological mapping of the whole outcrop area of the unit (approximately 500 km 2 , Figs. 3-4) and logging of 12 complete stratigraphic sections (Fig. 4), measured with a dm-resolution and logged at 1:100 scale (or larger where details made it necessary, especially in microbialite-bearing deposits). Throughout these sections and in additional relevant outcrops, >800 samples (~200 of them from microbialites) were collected and at least one thin section (of 46 × 25 mm and/or 80 × 50 mm size) was prepared for each of them. Low, rounded domes, 2.5-5 cm high and 10-13 cm in diameter Parallel or concentric darklight lamination Thicker light laminae (0.5-1.75 mm), composed of soft and uncemented grains (0.1-1 mm grain-size), separated by thinner (~0.1 mm), dark, green-brown, organic-rich laminae Monty (1965Monty ( , 1967 Eastern Andros Island, Bahamas Intertidal-subtidal zones of back-reef lagoon. Brackishnormal marine salinity Flat mats, mamillated structures, domes, and knobby or subspherical bodies. Up to 10 cm in diameter and 5 cm thick Non-laminated and laminated Non-laminated: well-sorted grains bound by filaments and eventually capped by 0.1 mm thick biofilm. Laminated: alternating grainy laminae and 0.2-0.9 mm filamentous laminae Gebelein (1976a) Joulters Cay, Bahamas Subtidal (<1 m) shoal areas and tidal channels Oncoids (1 mm -10 cm) Laminated Thicker laminae with vertical filaments and abundant trapped grains and thinner laminae with horizontal filaments and less grains Dravis (1983) Eleuthera Bank, Bahamas Earth-Science Reviews xxx (xxxx) xxx-xxx

Laminated
Alternating laminae rich in bioclastic-peloidal sand and laminae rich in microbially induced carbonate precipitation amongst the filaments" (p. 168). Ginsburg et al. (1954) later found microbial structures in South Florida that also accreted by 'trapping and binding', and they were the first to suggest an extrapolation of this process to the fossil record, proposing two main criteria for the recognition of ancient stromatolites: "detrital texture" of the laminae and "structures indicative of sediment binding" (pp. 30-31). Logan (1961) recognized columnar shallow-marine stromatolites in Shark Bay (Australia) formed by "binding of mechanically deposited sediment" (p. 517) and, using these examples as referents, Logan et al. (1964) proposed a general definition of stromatolites as "laminated organosedimentary structures composed of particulate sand, silt, and clay-size sediment, which have been formed by the trapping and binding of detrital sediment particles" (pp. 69, 81). Further studies of these modern examples ( Fig. 1), and the recognition of similar agglutinated microbialites in other modern shallow-marine settings such as Bermuda (Gebelein, 1969(Gebelein, , 1976a, led to what Monty (1977) called the "trapping and binding dogma" (p. 22): the assumption that most fossil examples would also have mainly formed by trapping and binding of particles. Quite early in the evolution of that idea, some researchers were already opposing it (see Monty, 1972Monty, , 1977Serebryakov and Semikhatov, 1974; and references therein), noting that agglutinated textures are very rare in fossil microbialites, a claim that kept being supported later (see Awramik and Riding, 1988;Ginsburg, 1991). In fact, it was not until the 90's (Riding et al., 1991a) that a clear fossil agglutinated microbialite, analogous to modern specimens, was described.  In the last decades, the knowledge about modern agglutinated microbialites has increased significantly (e.g. Dravis, 1983;Dill et al., 1986;Riding et al., 1991b;Reid et al., 1995Reid et al., , 2000Reid et al., , 2003Macintyre et al., 1996Macintyre et al., , 2000Feldmann and McKenzie, 1998;Sprachta et al., 2001;Planavsky and Ginsburg, 2009;Collins, 2012, 2013;Suosaari et al., 2016a; see Table 1), but fossil counterparts are still rarely described (Table 2). Despite this scarcity, and although nowadays it is widely recognized that the main process of microbialite development is in situ mineral precipitation within microbial communities (e.g. Dupraz et al., 2009;Bosak, 2011;Reitner, 2011;Riding, 2011a), the 'trapping and binding dogma' seems to be still permeated in the general geological literature, as it can be seen in popular science books (e.g. Zalasiewicz, 2009, p. 97), many textbooks (e.g. Chernicoff et al., 1997, p. 934;Lunine, 1999, p. 134;Marshak, 2009, p. 301;Stanley, 2009, p. 119;Grotzinger and Jordan, 2014, p. 295;Tarbuck and Lutgens, 2014, p. 760), and even in more specialized sedimentological works (e.g. Collinson et al., 2006, p. 174). Maybe because of this persistence of the 'dogma', the debate about the actual relevance of 'trapping and binding' has recently gained new attention (Browne, 2011;Suarez-Gonzalez et al., 2014;Frantz et al., 2015), trying to shed light on this peculiar organo-sedimentary process, ubiquitous in scientific literature but elusive through geologic time.

The present and past of 'trapping and binding'
Here, the published examples of modern and ancient agglutinated microbialites (summarized in Tables 1 and 2), and even of those only partially including grains in some of their microfabrics, are compiled, compared and discussed.
The environments where all modern agglutinated microbialites have been observed are consistently coastal and very shallow marine (normally <10 m deep, but on average <2 m, Table 1; Fig. 1), with brackish, normal-marine or hypersaline salinities, and generally with tidal influence or within restricted lagoons (Table 1). This limited environmental distribution contrasts with the wide range of settings in which modern microbialites occur outside of the marine realm (e.g. Golubic, 1991;Dupraz et al., 2011;Della Porta, 2015;Chagas et al., 2016). In all these varied settings, 'trapping and binding' of grains is very rarely cited as a relevant accretion process in modern micro bialites, which do not show clear well-developed agglutinated microfabrics, since grains are in general only locally or sporadically included within them (e.g. Jones, 1991;Winsborough et al., 1994;Castro-Contreras et al., 2014;Della Porta, 2015;Brasier et al., 2018). In fact, since the very first description of agglutinated microbialites, Black (1933) noted this interesting contrast in the environmental distribution of 'trapping and binding', describing not only the marginal-marine agglutinated specimens (see previous section 4), but also other structures developing in neighbouring freshwater settings, which consisted of "radiating filaments, without much interstitial sediment" (p. 170; and which were further studied by Monty, 1967, and Monty and Hardie, 1976. Therefore, the present-day microbialite record suggests an environmental distribution of the accretion process of 'trapping and binding' and of agglutinated microbialites, limited to coastal and shallow-marine settings, commonly with tidal influence.

Fossil analogues of modern agglutinated microbialites
Despite the popularity of the 'trapping and binding' process in the microbialite literature since the 60's, it was not until the 90's that actual fossil agglutinated microbialites, clearly analogous to modern counterparts, were described, and their geological record is still relatively poor (Table 2). Riding et al. (1991a) showed that 'trapping and binding' was the main accretion process of large Messininan (Miocene) microbialites in Almería, SE Spain. These specimens became very popular and have been further studied (Braga et al., 1995;Bourillot, 2009;Bourillot et al., 2010aBourillot et al., , 2010bGoldstein et al., 2013) Earth-Science Reviews xxx (xxxx) xxx-xxx as formed in shallow-marine high-energy environments, in which the relative influence of waves, storms and tides is debated (Table 2). Similar Miocene agglutinated microbialites have been described in Mallorca (E Spain) by Arenas and Pomar (2010), being also interpreted as formed in shallow-marine environments with alternating calm and agitated periods. Other Miocene microbialites that may not be classified as agglutinated, but which also include some allochthonous grains in their microfabrics are described by Irtem (1987) from tidal-flat paleoenvironments of E Saudi Arabia. In addition to these Miocene examples, Pliocene shallow-marine oncoids from an uplifted atoll in New Caledonia display micritic microfabrics with abundant trapped grains (Pederson et al., 2015). Older than the Miocene, agglutinated microbialites are very scarce. Suarez-Gonzalez et al. (2014, 2016a) described Lower Cretaceous agglutinated stromatolites from La Rioja (Spain), deposited in the distal tide-influenced areas of coastal wetlands. Some Upper Jurassic agglutinated microbialites have been cited by Matyszkiewicz et al. (2006Matyszkiewicz et al. ( , 2012 in shallow, high-energy marine paleoenvironments from Poland, and three Triassic examples of agglutinated microbialites have been described (Woods, 2013, Nevada, USA;Vennin et al., 2015, Utah, USA;Mercedes-Martín et al., 2013a, 2013b, all of them formed in environments interpreted to be shallow-marine and commonly with tidal influence. Throughout the Mesozoic, there are other examples of microbialites that include trapped grains only in some of their microfabrics (Achauer and Johnson, 1969;Leinfelder et al., 1994;Herrmann, 1996;Immenhauser et al., 2005;Rodríguez-Martínez et al., 2012;Quijada et al., 2015Quijada et al., , 2016, but which are not considered agglutinated microbialites as a whole. All of these partly-agglutinated Mesozoic examples are also interpreted to be de posited in shallow-marine peritidal settings, with the exception of those described by Acosta et al. (1988) and Massari and Westphal (2011) in Jurassic deep-marine Ammonitico Rosso facies, which also show trapped and bound grains in some of their microfabrics.
In Paleozoic rocks there is, to our knowledge, only one example of microbialites almost exclusively formed by trapping and binding of grains: the one described by Chow and George (2004) from the Upper Devonian of W Australia, interpreted as deposited in high-energy shallow-subtidal settings. Beside this case, other Paleozoic microbialites, formed in shallow-marine peritidal settings (Słowakiewicz et al., 2013, Upper Permian;Wright and Wright, 1985, Lower Carboniferous;Warusavitharana and Parcell, 2013, Lower Ordovician;Harwood Theisen and Sumner, 2016, Cambrian) have been described to include allochthonous particles only in some of their microfabrics, and therefore are not analogues of modern agglutinated examples.
The aforementioned examples show that purely agglutinated microbialites are quite rare during the Phanerozoic (Table 2), but their Earth-Science Reviews xxx (xxxx) xxx-xxx scarcity is much more remarkable throughout their 3000 Myr-long Precambrian history. Throughout this long period, trapping and binding was an infrequent accretion process (Awramik and Riding, 1988;Sami and James, 1996;Knoll and Semikhatov, 1998;Altermann, 2008;Planavsky and Grey, 2008;Bosak et al., 2013), with few mentions of microbialites that only partially or locally include grains within their microfabrics (Walter, 1972;Horodyski, 1976;Fairchild, 1991;Allwood et al., 2009;Martindale et al., 2015;Fedorchuk et al., 2016;Siahi et al., 2016), thus being not clear analogues of the modern marine examples. In summary, the literature review presented here shows that fossil agglutinated microbialites have been continuously rare through Earth history, in comparison with the abundant and diverse spectrum of fossil microbialites. The few described agglutinated examples seem to have consistently formed in shallow-and marginal-marine settings under agitated conditions, commonly with tidal influence (Table 2). Moreover, the non-agglutinated microbialites that include trapped grains in some of their microfabrics are also mostly found in shallow-marine facies, with those of the Jurassic Ammonitico Rosso being the exception to this pattern. In fact, the literature also shows that in non-marine paleoenvironments allochthonous grains are rarely a significant component of microbialite microfabrics (Frantz et al., 2014;Bunevich et al., 2017;Vennin et al., 2018). When grains are observed, it is commonly not in accretionary laminae but filling primary cavities within the microbialite structure (e.g. Freytet and Plet, 1996;Freytet, 2000;Suarez-Gonzalez et al., 2016a), or in cases where marine influence has been suggested and should not be ruled out (Arp et al., 2005). Therefore, both the modern and ancient records of agglutinated microbialites suggest a link between the accretionary process of trapping and binding and shallow-marine environments, often agitated and commonly influenced by tidal currents, which deserves to be investigated in further detail.

A cretaceous microbial paradise
The Lower Cretaceous Leza Formation (La Rioja, N Spain) includes one of the few fossil examples of agglutinated stromatolites (Table 2), with some of its microfabrics being remarkably similar to those of modern agglutinated counterparts, and also formed in marginal-marine settings (Suarez-Gonzalez et al., 2014). But besides the agglutinated specimens, this unit includes many other microbialites ( Fig. 2; Table 3), some with and some without agglutinated microfabrics, and each of them formed in a different paleoenvironment, ranging from alluvial to shallow-marine (Figs. 4-5;Suarez-Gonzalez et al., 2015). Thus, comparing the agglutinating and the non-agglutinating microbialites of this unit provides an optimal opportunity to explore the environmental constraints to the trapping and binding process, and to shed light into the dilemma of why trapped and bound grains are so rare in the geological record of microbialites.
The Leza Fm belongs to the Cameros Basin (Fig. 3), which developed during the Late Jurassic-Early Cretaceous extensional phases of the Iberian Plate, over a pre-extensional Jurassic substrate dominated by carbonates (Fig. 3C-D; Mas et al., 1993;Benito et al., 2001;Salas et al., 2001;Mas, 2002, 2006;Mas et al., 2002Mas et al., , 2011Suarez-Gonzalez et al., 2013, 2016bOmodeo Salè et al., 2014;Sacristán-Horcajada et al., 2015). Throughout its evolution, this basin recorded up to 6500 m of siliciclastic, carbonate and minor evaporite sediments deposited in continental, coastal and shallow-marine environments (Mas et al., 2011;Quijada et al., 2013aQuijada et al., , 2013bQuijada et al., , 2016Suarez-Gonzalez et al., 2013, 2016aOmodeo Salè et al., 2014;Mas et al., 2018). During the late Barremian-early Aptian extensional phase, the Leza Fm was deposited at the distal northernmost margin of the basin (Fig. 3), in a series of small tectonic depressions formed by faulting of the Jurassic substrate of the basin ( Fig. 3D; . Erosion of the faulted carbonate-dominated substrate led to deposition of alluvial fans in the margins of the depressions, which changed laterally to carbonate coastal wetlands (Fig. 3D) formed by a complex mosaic of diverse interrelated environments with influence of both freshwater and marine water (see Fig. 12C of Suarez-Gonzalez et al., 2015). This unit shows significant variations in thickness and facies distribution (Fig. 4). Two main paleogeographic sectors are distinguished, western and eastern, with relevant sedimentological differences between them (Fig. 4): input of clastic material was stronger in the western sector, whereas marine influence was stronger and more direct in the eastern sector . The complex sedimentology of the Leza Fm is grouped into five facies associations, all of them including microbialites, and each of them corresponding to a different paleoenvironmental setting (Figs. 4, 5; and see Fig. 12C of Suarez-Gonzalez et al., 2015). Here, only the key features of each paleoenvironment are summarized, focusing later on the microbialites and their facies.

General paleoenvironmental settings of the microbialites
The alluvial fan paleoenvironments are characterized by conglomerates and sandstones mainly composed of lithoclasts eroded from the carbonate-dominated Jurassic basin substrate (Figs. 3D, 5A). Part of the material transported by the alluvial fans was deposited within the shallow-water bodies that formed the carbonate coastal wetlands of the Leza Fm (Figs. 4, 5;Suarez-Gonzalez et al., 2015). These paleoenvironments locally included oncoids, and paleosols were often developed over alluvial fan deposits. The freshwater to marine-influenced wetland paleoenvironments are characterized by black, fetid and locally bituminous limestones and marls, which are the most widespread deposits of the unit (Fig. 4), being generally arranged in shallowing-upwards sequences up to 4 m thick ( Fig. 5B-D). They are interpreted as formed in wide wetland areas with abundant shallow-water bodies with recurrent periods of desiccation and inundation, surrounded by vegetated areas, and laterally associated with the alluvial fan paleoenvironments . These wetlands had a rich biota, including ostracods, charophytes, dasycladales, gastropods and vertebrates, as well as abundant microbialites (oncoids, skeletal stromatolites and thrombolites). Despite the presence of freshwater (e.g. charophytes) and marine (dasycladales) fossils, these do not typically occur together within the same sequence ( Fig. 5B-D), pointing at different degrees of marine influence, which produced water bodies with salinities from fresh to near-marine . The peritidal wetland paleoenvironments are distributed only in the western sector of the studied area (Fig. 4) and are characterized by thinly-bedded gray limestone deposits, interpreted as formed in very shallow and often desiccated coastal water bodies with a marine signature stronger than the previous paleoenvironments . They have a distinct biotic composition, dominated by ostracods, miliolid foraminifers and gastropods, and display fenestral laminites (Fig.  5E). Peloids, intraclasts and silt-sized quartz grains are also common in these facies, together with desiccation and edaphic features, which indicate alternating episodes of inundation and desiccation. The tide-influenced oolitic paleoenvironments are recorded only in the eastern sector (Fig. 4) and are characterized by oolitic deposits with sedimentary structures that indicate influence of tidal currents , 2016a, laterally and vertically associated with agglutinated stromatolites, flat-pebble breccias and desiccation features (Fig. 5F). Locally, pseudomorphs after evaporites occur within the stromatolite laminae. Besides the stromatolites, the biotic community of these paleoenvironments includes ostracods and miliolid foraminifers. Therefore, these deposits are interpreted as formed in shallow, tide-influenced areas of the distal part of the coastal wetland system, closer to the marine realm. These areas were commonly subaerially exposed and dominated by seawater, although salinity may have been very variable due Earth-Science Reviews xxx (xxxx) xxx-xxx to influence of freshwater from proximal areas of the system and/ or to desiccation (Suarez-Gonzalez et al., 2014. The evaporitic paleoenvironments are distributed only in the eastern sector and were laterally associated with the tide-influenced oolitic paleoenvironments (Fig. 4). They are characterized by laminated dolomitic deposits with abundant pseudomorphs after gypsum and anhydrite, which locally include micritic-evaporitic stromatolites (Fig. 5G). The biotic community of these paleoenvironments was very poor (only rare ostracods and miliolid foraminifers) and desiccation episodes were very common. Thus, these paleoenvironments were very shallow and relatively restricted marine-influenced areas, which commonly reached high salinity through evaporation .

Linking microbialite accretion processes and their paleoenvironments
The case study presented here includes a remarkable diversity of microbialites, comprising most of the wide array of macro-, meso-and micro-structures that characterize these organosedimentary deposits ( Fig.  2; Table 3; cf. Kennard and James, 1986;Riding et al. (1991a);Riding, 2011a;Dupraz et al., 2011). Interestingly, each microbialite variety occurs within a particular facies and in a particular paleogeographic sector (Figs. 4, 5), suggesting an important environmental control on the development of microbial structures. Here, the different microbialites will be described, highlighting their relationship with the surrounding sediment, in order to interpret their accretion processes and the environmental factors that may have controlled them.

Oncoids
Oncoids are the most abundant microbialites, occurring in the freshwater to marine-influenced wetland facies and in the alluvial fan facies, and in both eastern and western sectors (Figs. 4, 5B-D). They are most common in limestones rich in charophytes and in clastic-rich limestone beds with cross-bedding and irregular bases (Fig. 5B, D, 6A-B). Therefore, oncoids developed in shallow-water bodies dominated by freshwater and in small channels or creeks associated with them and linked to alluvial fans that delivered lithoclastic material eroded from the substrate of the basin (Fig. 5A-D). Most oncoids are <4 cm in diameter, but specimens up to 15 cm have been observed and they Earth-Science Reviews xxx (xxxx) xxx-xxx range from ellipsoidal to subspherical (Fig. 6). Internally, oncoid cortices are very well laminated (Fig. 6C), with laminae (50 μm to 2 mm thick) that either surround the whole oncoid, or cover only a portion of it (cf. Hofmann, 1969;Freytet and Plaziat, 1972). Erosive surfaces are also observed, truncating previous laminae (Fig. 6C). Various microfabrics are observed in the oncoid laminae, including micritic and clotted-peloidal, but filamentous microfabrics are conspicuously predominant, characterized by well-preserved calcified filaments (<1 mm long with 5-15 μm lumina surrounded by thinner micritic walls), showing an erect orientation perpendicular to the laminae (Fig. 6C-F). Filaments are arranged either as closely-packed palisades or as tufts ( Fig.  6C-D). In spite of occurring in bioclastic and clastic-rich facies, oncoids do not commonly include allochthonous material in their microfabrics, with only local and minor silt-sized quartz grains being observed within micritic laminae. Some oncolitic levels show a laminated (i.e. stromatolitic) overgrowth that covers various oncoids (Fig. 6B, E, F). They have filamentous microfabrics markedly different from those of the on coid cortices, with much thicker laminae (up to 7 mm thick) formed by fan-like structures of longer and thicker (13-30 μm lumina) filaments (Fig. 6F), which are similar to those of skeletal stromatolites (see section 6.2.3, below). 6.2.1.1. Accretion processes and paleoenvironment Oncoid filaments have sizes and shapes consistent with those traditionally considered as the calcified sheaths of fossil filamentous cyanobacteria (e.g. Pollock, 1918;Pia, 1927;Black, 1933;Johnson, 1961;Golubic, 1973;Pentecost, 1978;Riding, 1983;Merz, 1992), being almost identical to the filaments of many cyanobaterial-dominated modern freshwater and fluvial microbialites (e.g. Irion and Müller, 1968;Ordóñez et al., 1986;Freytet and Plet, 1996;Freytet and Verrecchia, 1998;Arp et al., 2001b;Shiraishi et al., 2008;Arenas et al., 2014Arenas et al., , 2015Auqué et al., 2014), and even to those formed in the freshwater-influenced areas of coastal systems (e.g. Bahamas, cf. Black, 1933;Monty, 1967Monty, , 1972Monty, , 1973  Dichothrix (Monty, 1976;Schäfer and Stapf, 1978;Anadón and Zamarreño, 1981;Monty and Mas, 1981;Nickel, 1983;Leinfelder, 1985;Arenas et al., 2000;Hägele et al., 2006). The filaments that dominate the stromatolitic overgrowths of oncoids are clearly different and more similar to those of the cyanobacteria genus Rivularia (e.g. Schäfer and Stapf, 1978;Nickel, 1983;Leinfelder, 1985;Dragastan, 1985;Kuss, 1990). Thus, it is interpreted that the main process that formed these oncoids was the recurrent accretion and early mineralization of cyanobacteria-dominated biofilms that surrounded a clastic nucleus. They developed in freshwater environments linked to alluvial discharges of material eroded from the carbonate-dominated substrate of the basin (Fig. 3D) and, thus, rich in dissolved carbonate, which matches the environmental setting of modern filamentous oncoids (e.g. Roddy, 1915;Jones and Wilkinson, 1978;Schäfer and Stapf, 1978;Rott, 1991;Freytet and Plet, 1996;Hägele et al., 2006). In these settings, the combination of carbonate supersaturation with the metabolic Earth-Science Reviews xxx (xxxx) xxx-xxx activity of cyanobacteria led to carbonate precipitation within their sheaths (e.g. Kempe and Kazmierczak, 1990;Merz-Preiß, 2000;Arp et al., 2001a). The grainy facies where the oncoids often occur, together with the presence of continuous laminae and truncations in the oncoid cortices, suggest that they accreted in agitated environments, but the presence of discontinuous laminae and of stromatolitic overgrowths indicates that there were also periods when the hydrodynamic energy was not enough to continuously overturn the oncoids (cf. Dahanayake, 1977;Lanés and Palma, 1998;Campos-Soto et al., 2016). Despite the agitation of the environment and the abundance of particles, these were very rarely incorporated within the oncoid cortices, unlike in some modern (Ginsburg, 1960;Gebelein, 1976a;Jones and Goodbody, 1985) and fossil (Pederson et al., 2015) shallow-marine agglutinated oncoids.

Thrombolites
Thrombolites also occurred in the freshwater to marine-influenced wetland paleoenvironments, but they have only been observed in one locality of the western sector (Leza River section, Fig. 4), and they occur in limestones rich in dasycladales (Fig. 5C). Thrombolites form either laterally continuous beds (biostromes), up to 30 cm thick (Fig. 7A), or irregular masses (bioherms), up to 50 cm tall and 1 m wide ( Fig. 7B-D). Macro-and mesoscopically, these microbialites are not laminated and have irregular shapes with patchy or clotted fabrics, formed by interconnected mesoclots (sensu Shapiro, 2000) with a vague upwards-elongated distribution that suggests vertical growth (Fig. 7C-D) and, thus, they can be classified as thrombolites (cf. Aitken, 1967;Kennard and James, 1986;Shapiro, 2000;Riding, 2011a). The internal framework of mesoclots is very open, leaving many interstitial spaces that are currently filled by micrite and/or cement (Fig. 7E-H). In hand specimen, mesoclots are irregular, 0.1-1 cm wide masses (Fig. 7E), and under the microscope, their internal microfabric is typically poorly preserved and dominated by microsparitic textures with relicts of clotted-peloidal micrite ( Fig. 7F-H). Locally, poorly preserved filamentous structures are observed (Fig. 7G). The interstitial space between mesoclots often includes dasycladales (Fig. 7H-I), and in the specimens richest in dasycladales, these are also included within the mesoclots (Fig. 7H). 6.2.2.1. Accretion processes and paleoenvironment Thrombolites formed locally in areas of the coastal-wetland system with seawater influence that allowed the development of abundant dasycladales ( Fig. 4; and see Fig. 12C of Suarez-Gonzalez et al., 2015). The clotted-peloidal microfabric of the thrombolite mesoclots is widely regarded as the product of carbonate precipitation within microbial mats (e.g. Monty, 1976;Kennard and James, 1986;Thompson et al., 1990;Chafetz and Buczynski, 1992;Reitner, 1993;Arp et al., 1998;Dupraz et al., 2004;Riding and Tomás, 2006;Spadafora et al., 2010). Thus, it is interpreted that the thrombolites represent microbial communities that accreted developing buildups or laterally continuous beds, and which were relatively early lithified, in order to preserve their original framework. The highly porous and seemingly delicate appearance of this framework, together with the general absence of clastic particles in the thrombolites and in their adjacent sediment, suggest a quiet environment and also exclude trapping and binding as a significant process. Nevertheless, the local presence of dasycladales within the mesoclots indicates that these bioclasts could be transported by episodic currents from adjacent algal meadows, being eventually bound within the microbial communities. The close interrelation between dasycladales and microbialites is extremely rare (Martin and Delgado, 1980) and deserves further work.

Skeletal stromatolites
Stromatolites also formed in the freshwater to marine-influenced wetland paleoenvironments, but only in the western sector (Fig. 4).

Accretion processes and paleoenvironment
The filaments that dominate the skeletal stromatolites correspond to those traditionally considered as fossil filamentous cyanobacteria (e.g. Pollock, 1918;Pia, 1927;Black, 1933;Johnson, 1961;Golubic, 1973;Pentecost, 1978;Merz, 1992), and the size and shape of their abundant filament fans are equivalent to those interpreted as the extant genus Rivularia (e.g. Schäfer and Stapf, 1978;Nickel, 1983;Leinfelder, 1985;Dragastan, 1985;Kuss, 1990;MacNeil and Jones, 2006), similar to the filaments observed in the overgrowths of oncoids (see section 6.2.1, above; compare Fig. 8E-G with Fig. 6F). The extraordinary preservation of the filament microstructure suggests a very early precipitation of carbonate in the mucilaginous sheath of cyanobacteria, which was favored by their photosynthesis but was also controlled by environmental factors, mainly carbonate saturation state (e.g. Kempe and Kazmierczak, 1990;Merz, 1992;Arp et al., 2001aArp et al., , 2001bArp et al., 2012;Riding and Liang, 2005;Aloisi, 2008). The paleoenvironment of these skeletal stromatolites probably had a high carbonate supersaturation, as it was linked to discharges of clastic material from the carbonate-dominated basin substrate (Figs. 3D, 5B). Clastic discharges were probably episodic, as shown by the thin grainy intercalations between stromatolite laminae or between filament fans (Figs. 8-9). However, trapping and binding did not play a significant role in the development of these stromatolites, which mainly accreted through the early calcification of cyanobacteria-dominated microbial mats (Fig. 9). Similar modern stromatolites, dominated by well-preserved filamentous microfabrics, also occur in carbonate-rich freshwater settings (e.g. Caudwell, 1983;Pentecost, 1987;Obenlüneschloss, 1991) or within the freshwater-influenced areas of coastal systems (Portman et al., 2005;Smith et al., 2005;Gischler et al., 2008Gischler et al., , 2011Cooper et al., 2013;Castro-Contreras et al., 2014;Saint Martin and Saint Martin, 2015;Edwards et al., 2017), such as that of the studied unit.
Earth-Science Reviews xxx (xxxx) xxx-xxx

Agglutinated stromatolites
The tide-influenced oolitic paleoenvironments only occurred in the eastern sector (Fig. 4). They are characterized by lateral and vertical interrelation of oolitic deposits and stromatolites, which range from stratiform to domal, with domes up to 70 cm across and 40 cm tall (Figs. 5F, 10A-C). At mesoscale, they show a clear lamination formed by alternating darker and lighter laminae up to 4 mm thick (Fig. 10B Suarez-Gonzalez et al., 2014). These laminae show two end-member microfabrics: grainy and micritic (Fig. 10D-E). The grains observed within the stromatolites are the same as those of the surrounding oolitic deposits (ooids, peloids, micritic intraclasts, ostracods and miliolid foraminifers) but generally finer-grained, and they occur throughout the stromatolite domes, including the steeply dipping flanks (Fig. 10D). Micritic laminae show typically clotted or clotted-peloidal microfabrics (Figs. 10D, 11D-E), and dense micrite laminae are rare. Lami Earth-Science Reviews xxx (xxxx) xxx-xxx  (Figs. 10D, 11, 12). In fact, lateral and vertical variations in the relative abundance of both components are often observed through the same lamina (Fig. 12). In addition, thin micritic crusts are observed topping many stromatolite laminae: they have dense micritic or clotted textures and show sharp upper surfaces commonly associated with micritized and truncated grains (Figs. 9, 10E, 11, 12;Suarez-Gonzalez et al., 2014). Filaments are not abundant but are observed within some laminae, typically preserved as vertically elongated clusters of clotted-peloidal micrite (Fig. 11). Locally, pseudomorphs after gypsum and anhydrite have been observed displacing and replacing stromatolite laminae (Suarez-Gonzalez et al., 2014).

Accretion processes and paleoenvironment
The most distinctive feature of these stromatolites is the abundance of grains in their laminae. The facts that grains are the same as in the adjacent deposits, but finer, and that they occur both in flat and dipping stromatolite laminae, prove that these grains were not deposited merely by gravity but rather suggest that they were mobilized by currents (tides, waves and storms, Suarez-Gonzalez et al., 2015, 2016aFig. 9) and eventually stuck to the mucilaginous surface of the microbial mats that formed the stromatolites (cf. the criteria used to interpret trapping and binding in modern agglutinated examples: e.g. Gebelein, 1969;Riding, 1991;Reid and Browne, 1991;Frantz et al., 2015). Therefore, trapping and binding can be considered a significant accretion process in them, and for this reason they are classified as "agglutinated stromatolites" (sensu Riding et al., 1991a). Nevertheless, the presence of clotted and clotted-peloidal micritic laminae without trapped grains indicates that these stromatolites accreted not only when grains were supplied to the microbial mats but also during periods of sediment stasis and no grain supply ( Fig. 12; Suarez-Gonzalez et al., 2014), a fact that has only recently been suggested also for the classical examples of modern agglutinated microbialites in Shark Bay (Hagan, 2015;Suosaari et al., 2016a). The fact that filaments are scarce and poorly preserved ( Fig.  11; unlike other microbialites of the same unit, i.e. oncoids and skeletal stromatolites, Figs. 6, 8) suggests that they did not undergo very early calcification (similarly to modern analogues, Fig. 1F-G), and that the clotted and clotted-peloidal micrite precipitated during subsequent microbial degradation of the organic matter of the mat, as interpreted in many modern and ancient microbialites (Figs. 9, 12; e.g. Chafetz and Buczynski, 1992;Reitner, 1993;Arp et al., 1998;Dupraz et al., 2004;Riding and Tomás, 2006;). In addition, laminae of mixed grainy-micritic composition record variations in grain supply and mat accretion even at the relatively short time-scale represented by a single stromatolite lamina (Fig. 12, compare with Fig.  1D). Settling of allochthonous micrite on the stromatolite surface may have formed the rare dense micritic laminae, as interpreted for similar laminae in other fossil examples (e.g. Rodríguez-Martínez et al., 2012). Thin micritic crusts, common at the top of laminae, are strikingly similar to those thoroughly studied in modern marine agglutinated examples (compare Figs. 10E, 11, 12 with Fig. 1H-I; e.g. Monty, 1976;Reid et al., 1995Reid et al., , 2000Reid et al., , 2003Macintyre et al., 1996;Feldmann and McKenzie, 1998;Visscher et al., 2000) and, thus, they are similarly interpreted as the product of microbially induced alteration and precipitation at the top of microbial mats during hiatuses in stromatolite accretion (Suarez-Gonzalez et al., 2014).

Micritic-evaporitic stromatolites
Another type of stromatolite occurred locally in the evaporitic paleoenvironments, which were only developed in the eastern sector ( Fig.  4; see Fig. 12C of Suarez-Gonzalez et al., 2015). Stromatolites are laterally-linked domes up to 10 cm tall, very well laminated, and with laminae showing dense, clotted or clotted-peloidal microfabrics, which are often diagenetically altered (Fig. 13). No filaments have been observed and grains occur very scarcely in rare laminae. Displacive and replacive pseudomorphs after gypsum and anhydrite, from μm-to mm-scale, are very common within the stromatolites (Fig. 13D), and are often grouped in cm-scale macroscopic nodules (Fig. 13C). 6.2.5.1. Accretion processes and paleoenvironment The restricted and marine-influenced evaporitic paleoenvironments locally developed benthic microbial communities that produced stromatolites. The absence Earth-Science Reviews xxx (xxxx) xxx-xxx of clear microbial filaments suggests that these microbial communities were not very early lithified and that micrite precipitation probably took place subsequently, induced during degradation of the organic matter of the mat (cf. Chafetz and Buczynski, 1992;Reitner, 1993;Arp et al., 1998;Dupraz et al., 2004;Riding and Tomás, 2006), although settling of allochthonous micrite should not be ruled out, especially for the dense micrite laminae (cf. Rodríguez-Martínez et al., 2012). The scarcity of grains in their paleoenvironment may explain that they are only rarely observed within the stromatolite laminae. Important evaporation produced significant supersaturation in the interstitial waters within the stromatolites, allowing the precipitation of intrasedimentary evaporitic sulfates (cf. Schreiber and El Tabakh, 2000;Warren, 2006;Ortí, 2010).

Fenestral laminites
Peritidal wetland paleoenvironments only developed in the western sector ( Fig. 4; see Fig. 12C of Suarez-Gonzalez et al., 2015) and include very abundant fenestral laminites (Fig. 5E). They are thinly-bedded and display flat, irregular, wrinkly lamination, formed by mm-scale alternations of micritic laminae and laminae of horizontally-elongated fenestrae (Fig. 14A-B). Fenestrae typically show irregular shapes (Fig.  14C-F) and locally have stromatactis-like structures with flat bases and irregular tops (Fig. 14D, F). Fenestral porosity is currently filled by geopetal sediment and cement ( Fig. 14D-F). Micritic laminae mainly have clotted or clotted-peloidal microfabrics (Fig. 14D-F) with rare dense micritic laminae and only local and poorly-preserved relicts of calcified filaments. Micritic laminae commonly include grains (Fig.  14D-E): peloids, carbonate intraclasts, quartz grains and bioclasts (ostracods and less common foraminifers). Some micritic laminae display vertical, often v-shaped fractures filled by cement, which may represent mud-cracks (Fig. 14E). 6.2.6.1. Accretion processes and paleoenvironment Fenestral laminites are a widespread carbonate facies commonly found in peritidal carbonate settings from the Archean to the present (e.g. Logan, 1974;Hardie and Ginsburg, 1977;Pratt et al., 1992;Sumner and Grotzinger, 2004;Riding, 2008;Duda et al., 2016), being even considered "unequivocal intertidal deposits" (Tucker and Wright, 1990, p. 151). They are widely interpreted as being formed by the successive accretion, lithification and desiccation of microbial mats (e.g. Ham, 1952;Tebbutt et al., 1965;Shinn, 1983;Mazzullo and Birdwell, 1989;Demicco and Hardie, 1994). In fact, the fossil examples presented here are very similar to some flat, laminated microbial mats of modern coastal settings, some of them agglutinated (cf. Davies, 1970;Kinsman and Park, 1976). The fact that filaments are so rare and poorly-preserved, compared to other Earth-Science Reviews xxx (xxxx) xxx-xxx Fig. 11. A-E Photomicrographs of the rare filament remains observed in the agglutinated stromatolites of the Leza Fm. Note that filament remains (blue arrows and ellipses) are poorly preserved, mostly as individual elongated clusters of clotted-peloidal micrite, being only locally associated in tufts (ellipses of C and E). Compare the preservation of filaments with that of modern agglutinated microbialites ( Fig. 1F-G). Green arrows point to thin micritic crusts between successive laminae, strongly similar to those of modern analogues ( Fig. 1H-I). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) microbialites of the unit (i.e. oncoids and skeletal stromatolites), suggests that fenestral laminites did not undergo very early cyanobacterial calcification, and that clotted and clotted-peloidal micrite precipitated during subsequent microbial degradation of the organic matter of the mat (cf. Chafetz and Buczynski, 1992;Reitner, 1993;Arp et al., 1998;Dupraz et al., 2004;Riding and Tomás, 2006), although settling of allochthonous micrite may have contributed to the formation the rare dense micritic microfabrics (cf. Rodríguez-Martínez et al., 2012). The grains observed within the micritic layers are the same as those observed in laterally associated facies (see section 6.1, above) and, thus, they were most likely mobilized from adjacent areas by waves or storms. In summary, fenestral laminites studied here were deposited in very shallow and commonly desiccated near-marine areas of a coastal-wetland system, which were often colonized by thin and flat microbial communities that evolved through successive episodes of accretion and desiccation, and which underwent input of grains that were trapped and bound within some of their laminae.

Are microbialite accretion processes environmentally controlled?
Microbialites are extremely diverse organosedimentary structures and their diversity can be explained by the biotic complexity and variability of the microbial communities that formed them, as well as by the many different environments in which they develop (e.g. Dupraz et al., 2011;Riding, 2011a). This is especially appreciated in modern and ancient systems in which different microbialites occur in different settings (e.g. Black, 1933;Braga et al., 1995;Bourillot, 2009;Jahnert and Collins, 2013;Vennin et al., 2015). In this regard, the case study presented here shows an unusual abundance and diversity of microbial deposits, with six types of contrasting microbialites that occurred in different paleoenvironments (Figs. 2, 4, 5, Table 3), ranging from alluvial-influenced freshwater to tide-influenced marginal marine. For this reason, this Lower Cretaceous example is a perfect field laboratory for an Earth-Science Reviews xxx (xxxx) xxx-xxx Fig. 12. The detailed analysis of stromatolite laminae reveals, even at the small temporal and spatial scale of a single lamina, the complex interplay between microbial accretion and sediment supply that produces the microfabrics of the Leza Fm agglutinated stromatolites, which are strikingly similar to those of modern analogues (Fig. 1F-I). A: During some periods, a benthic microbial community could accrete on the stromatolite surface even with relatively low sediment supply. If early calcification occurred locally, some filament remains would eventually be preserved. B: During periods of low microbial accretion relative to the sediment supply, thin levels especially rich in grains developed. C: When the rates of microbial accretion and grain supply were balanced, grainy levels were recorded. Meanwhile, precipitation of clotted-peloidal micrite could start in underlying parts of the microbial community, probably induced by the degradation of EPS by heterotrophic microbes. D: Interruption periods of both microbial accretion and grain supply are recorded by thin micritic crusts caused by intense microbial activity at the top of the microbial community, which induced micritization and truncation of underlying grains and micrite precipitation. E: Photomicrograph of the final result in the fossil record.
alyzing how biotic and abiotic factors interact in the development and in the spatial and temporal distribution of fossil microbialites. Shedding light on this question is necessary to understand why agglutinated microbialites are so scarce in the geological record and which factors control the 'trapping and binding' process that formed them.
The diversity and variability of the case study paleoenvironments, which constantly underwent changes in salinity and/or inundation , are common to many coastal systems (Frey and Basan, 1978;Baldwin et al., 2009;Wolanski et al., 2009;22 P. Suarez-Gonzalez et al. Earth-Science Reviews xxx (xxxx) xxx-xxx Davidson-Arnott, 2010). This environmental variability generates stressful conditions for most metazoans (e.g. Brenchley and Harper, 1998), which are typically favorable for the development of microbial communities (e.g. Telesh et al., 2013). This explains the relatively poor diversity of metazoan associations in the case study  and the important productivity and preservation of organic matter (i.e. non-mineralized microbes from the water column and the sediment, preserved as abundant black, fetid and locally bituminous limestones) and microbialites. But even more striking than the abundance of microbialites in the case study is their diversity (Figs. 2,(4)(5). All the main macroscopic categories of microbialites (sensu Kennard and James, 1986;Riding, 1991Riding, , 20002011a, b;Schmid, 1996;Dupraz et al., 2011) are recorded: oncoids, stromatolites, thrombolites, and fenestral laminites (Fig. 2). Each of these microbialite types occurred in a different paleoenvironment (Fig. 4, Table 3), highlighting the traditional interpretation that environmental factors are the main controls of macrostructure and external morphology of microbialites (e.g. Logan et al., 1964;Hoffman, 1976;Semikhatov et al., 1979;Trompette, 1982;Ginsburg, 1991;Andres and Reid, 2006). However, this case study also shows that microscopic aspects of microbialites can be strongly dependent on external environmental parameters, because morphologically similar microbialites (e.g. domal and well-laminated stromatolites) may show different microfabrics (1 -skeletal; 2 -agglutinated; and 3 -micritic-evaporitic) when occurring in different paleoenvironments (1 -freshwater bodies with alluvial input; 2 -tide-influenced oolitic areas; and 3 -restricted evaporative areas), indicating that in each paleoenvironment a contrasting process dominated their accretion (1 -early filament calcification; 2 -'trapping and binding' of grains; and 3 -pervasive micrite precipitation; Table 3 ,Figs. 2,4,9). Development of microbialite microfabrics has been shown to be highly controlled by the intrinsic biotic composition and processes of the microbial communities that form them (e.g. Semikhatov et al., 1979;Trompette, 1982;Andres and Reid, 2006), but the fossil examples studied here, as well as some modern cases (Bowlin et al., 2012;Jahnert and Collins, 2013), show that the influence of extrinsic environmental factors on the variability of microbial communities (and, thus, on the diversity of microfabrics they produce) should not be underrated. This environmental control on microfabrics (especially on agglutinated microfabrics) is one of the main interests of this study and is discussed in detail here.
For example, the fact that filamentous microbialites of the case study (oncoids and skeletal stromatolites,Figs. 6,8) only occurred in freshwater-dominated paleoenvironments (Figs. 4,5), whereas the rest of microbialites Figs. 7,(10)(11)(12)(13)(14) occurred in paleoenvironments with various degrees of marine influence (Figs. 4,5), is a clear example of environmental influence on microfabric. The most important factor controlling strong and early calcification of filamentous microbes (mainly cyanobacteria) is supersaturation in CaCO 3 of their ambient waters (e.g. Riding, 1982;Kempe and Kazmierczak, 1990;Merz, 1992;Arp et al., 2001aArp et al., , 2001bArp et al., 2012;Riding and Liang, 2005;Aloisi, 2008) and, therefore, this is a crucial environmental requirement for the development of microbialites with well-preserved filamentous microfabrics. In fact, it has long been noted that filamentous microbialites are extremely rare in marine environments since the Cretaceous until now, being practically restricted to freshwater settings (Monty, 1973;Gebelein, 1976b), a trend that has been explained as due to the strong and continuous decline in the CaCO 3 saturation state of surface sea water at least since the Early Cretaceous (Arp et al., 2001a(Arp et al., , 2001bRidgwell, 2005;Ridgwell and Zeebe, 2005;Riding and Liang, 2005;Aloisi, 2018). Therefore, the development of Cretaceous, Cenozoic, and modern calcified filamentous microfabrics has been environmentally constrained to continental and coastal settings where freshwater could reach a strong CaCO 3 supersaturation, such as in the case study presented here (see sections 6.2.1 and 6.2.3, above). P. Suarez-Gonzalez et al. Earth-Science Reviews xxx (xxxx) xxx-xxx Another link between microstructure and paleoenvironment provided by the studied unit concerns agglutinated microbialites. Both the case study and the literature review show that microbialites dominated by agglutinated microfabrics occur, throughout geological history, mainly in marginal-marine environments, being especially abundant in those with evidence of tidal influence (see section 5 above and Tables 1-3). This pattern has not been studied in detail before and will be discussed in the following sections, since it may be crucial to understand which biotic and environmental conditions favor 'trapping and binding' and which hinder it.

To trap or not to trap: factors controlling grain agglutination
Two main requirements have been traditionally referred to as essential for a microbialite to trap and bind the sedimentary grains of its surroundings (Burne and Moore, 1987;Riding, 2011a): a) most obviously, the presence of grains in the environment, together with the conditions necessary (i.e. sufficient water agitation) for the supply of those grains onto the microbialite surface; and b) a sufficient 'stickiness' of its surface.
In the freshwater examples (oncoids and skeletal stromatolites), grains are not significant components of their microstructures, dominated by filamentous textures (Figs. 6,(8)(9). One possible explanation for this pattern could be that in the freshwater examples there was little and only sporadic grain supply, or that the input of grains occurred after microbialite development. It is true that in the agglutinated stromatolites, the shallow-marine tidal setting would provide continuous and recurrent water agitation (tides, waves and storms), facilitating a constant supply of grains onto the stromatolite surface. Nevertheless, many of the oncoids occur embedded in a sandy matrix, and thus it is very likely that their freshwater environment was also continuously agitated (e.g. small channels or creeks; Suarez-Gonzalez et al., 2015), transporting the oncoids together with other smaller particles that, however, were not commonly incorporated into their laminae (Fig. 6). In the case of skeletal stromatolites, the grainy intercalations between stromatolite laminae or between filament fans  show that grain input, although sporadic, was simultaneous with the stromatolite accretion. Similarly, many other fossil and modern examples of microbialites that developed in grainy and commonly agitated environments do not show significant grains trapped within their microfabrics (e.g. Kalkowsky, 1908;Cole and Picard, 1978;Neuhauser et al., 1987;Camoin et al., 1997;Paul and Peryt, 2000;Seard et al., 2013;Chidsey et al., 2015;Bouton et al., 2016b). In fact, only a few examples associated with shallow-marine settings, and especially with tidal influence, do (Tables 1, 2). Therefore, other factors, in addition to the grain availability and the hydrodynamic agitation, are necessary to explain the environmental pattern observed in the distribution of agglutinated microbialites.

Sticking grains
Even if a microbialite accretes in a grainy environment, and if the grains are regularly and abundantly supplied onto it, those grains still have to be stuck to its surface and bound by the microbial communities that form it, in order to achieve an agglutinated microfabric (Burne and Moore, 1987;Riding, 2011a;Frantz et al., 2015). The 'sticky' quality of these microbial communities is provided by their extracellular polymeric substances (EPS), which are responsible (among many other functions) for the cohesion of microbes with each other and for their adhesion to substrates (e.g. Sutherland, 1982;Characklis and Wilderer, 1989;Meadows et al., 1994;Wingender et al., 1999). The mechanisms that provide this adhesive capacity to EPS are not fully understood yet , but many studies of microbial attachment to surfaces and of sediment biostabilization by microbial communities (e.g. Sutherland, 1982;Fletcher, 1988;Dade et al., 1990;Decho, 1990;Mayer et al., 1999;Staats et al., 1999;de Brouwer et al., 2005;Flemming et al., 2007;Spears et al., 2008;Gerbersdorf and Wieprecht, 2015; and references therein) have shown that one of the most relevant controls is the presence of abundant cations, facilitating electrostatic bridging between the anionic groups of polymers and the charged surfaces of substrates or sediment grains. Therefore, since EPS are secreted by the microbes, the adhesiveness of a microbialite surface could be viewed as an intrinsic factor controlled by biotic features. However, given the influence of electrolyte concentration, extrinsic hydrochemical conditions of the environment could play a significant role. In this regard, some studies have described a pattern that relates the adhesive property of EPS with salinity: microbial communities of coastal and marine settings seem to stabilize sediment more effectively than those of freshwater settings, even though the latter may show higher abundance of EPS (Spears et al., 2007(Spears et al., , 2008Gerbersdorf and Wieprecht, 2015). Nevertheless, biostabilization of sediment by micro Earth-Science Reviews xxx (xxxx) xxx-xxx bial EPS does also occur in freshwater environments (e.g. Droppo et al., 2007;Hagadorn and McDowell, 2012;Gerbersdorf and Wieprecht, 2015;Schmidt et al., 2015;Thom et al., 2015), but the higher abundance and diversity of dissolved ions in brackish and marine environments may enhance the ability of EPS to adhere to sediment grains (Spears et al., 2008). This present-day pattern is consistent with that shown by the literature review and the case study presented here, because modern and fossil agglutinated microbialites occur only in shallow-marine environments, contrasting with the many non-marine microbialites that do not accrete mainly by 'trapping and binding', despite occurring in grainy settings (e.g. Kalkowsky, 1908;Cole and Picard, 1978;Neuhauser et al., 1987;Camoin et al., 1997;Paul and Peryt, 2000;Seard et al., 2013;Chidsey et al., 2015;Bouton et al., 2016b;Suarez-Gonzalez et al., 2016a, 2016b; Table 3). Furthermore, microbialite EPS form not only the sticky surface to which grains adhere, but they are also, and mainly, the locus of mineral precipitation (Burne and Moore, 1987;Dupraz et al., 2009;Riding, 2011a). Therefore, early mineral precipitation within the surface layer of microbialites should also be taken into account as another significant factor. Studies approaching the 'trapping and binding' issue experimentally (using modern stromatolitic microbial communities) have considered the importance of this factor, pointing as a limitation of their tests the fact that they "did not evaluate the impact of mat calcification and stromatolite lithification" (Frantz et al., 2015;p. 417). The Cretaceous case study presented here may help to overcome that limitation through the analysis of its microbialites dominated by filamentous microfabrics (oncoids and skeletal stromatolites, Figs. 6, 8-9). As discussed above (sections 6.2.1, 6.2.3), these microbialites developed in freshwater environments where filamentous microbial communities (most likely cyanobacteria) were heavily calcified very early in their development, maybe even during their metabolic processes, as photosynthesis is known to promote the early precipitation of carbonate within filamentous cyanobacterial communities (e.g. Merz, 1992;Merz-Preiß, 2000;Arp et al., 2001aArp et al., , 2001b. Since calcification takes place within and/or upon the EPS surrounding filamentous microbes (e.g. Golubic, 1973;Pentecost, 1978;Pentecost and Riding, 1986;Merz, 1992), the strong and early calcification would imply a significant reduction in the 'sticky' EPS available at the microbialite surface. Thus, very early and pervasive mineral precipitation could further decrease the ability of a microbial community to trap and bind sediment grains. This would explain the fact that the studied oncoids and skeletal stromatolites do not include abundant grains in their microfabrics (Fig.  15), despite being formed in grainy and agitated environments (Fig.  9). Conversely, microbes of the marine-influenced microbialites of the same sedimentary system (Table 3) were not as early, rapidly or pervasively calcified as in the freshwater examples, allowing uncalcified 'sticky' EPS to be available for a longer time at the microbialite surface (Figs. 9, 12, compare with Fig. 1D-G). Therefore, the ability of the surface EPS of a microbialite to adhere and include grains seems to be at least partially controlled by the hydrochemistry of its environment (as proposed by Riding, 2011a, p. 649). In this regard, continental saline lakes are interesting environments to consider, because their hydrochemistry could provide abundant and diverse electrolytes to enhance EPS 'stickiness' (which could explain the local presence of trapped grains in sporadic examples, e.g. Brasier et al., 2018;Vennin et al., 2018), but at the same time saline lakes often have high alkalinity and reach a high CaCO 3 saturation state (e.g. Arp et al., 1998;Dupraz et al., 2004Dupraz et al., , 2013Brasier et al., 2018), which may trigger early precipitation within EPS and, thus, hinder the 'trapping and binding' process. Moreover, although continental saline lakes may have significant currents, these are less likely to be as common as in shallow-marine settings, continuously washed by waves, tides and storms. Thus, these hydrodynamic and hydrochemical features may explain the fact that ag glutinated microfabrics are not widespread in modern or fossil microbialites formed in continental saline lakes.
In summary, the previous discussion suggests that trapping and binding of grains by microbialites may be a process largely controlled by the following environmental factors (Fig. 15): a) the presence of grains in the environment, together with b) sufficient and continuous water agitation; and c) significant concentration and diversity of electrolytes, to increase the EPS 'stickiness', but d) with a CaCO 3 saturation state not so high as to promote early and strong carbonate precipitation in the EPS. Of course, intrinsic biotic factors also influence trapping and binding, as taxonomic differences between microbial communities entail differences in EPS production (e.g. Hu et al., 2003;Underwood and Paterson, 2003;Bahulikar and Kroth, 2008) or mineral precipitation (e.g. Obenlüneschloss and Schneider, 1991;Gautret et al., 2004). For example, some studies have shown that microbial communities with abundant eukaryotes (e.g. diatoms and chlorophytes) are more effective in trapping and binding grains than purely bacterial communities (Awramik and Riding, 1988;Frantz, 2013;Frantz et al., 2015), suggesting the eukaryotic influence as a time-limiting factor for agglutinated microbialites (Awramik and Riding, 1988;Riding, 2011a), given the relatively recent introduction of some eukaryotes in microbial mats (e.g. diatoms, whose marine fossil record starts in the Early Cretaceous; Suzuki and Oba, 2015). However, the description of agglutinated microbialites in Devonian, Triassic and Jurassic times (Table 2), and the rarity of diatom and chlorophyte remains in fossil agglutinated microbialites qualify this intriguing hypothesis, which deserves further analysis. In addition, some of the studies that noted the relevance of eukaryotes also highlighted the role of extrinsic conditions (such as water flow) in the agglutination process (Frantz, 2013;Frantz et al., 2015). Thus, the environmental (sedimentological, hydrodynamic and hydrochemical) controls seem to be overall very strong (cf. Monty, 1972;Golubic, 1973;Gautret et al., 2006;Vennin et al., 2015).

Clearing up 'trapping and binding': a new look at an old debate
The process of 'trapping and binding' has been essential in the history of microbialite research, but it has also been misleading, because fossil agglutinated counterparts showing clear evidence of that process are extremely scarce (see section 4, above). This problem has been long debated (Monty, 1972(Monty, , 1977Serebryakov and Semikhatov, 1974;Awramik and Riding, 1988;Ginsburg, 1991) and is still unclear. Interestingly, even the preponderance of the 'trapping and binding' process in the classical modern examples is also starting to be questioned (Suosaari et al., 2016a). The present study pinpoints a series of environmental factors that seem to enable a microbialite to accrete mainly by trapping and binding allochthonous grains (see previous section 7.2). Both the literature review and the case study presented here show that only microbialites formed in environments that fully reach all the conditions show significant development of agglutinated microfabrics, and the best conjunction of conditions typically occurs in shallow-marine tide-influenced environments (Fig. 15, Tables 1-3). In fact, going back to the origin of the debate, Black's (1933) description of microbialites in the Bahamian coastal system, it is significant that he already noted how microbialites in freshwater-dominated areas of the system show early-calcified filamentous textures and lack trapped grains, whereas microbialites in adjacent shallow-marine areas (which can be even formed by the same microbes as the freshwater specimens) lack significant early filament calcification and mainly accrete by trapping and binding, generating agglutinated microfabrics (Black, 1933;Monty, 1967Monty, , 1972Monty, , 1973. Moreover, microbialites of hypersaline areas of the Bahamian coastal systems typically develop micritic microfabrics, devoid of grains and of calcified filaments (Dupraz et al., 2004(Dupraz et al., , 2013Dupraz and Visscher, 2005), as it is also observed in the Cretaceous case study (Fig. 13, Table 3). P. Suarez-Gonzalez et al. Earth-Science Reviews xxx (xxxx) xxx-xxx Furthermore, the geological record of agglutinated microbialites (Table 2), supports a strong environmental control on the process of trapping and binding, indicating that this process has been most easily achieved in shallow-marine environments, especially those with tidal influence. According to the factors proposed here (Fig. 15), tides do not seem to be strictly necessary for 'trapping and binding'. In fact, other mechanisms such as waves or storms have also been proposed as relevant for the delivery of grains onto modern agglutinated microbialites (Dravis, 1983;Riding et al., 1991a;Feldmann and McKenzie, 1998;Sprachta et al., 2001). Actually, any grain-rich environment that would provide common agitation by any type of current, plus high electrolyte concentration to enhance EPS adhesiveness, and a carbonate supersaturation not too high as to promote strong early calcification of EPS, should be suitable for the development of agglutinated microbialites. Therefore, the key to the 'trapping and binding' debate may reside in the difficulty of reaching the "favorable conspiracy" (Bosak et al., 2013) of all those factors together and continuously, in order to promote 'trapping and binding' long enough to produce a whole agglutinated microbialite. This difficulty could explain why agglutinated microbialites have remained more an exception than a rule throughout the geological record. For example, the scarcity of clearly agglutinated microfabrics in Precambrian microbialites might be linked to the commonly accepted interpretation that Precambrian oceans had a carbonate saturation state much higher than modern oceans (e.g. Grotzinger and Kasting, 1993;Grotzinger and Knoll, 1999;Bosak and Newman, 2003;Ridgwell and Zeebe, 2005;Aloisi, 2008). In the metazoan-dominated Phanerozoic world, microbialites in general were much less abundant than before (e.g. Riding, 1997;Riding, 2006;Grotzinger and Knoll, 1999), but the decrease in seawater carbonate saturation allowed some agglutinated microbialites to develop, only sporadically and in local refuges: coastal or shallow-marine, often with tidal influence, where the rest of the factors controlling 'trapping and binding' were also achieved (Table 2). Furthermore, the rarity of agglutinated microfabrics outside marine or coastal settings can be due to a combination of factors: a) that strong and continuously agitated conditions are more easily achieved in wave-, tide-and storm-swiped shallow-marine areas; b) that water in non-marine settings commonly includes lower electrolyte abundance and diversity than seawater (except in saline lakes, see section 7.2 above), probably decreasing EPS adhesiveness; and c) that microbialite-bearing environments in these settings (especially in saline lakes) are often supersaturated in CaCO 3 , facilitating early mineral precipitation within EPS. Nevertheless, these factors are not necessarily unfeasible in continental settings, and the fact that some continental microbialites include sporadic grains within their microfabrics (e.g. Frantz et al., 2014;Della Porta, 2015;Bunevich et al., 2017;Brasier et al., 2018;Vennin et al., 2018) suggests that those conditions were at least locally and temporarily achieved. In fact, the recent developments on this subject together with the new perspective provided by this study allow to foresee that future research will further enlighten the four-decade long debate about 'trapping and binding' in microbialites, by finding new constraints of that process, especially if new examples of agglutinated microbialites are described in pre-Mesozoic rocks or in non-marine settings.

Conclusions
This study provides the first exhaustive database of agglutinated microbialites (those mainly formed by 'trapping and binding' allochthonous particles) in modern and ancient settings. The database shows that agglutination of grains by microbialites, despite being an often-cited process, is relatively rare (a fact that has been noted before in the last four decades, but not comprehensively studied yet). Modern agglutinated microbialites have been found only in eight localities worldwide, all of them in shallow-marine environments, and most un der tidal influence. Fossil agglutinated microbialites, analogous to modern examples, have been described only in nine localities worldwide, three Cenozoic in age, five Mesozoic and only one Paleozoic. All of them were formed in shallow-marine paleoenvironments and most are interpreted to have had tidal influence. Therefore, the literature review shows that microbialites mainly formed by 'trapping and binding' are scarce throughout the long geological history of microbialites, and that they seem to be environmentally restricted to shallow-marine settings, and especially those influenced by tides.
A Lower Cretaceous case study is presented here, which includes a wide diversity of microbialites (six different types) formed in a coastal wetland system, with paleoenvironments ranging from freshwater to shallow-marine and hypersaline. Four microbialite types occurred in grainy paleoenvironments, but those formed under freshwater conditions do not significantly include grains in their microfabrics, whereas those formed in shallow-marine settings do, especially the agglutinated stromatolites, which developed in tide-influenced paleoenvironments. Thus, the case study supports the environmental pattern observed in the database of modern and fossil agglutinated microbialites.
The combination of literature review and case study prompts discussion about the parameters that control microbialite accretion processes and the microfabrics they produce, and it shows that environmental factors may have a stronger influence on microfabric development than previously thought. In particular, microbialite accretion through agglutination of allochthonous grains is mainly controlled by two extrinsic factors (occurrence of grains and continuous water agitation) and one intrinsic factor (presence of abundant 'sticky' EPS on the microbialite surface). However, the literature suggests that the latter biotic factor may be largely influenced by two environmental parameters: high concentration and diversity of electrolytes in the water, which increase EPS adhesiveness; and a CaCO 3 saturation state not so high as to promote early and strong carbonate precipitation within EPS, which would decrease its availability to adhere grains. The combination of these hydrodynamic and hydrochemical parameters is not easily achieved, at least not prolonged enough to produce a whole agglutinated microbialite. This is exemplified by the case study presented here and by the distribution of modern agglutinated microbilates, and it would explain the scareceness of agglutinated microbialites in the geological record. In addition, these parameters may also explain the environmental and stratigraphic distribution of agglutinated microbialites, because they are more prone to be attained in commonly agitated shallow-marine settings (especially those daily washed by tides), at least in post-Paleozoic times. Therefore, this review provides answers to the long-standing debate of the rarity of agglutinated microbialites, and it also provides a starting point for future research on the widely cited but still intriguing process of 'trapping and binding'.

Aknowledgements
We dedicate this work to Laura Fernández Labrador, who was going to be an excellent scientist because she always asked the right questions. Now, her enquiring spirit will be forever in our hearts helping us to keep asking interesting questions and looking for answers. This work was funded by the research projects CGL2014-52670-P and CGL2011-22709 of the Spanish Government, the 'Sedimentary Basin Analysis' research group of the Complutense University of Madrid, a predoctoral FPU scholarship of Spanish Department of Education, and a postdoctoral fellowship of the German Alexander von Humboldt Foundation. We appreciate detailed and constructive comments by Dr. André Strasser and by an anonymous reviewer. We are thankful to Beatriz Moral, Gilberto Herrero and Juan Carlos Salamanca for thin-section preparation, and to Laura Donadeo and María Victoria Romero for help with the bibliography. P. Suarez-Gonzalez et al. Earth-Science Reviews xxx (xxxx) xxx-xxx Uncited references Paterson, 1994Serebryakov, 1976Suárez González, 2015Suarez-Gonzalez et al., 2017