Whatever the depositional environment and the main skeletal metazoans, the studied coral- and sponge-microbialite reefs show very similar architectures and growth modes. Bioconstructions are all made up of elementary units (or ‘high-frequency reef-growth phase’). The first stage of development of these elementary units corresponds to the edification of a primary coral or sponge bioconstruction (Fig. 4). This primary growth fabric is constratal in sponge bioherms, whereas it is either superstratal or constratal in coral reefs. A first and thin (millimetre-scale) microbialite layer developed on the local dead part of corals and sponges. This layer is considered as contemporaneous of the coral or sponge growth [11], [12], [47] and [48]. The first microbialite layer does not necessarily represent the first stage of the encrustation. Some microencrusters, such as Bacinella and Lithocodium, are directly observed on the coral surface, below the first microbialite layer. Both in coral- and sponge-microbialite bioconstructions, the second centimetre-thick microbialite layer entirely covers the coral- or sponge-reef surface, playing an important binding role and becoming the main reef builder. The succession between a first skeletal reef component (i.e. corals or sponges) and an important volume of microbialites at the reef front suggests an ecological disruption (Fig. 4). More or less abundant and diverse microencrusters can be associated with both the first and second microbialite layers. The third microbialite layer is observed only within coral or sponge bioconstructions of constratal growth fabric. This microbial crust of stromatolitic fabric onlapped the previous reef components, playing probably an important binding role before being covered by sediments. Only sparse microencrusters (Terebella) are observed within the third microbialite layer. Commonly, sediments overlay coral- or sponge-microbialite elementary units, pointing to a reef growth interruption. In some cases, notably in most of coral reefs of superstratal growth fabric, sediments are lacking between two successive elementary units, emphasizing a relief formation.

The reef development is marked by major reef-growth interruptions that delimit ‘medium-frequency reef-growth phases’ constituted of several elementary units. In mixed, clay-rich contexts, these periods of reef-growth interruption are particularly well marked and correspond to centimetre-thick marly levels (Fig. 2C). In pure carbonate or mixed carbonate-rich contexts, these periods of reef growth interruption seem shorter and are laterally correlated to a thin (millimetre-scale) marly interval or to a bed joint (Fig. 2A and B).

Sponge- and coral-microbialite reefs always initiated laterally to limestones. Their ‘low-frequency reef-growth phase’ final demise can follow different pathways. In pure carbonate contexts of Pagny-sur-Meuse, coral-microbialite bioherms were definitively covered by limestone beds. In mixed carbonate-rich contexts, the final demise of coral-microbialite reefs of the Chay Peninsula is marked by an erosional surface, leading to a final flat-topped bioconstruction. At the Chay Peninsula, coral-microbialite reefs of mixed carbonate-rich contexts are definitively covered by marly levels. If sponge-microbialite bioherms can be definitively covered by a limestone bed in mixed carbonate-rich contexts, they are covered by either a marly level or a limestone bed in mixed clay-rich contexts.

Using a cyclostratigraphic approach in Swabian deep-shelf deposits, where developed sponge-microbialite bioherms, a marl-limestone couplet can be assimilated to the 20-kyr precession cycle [48] and [53]. Such a marl-limestone couplet is laterally correlated to a ‘medium-frequency reef-growth phase’ that can be subdivided into 3 to 10 elementary units. Thus, the formation of an elementary unit (i.e. the succession between a primary coral or sponge framework and a microbialite crust) can be at least reasonably estimated to occur at a millennial timescale. Such duration is compatible with an estimation of the approximated time necessary for a coral- or sponge-microbialite elementary unit to develop. Following the banding structure observed in fossil corals that is assumed to represent annual growth increments [2], the mean growth rate of Jurassic corals is estimated to be in the order of 1 mm yr⁻¹ (e.g., [32], [33] and [44]). Estimation of Upper Jurassic sponge growth rate is more difficult. Based on modern sponge reefs of the west coast of Canada (British Columbia), although quite uncertain, a cm yr⁻¹ growth rate for Upper Jurassic siliceous sponges can be assumed [30] and [68]. Thus, a centennial to millennial duration can be considered for coral and sponge primary frameworks edification within an elementary unit.

Due to the lack of modern equivalent, the evaluation of the microbialite growth rates is more difficult. Microbialite crusts observed in some modern coral reefs have an extremely low growth rate, of about 0.005 mm yr⁻¹ [55]. On the other hand, thrombolites from some Pleistocene coral reefs were interpreted to present a very high growth rate, estimated to be equal to the reef accretion, which is comprised between 1.1 and 2.6 cm yr⁻¹ [5]. Following the working hypothesis of a millennial time scale for an elementary unit to form, a microbialite growth rate ≤ 1 mm yr⁻¹ is suggested. Higher growth rate would lead to consider long periods of reef growth interruptions that are not corroborated by field observations such as heavily bored surfaces. Considering a microbialite growth rate of about 1 mm yr⁻¹, thicker microbialite crusts (up to 15 cm) will form in one or two centuries, corroborating a millennial timescale for the formation of one elementary unit.

Although a more precise estimation of the microbialite growth rate would be speculative, their petrographical characteristics support substantial variations in studied coral and sponge reefs. During the second microbialite layer development, differences in microfabrics and microencruster abundances can be interpreted in terms of variations in the microbialite growth rate. In sponge and coral reefs of pure carbonate or mixed carbonate-rich contexts, the second microbialite layer is generally made up of clotted or peloidal micrites that developed columnar shapes. In that case, microencrusters associated to this second layer are very sparse, suggesting a relatively continuous and high microbialite growth rate [47]. In mixed clay-rich contexts, the second microbialite layer is made of dense or clotted micrites with a domal shape or a wavy upper surface. In that case, numerous microencrusters alternate with this second microbialite layer. Thin (up to 1-cm-thick) and dark horizons of massive microbialites, underlined by numerous boring bivalves and oysters, are also commonly observed and can be compared with the basal crusts described by Schmid [60] or with modern crusts covering hardgrounds [57]. Such horizons emphasize particularly long microbialite growth interruption events. Thus, the presence of abundant encrusters associated with a dense to clotted micrite emphasizes a lower and more irregular microbialite growth rate in siliciclastic-rich environments compared to pure or carbonate-rich contexts, where microbialites are commonly made of peloidal micrite with rare encrusters [47].

The amount of nutrients in the water column defines oligo-, meso-, and eutrophic conditions, which control the trophic structure and the feeding modes in modern reef systems [20]. Numerous studies emphasize an important role played by nutrients in controlling the formation of Jurassic microbialite-rich coral or sponge build-ups (e.g., [11], [29], [36], [38] and [60]). Unfortunately, modern equivalent of Upper Jurassic coral- and sponge-microbialite reefs are unknown, making difficult an actualistic approach. In modern siliceous sponge reefs on the western coast of British Columbia, the presence of microbial deposits is not proven [9] and [68]. If microbialites are commonly observed in modern coral reefs, these crusts are generally confined in the internal parts of the bioconstructions (e.g., [55] and [69]). Nevertheless, some modern coral reefs of French Polynesia reveal a microbialitic formation at the reef surface, following an increase in the nutrient availability [63]. Microbialite formation induced by temporal pulses of nutrient release has been mentioned within some Pleisto-Holocene coral reefs [4] and [6]. Similarly, Dupraz and Strasser [11] and [12] have explained the development of large amounts of microbialites at the surface of some Upper Jurassic coral reefs by an increase of the nutrient content linked to terrigenous inputs.

The causal mechanism responsible for the nutrient content fluctuations in the water column can strongly differ according to the bioconstruction considered and its depositional setting. The presence of upwellings can bring nutrient-rich waters in shallow platforms [38]. However, neither sedimentary nor palaeontological field arguments confirm such hypothesis in the studied cases. Nutrients can also be released from sediments after, for example, a storm event in pure carbonate contexts of Pagny-sur-Meuse [47]. In mixed clay- or carbonate-rich contexts, it is assumed that nutrients mainly derived from terrigenous inputs, probably triggered by climatic oscillations. According to the amount of clay content in the system, studied sponge- and coral-microbialite reefs show significantly different compositions and dimensions (Fig. 5).

In mixed clay-rich contexts, coral- and sponge-microbialite bioherms are small, with lateral extents that do not exceed 15–20 m. Skeletal metazoans also display reduced sizes. In sponge bioherms, dish-shaped and lamellar sponges generally rarely exceed 10 cm in diameter. Similarly, sizes of branching and domal corals generally remain below few tens of centimetres in height and in diameter, respectively. Nutrient-rich waters are also emphasized by sponge or coral assemblages. Sponge bioherms are made of a relatively important amount of lithistids (up to 33% of the sponge assemblage) and microbialites (up to 58% of the reef volume). Such an amount of lithistids, considered as active filter feeding organisms [38], suggests relatively high-trophic conditions. In coral reefs, the amount of terrigenous material and nutrients deduced from the coral assemblages seems also correlated with the microbialite content. In mixed clay-rich contexts of Pagny-sur-Meuse, microbialites represent 16–30% of the reef volume when the coral assemblage (mainly Thamnasteria, Microsolena, and stylinids) is mixed photo-heterotrophic, and up to 50% with a heterotrophic association (mainly Microsolena, Calamophylliopsis, and Thecosmilia). In this later case, microbialites show numerous surfaces of growth interruption, which are marked by abundant heterotrophic encrusters (e.g., oysters and bryozoans) and an intense bioerosion, enhancing a high nutrient level (Fig. 5).

In pure carbonate context of Pagny-sur-Meuse, reef composition and dimension emphasize oligo- to low-mesotrophic waters. These coral-microbialite bioconstructions display very large dimensions, up to 15–20-m-thick and more than 100 m of lateral extent. Corals are diversified and commonly display metre-scale dimensions. The coral assemblage (i.e. mainly Aplosmilia and stylinids) and the microencruster association (Bacinella and Lithocodium) are characteristic of oligotrophic conditions [11] and [36]. Microbialites are not abundant and their contribution to the reef volume does not exceed 16%. However, they can locally form a relatively thick crust (up to 5 cm), made of thrombolitic columns. Considering a nutrient release from sediments after a storm event, the time interval during which waters are nutrient-rich is relatively short. Even so, the coral reef damage, coupled with a possible biofilm capacity to prevent or limit the coral recovery and settlement, allowed rapid but reduced microbial development. Relatively fast and continuous microbialite growth is indeed suggested by rare microencrusters and no significant boring activity.

In mixed carbonate-rich contexts, intermediate reef patterns characterized sponge- and coral-microbialite bioconstructions. Reef composition and dimension emphasize low- to high-mesotrophic conditions. Bioconstructions show relatively high dimensions, up to 10 m thick and 50 m of lateral extent. Dish-shape hexactinellids commonly exceed 1 m in diameter. Some branching coral colonies (e.g., Calamophylliospsis) also exceed 1 m in diameter and height. The coral reefs are represented by a mixed photo-heterotrophic coral assemblage. Heterotrophic microencrusters are common, whereas Bacinella and Lithocodium are only locally observed in some coral bioherms (e.g., Chay Peninsula). Mixed carbonate-rich contexts seem to be the more favourable environment for microbialite development in coral reef (up to 70% of the reef volume; Fig. 5). In sponge bioherms, the high amount of microbialites (46% of the reef volume), their thickness (up to 15 cm), and their columnar shape also suggest very favourable conditions to a rapid development.

The nutrient content controlled the general reef composition, but its fluctuations have also an impact on the reef development. In the model of Fig. 4 that illustrates the main factors controlling the formation of an elementary unit, the microbialite development at the front of coral and sponge reefs is mainly explained by an increase in the nutrient content. Independently of trophic conditions that occurred during coral or sponge growth, this model emphasizes the rapidity of the shift towards relative more nutrient-rich conditions that favoured the bloom of benthic microbial communities and the formation of the second microbialite layer at the reef surface. Olivier et al. [48] demonstrated that fluctuations of the nutrient content controlled sponge-microbialite reef growth in a mixed clay-rich context (Fig. 6). The bioherm development (i.e. ‘low-frequency reef-growth phase’) can be included in a low frequency fluctuation of the nutrient content. Considering calcareous microfossils, marly levels that surround the sponge-microbialite bioherms are characterized by the highest occurrence of small ‘eutrophic species’. In the middle part of bioherms, corresponding to their maximal lateral extent, lateral deposits display higher carbonate content and more oligotrophic nannofossils. By analogy, ovoid-shaped coral-microbialite reefs of mixed clay-rich contexts, which are stratigraphically surrounded by marly levels, may also reflect similar continuum in the trophic conditions. The coral-microbialite reef growth only occurred laterally to limestone deposits (mesotrophic conditions), whereas it finally demised under eutrophic conditions during the deposition of marly levels. Although less visible in the lithology, similar continuum in the trophic conditions can be applied to sponge- and coral-microbialite bioherms of mixed carbonate-rich or pure carbonate contexts. In both cases, maximum lateral extents of bioconstructions occurred under a relatively low nutrient content (oligo- to mesotrophic conditions), and the reef development reduction probably reflects more nutrient-rich waters. Nannofossil assemblages analyzed laterally to sponge-microbialite bioherms of Plettenberg also display significant differences at the scale of the ‘medium-frequency reef-growth phases’. In this mixed clay-rich context, the limestone beds, which are laterally correlated to the sponge-microbialite bioherm development (i.e. ‘medium-frequency reef-growth phase’), are characterized by a predominance of oligotrophic nannofossil assemblages [48]. In marly levels, during reef growth interruptions, meso- to eutrophic assemblages of nannofossils predominated. Less abundant sponges, and reduced microbialite development in marly intervals, led to the loss of a real reef-framework when high nutrient content (eutrophic conditions) might have occurred (Fig. 6).

A very low accumulation rate of sediments is necessary for the installation of coral or sponge larvae. For coral reefs of superstratal growth fabric, the accumulation rate should remain relatively low to null during the entire primary coral framework edification, as suggested by mammilated microbialites with a downward growth direction at the underside of coral colonies (Fig. 3A). This leads us to consider with cautions the usual and perhaps too much easily admitted interpretation of high-branching corals as a witness of oversedimentation. In bioconstructions of constratal growth fabrics, the presence of some encrusters such as bryozoans, serpulids, and thecideid brachiopods on the lower surface of dish-shaped siliceous sponges and lamellar or massive corals also implies a low accumulation rate during the formation of the primary skeletal framework (cf. [17] and [31]; Fig. 4).

Although the formation of ancient microbialites is generally considered as reflecting a sedimentation rate close to zero, because biofilms are not able to survive high sediment input [36], the successive microbialite layers observed within elementary units highlight accumulation rate variations. Both in coral and sponge reefs, the first microbialite layer development is contemporaneous with corals or sponges, and thus developed under a low-to-null accumulation rate. The second microbialite layer, with a domal or columnar shape, may reflect disturbing influence of sediment particles on the biofilm surface [13] and [55]. However, a columnar growth form of microbialites can also be considered as of biological origin and dependent on a sufficient accommodation space [3] and [65]. Thus, sediment accumulation could also remain strongly reduced during the second microbialite layer formation. In that case, columnar thrombolites more probably reflect rapid microbialite growth rather than a direct reaction against burial (Fig. 4). The downward growth direction characteristic of columnar mammilated microbialites of bioherm underside supports such interpretation. Sponge-microbialite bioherms are always characterized by the presence of a third stromatolitic layer that ends the microbialite encrustation [10], [17] and [48]. This third layer was also observed in some Bajocian coral-microbialite bioherms of constratal growth fabric [49]. Such upward succession from a thrombolitic (microbialite layer 2) to a stromatolitic (microbialite layer 3) fabric is commonly observed in the fossil record [1], [14], [28] and [42] and in modern settings [15], and can be interpreted as the result of an increase of the accumulation rate [10], [17], [48], [51] and [62]. Thus, at the scale of an elementary unit of constratal growth fabric, the fluctuation of the accumulation rate tends to be irregular and progressively increases during the formation of the third microbialite layer. Only a decrease of the accumulation rate permits the installation of a new generation of sponges or corals. The third stromatolitic layer is absent in coral-microbialite reefs of superstratal growth fabric. In these bioconstructions, sediments directly covered the second microbial crust, suggesting a too rapid increase of the accumulation rate that did not allow the formation of a stromatolite layer. Such a scenario seems to have occurred in pure carbonate contexts, where microencrusters are lacking at the second microbialite layer surface. In mixed clay-rich contexts, microbialites are generally heavily encrusted and bored, suggesting a longer period before being definitively covered by sediments. Whatever the depositional context and the reef-growth fabric considered, the increase of the accumulation rate progressively tends to surpass the microbialite growth rate, leading to the end of the elementary unit development (Fig. 4). Phases of sediment accumulation mainly occurred during periods of reef-growth interruption. The presence of limestone beds at the top of some coral- or sponge-microbialite reefs also suggest that final demise of some bioconstructions (i.e. at a ‘low-frequency reef-growth phase’) can be due to an increase of the accumulation rate.

Reef growth and environmental parameters can be considerably affected by sea-level fluctuations [38]. Water-depth estimations corresponding to deep ramp or epicontinental basin settings are generally assumed for sponge-microbialite bioherms [17,34, 41]. In recent studies on Upper Jurassic sponge-microbialite bioherms of southwestern Germany, an important control of sea-level fluctuations during the reef development was suggested [51] and [59]. These authors explained the transition between the second thrombolitic layer and the third stromatolitic layer by a depth decrease. Furthermore, they consider that elementary units initiated on an erosional surface, which probably resulted from a storm event. In studied Plettenberg and French Jura sponge-microbialite bioherms, such erosional surfaces have not been observed, and as described by Gaillard [17], elementary units are frequently delimited by stylolitic structures. Abundant ammonites, few solitary corals, as well as the absence of hummocky cross-stratifications and calcareous algae, suggest a depth probably below the storm-wave base [48] and [53]. The presence of strong deep currents, such as it is observed in modern sponge reefs on the western Canadian continental shelf [68], may be sufficient to explain the numerous tuberoids in the lateral deposits of the bioconstructions. A water depth in the range of 60–100 m is assumed for the studied sponge-microbialite bioherms. Thus, low amplitudes (a few metres) of bathymetric changes in the Upper Jurassic [52] cannot have a direct influence on ‘high-, medium- or low-frequency reef-growth phases’. On the other hand, such sea-level changes directly controlled the carbonate production on the Jura shallow platform, and the amount of carbonate exported to epicontinental basins [54]. Thus, sea-level changes indirectly controlled sponge-microbialite development via the accumulation rate. Concerning coral-microbialite reefs, changes in water depth may be particularly important and directly controlled their development. An effect of sea-level fluctuations is well visible at the scale of the ‘low-frequency reef-growth phase’ in the Chay Peninsula, where the bioconstructions of two reef levels are flat-topped, probably because they caught-up the sea level. Although more difficult to highlight, a similar direct depth-water stress cannot be excluded at the scale of ‘high-frequency reef-growth phase’, leading to the end of the sediment accumulation phase.

The existence of dysoxic to anoxic waters is one of the most cited factors of the literature explaining the formation of pure thrombolitic bioherms in the deep part of Jurassic epicontinental basins [35], [38], [59] and [60]. Authors considered that seawaters were oxygen depleted, as suggested by the presence of glauconite and the bivalve Aulacomyella in sediments. The predominance of microbial deposits associated with the Terebella–Tubiphytes association, coupled with rare metazoans, is also interpreted as being significant of oxygen-poor waters in the deeper part of epicontinental seas [60]. Such arguments are also applied to platform settings, in order to explain the transition between coral- or sponge-dominated levels and pure thrombolite-dominated levels [36]. Oxygen-depleted and nutrient-rich waters have been invoked in the formation of microbialite-rich coral reefs of the Chay Peninsula [35]. In studied sponge- and coral-microbialite reefs, the main microbialitic crusts (i.e. second and third microbialite layers) are posterior to the primary coral or sponge framework. Thus, the formation of microbialites could reflect dysoxic waters. The existence of oxygen-depleted waters during the formation of microbialites has been tested using rare-earth elements (REE; [45]). The specific behaviour of the cerium (Ce) in the lanthanide group gives information on the oxygenation state of ancient seawaters. In pure carbonate lagoon setting of Pagny-sur-Meuse, seawater-like REE patterns, highlighted by strong negative Ce anomalies measured on microbialite samples, suggest a well-oxygenated water column. Moderate negative Ce anomalies, reported in microbialites of carbonate-dominated sponge bioherms (Plettenberg), evoke relatively well-oxygenated seawaters. In mixed carbonate- and clay-rich contexts of the Chay Peninsula and Pagny-sur-Meuse, high amounts of siliciclastics masked the seawater signature, and do not allow us to define the redox conditions. Therefore, in the studied Upper Jurassic coral and sponge reefs, the oxygenation state has not played a major role in the formation of microbialites.

Terrigenous inputs can also increase the alkalinity of seawater, enhancing the carbonate precipitation related to microbialite formation [27], [43] and [55]. However, the absence of positive Ce anomalies, as well as strongly enriched Heavy REE patterns in the studied microbialites, suggest that ambient seawaters were characterized neither by a high alkalinity nor by a higher pH than that of modern seawaters [45].

Terrigenous inputs can increase the turbidity of the water column, influencing photophilic reef communities. The presence of light-dependent microencrusters such as Bacinella and Lithocodium in some coral reefs suggests well-illuminated waters [36]. A light dependence of microbialites in coral or sponge bioconstructions is highlighted by their upward growth direction, whereas sciaphilic organisms encrusted the downward facing surface of substrates [17] and [46]. Such an observation is compatible with the fact that 1 to 10% of the surface light intensity reaches depths of 60–100 m [66]. Periods of reduced light intensity in the water column probably occurred in mixed clay-rich contexts, due to higher amounts of terrigenous material (Fig. 5). During such periods of low light intensity, microbialites could stop their growth, allowing the formation of intensively bioeroded and encrusted surfaces.

Upper Jurassic coral diversity appears closely correlated to ambient seawater temperatures and displays significant variations according to climatic changes and latitudinal positions [8]. The relatively large latitudinal window of Upper Jurassic reefs is generally used to support an equable global greenhouse climate [34] and [35]. Thus, it is unlikely that temperature was a predominant controlling factor at the scale of ‘medium- and high-frequency reef-growth phases’ of coral- or sponge-microbialite bioconstructions.