Astronomically controlled deep‐sea life in the Late Cretaceous reconstructed from ultra‐high‐resolution inoceramid shell archives

The periodicity of the mutual position of celestial bodies in the Earth‐Moon‐Sun system is crucial to the functioning of life on Earth. Biological rhythms affect most of the processes inside organisms, and some can be recorded in skeletal remains, allowing one to reconstruct the cycles that occur in nature deep in time. In the present study, we have used ultra‐high‐resolution elemental ratio scans of Mg/Ca, Sr/Ca and Mn/Ca from the fossil, ca. 70 Ma old inoceramid bivalve Inoceramus (Platyceramus) salisburgensis from deep aphotic water and identified a clear regularity of repetition of the geochemical signal every of ~0.006 mm. We estimate that the shell accretion rate is on average ~0.4 cm of shell thickness per lunar year. Visible light–dark lamination, interpreted as a seasonal signal corresponding to the semilunar‐related cycle, gives a rough shell age estimate and growth rate for this large bivalve species supported by a dual feeding strategy. We recognize a biological clock that follows either a semilunar (model A) or a tidal (model B) cycle. This cycle of tidal dominance seems to fit better considering the biological behaviour of I. (P.) salisburgensis, including the estimated age and growth rate of the studied specimens. We interpret that the major control in such deep‐sea environment, well below the photic zone and storm wave base, was due to barotropic tidal forces, thus changing the water pressure.

extremely high resolution. This gives particularly interesting results in the case of bivalve, which are among some of the longest-lived animals (more than 500 years, e.g . Butler Jr. et al., 2013;Butler & Schöne, 2017). The bivalves biomineralization process and shell microstructure of bivalves allow the examination of growth laminae even with a subdaily resolution (e.g. de Winter et al., 2020;Poitevin et al., 2020). Thus, bivalve shells represent a remarkable biogeoarchive that allows one to analyse daily environmental changes over entire decades or centuries. These methods can be applied to fossil bivalve shells known from the Cambrian period onwards, providing insight into the development of bivalves throughout the Phanerozoic and constructing logs of environmental change over deep time in well-preserved specimens (Moss et al., 2021). The recording of diurnal changes over a long period, spanning decades of shell growth, also allows one to analyse the recording of biological rhythms occurring in nature. This is particularly of high interest in the case of fossil material dating back millions of years, as it gives the opportunity to reconstruct the functioning of the Earth-Moon system in deep time (de Winter et al., 2020). An exemplification of the above statement is the case described in the following article, in which we try to identify the biological rhythms recorded in the shell of a Late Cretaceous deep-sea bivalve belonging to an extinct group of inoceramids.
There are two kinds of biological rhythms of interest for sclerochronology which are influenced by the Sun or the Moon. The first one, the circadian rhythm is referred as a day-night, 24-h rhythm that presently cycles over 365 days (annual cycle). The second, the circalunar rhythm, is due to lunar phases that currently repeat every ~29.5 days (lunar month). However, the most important lunarinfluenced cycle is the biological circatidal rhythm that currently repeats every ~12.4 h ( Figure 1). Thus, the frequency of the circadian rhythm is slightly less than that of the couple of circalunar rhythms.
This small difference hampers the identification of the origin of rhythmicity recorded in some skeletal remains such as bivalve shells, and consequently, endogenous stimuli (zeitgeber) triggering biological rhythms in the past may be misinterpreted.
The Earth-Moon system relation evolved through time, with Earth's rotation slowing down due to tidal friction resulting in a decreasing number of days per year and increasing day length (e.g. Berry & Barker, 1968;Wells, 1966;Williams, 1990). The effect of transferring energy to the Moon results in lunar retreating, currently at rate of 3.82 cm a −1 (Dickie et al., 1994). Consequently, increasing Earth-Moon distance results in a change of the length of lunar rhythms. For example, the synodic month during the Early Ordovician (~470 Ma) was presumed to be about 1 day longer than present (Pannella, 1972), while a solar year contained about 40 days more, ca. 21.4 h each (Williams, 2000). Therefore, biologically controlled rhythms had to follow these changes by adapting to the periodicity of the main influencing stimuli. However, the Late Cretaceous (Maastrichtian, ca. 70 Ma), from which the studied specimen comes, was largely characterized by lunar rhythm lengths like those found in nature today (Williams, 2000). These were, respectively, for the lunar year cycle of about 12.6 months and for the lunar month of about 29.85 days (Pannella, 1972). In contrast, the duration of the solar year was significantly expanded, calculated in detail from a Torreites sanchezi rudist bivalve, resulting in 372 days, each 23.5 h long (de Winter et al., 2020). This example demonstrates that lunarrelated rhythms are more stable in Earth history and contain less uncertainty in paleoenvironmental reconstruction calculations compared with solar-dominant rhythms. However, interpreting the main origin of the leading biological rhythm seems problematic even in today's living organisms, and hence, in fossils with their often-poor timing and age constraints, may be even more challenging.
Knowledge of how biological clocks affect the behaviour of organisms in each of Earth's biomes, i.e. terrestrial (Navarro-Castilla & Barja, 2014), aerial (York et al., 2014) and marine (Last et al., 2016), is growing. Most of them, run either by circadian or circalunar clock and occur in light -dependent environments. The research mainly concerns organisms living in zones with periodic daylight, which is partly related to the availability of research material or the specificity of laboratory work. Most of the Earth's surface today and in the past is represented by deep marine environments (e.g. Costello & Chaudhary, 2017), where light stimuli influence is strongly limited or apparently absent. Therefore, for decades, 'blind' deep-sea ecosystems were considered aperiodic or neglected. Nevertheless, the presence of periodicity in organism behaviour from deep-marine light-free conditions has been recently noted (Hui et al., 2017;Modica et al., 2014). The examples of Bathymodiolus azoricus and B.
brevior confirm the presence of biological rhythms in recent bivalves at greater depths (Mat et al., 2020;Schöne & Giere, 2005). In these instances, the leading role of stimuli is replaced by tidal changes in hydrodynamic conditions and might be followed by endogenous biological clock. Moreover, evidence of lunar or even seasonal cyclic organism activity in deep-water conditions, i.e. in reproduction, has been reported (Mercier & Hamel, 2014). Therefore, lunar-related rhythms carry a significant impact on the biosphere, even at great depths period, since the setting up of the Earth-Moon (tidal) system. This has likely been the case through geologic time, the Late Cretaceous, is generally characterized by greenhouse conditions with relatively high atmospheric pCO 2 levels reaching >500 ppm (Wang et al., 2014), intermediate to deep ocean water temperature >20°C (Friedrich et al., 2012) and high sea-level, averaging 75-250 m greater than present (Haq, 2014). The seafloor topography and oceanic water mass circulation in this time interval underwent significant changes, e.g. opening of the South Atlantic and the Equatorial Atlantic Gateway (Friedrich & Erbacher, 2006;Voigt et al., 2013). During the middle Campanian to end-Maastrichtian period (~80-66 Ma), the environmental settings correspond to a general and gradual cooling from the mid-Cretaceous hothouse, a decrease in pCO 2 atmospheric concentration, a slight average sealevel drop and an increase in the magnitude of rapid short-term sea-level fluctuations (even <0.25 Ma cycle duration) of ~50 m (Ray et al., 2019). Hence, the end of the Mesozoic was volatile, the rearrangement of paleogeography and short-term rapid fluctuations of sea levels imply significant and dynamic changes affecting oceanic depositional environments and marine biota inhabiting them. Most of those relatively swift environmental changes have been accompanied by global biotic events such as the mid-Maastrichtian Inoceramid Acme Event (Dameron et al., 2017) or coincide with extinctions as in the case of the K-Pg boundary nannofossils crisis (Thibault & Husson, 2016).
The subject of this study, inoceramids, has had a worldwide distribution and belonged to a significant epifaunal group of marine communities during the Late Mesozoic (Harries & Crampton, 1998).
Their wide ecological tolerance and highly adaptive strategy of life allowed them to inhabit environments ranging from highly oxygenated shallow-marine to oxygen-deficient deep-marine ones (Kauffman & Harries, 1996). Hence, they can not only be used as an excellent stratigraphic tool (Walaszczyk, 2004) but also have high analytical capabilities in reconstructions of paleoenvironmental proxies (Walliser & Schöne, 2020). The present study reveals rhythmic patterns recorded based on high-resolution geochemical data derived from the Upper Cretaceous inoceramid bivalve shells of the species I. (P.) salisburgensis (Fugger and Kästner, 1885) representing a deep-marine aphotic environment. Therefore, the aim of this paper is to test and demonstrate the existence of astronomically controlled biological rhythms, driven by inner clock(s) -circatidal and/or circadian -where the main stimuli are provided here in lunar rhythm frequencies. Our work provides a pilot study to open chronobiological considerations into fossil material for a better understanding of main life-controlling forces (biological rhythms) and their evolution, enhancing also the accuracy of paleoenvironmental reconstructions.

| Geological settings and sampling
The material studied was collected in the Skole Unit area, in an exposure of Ropianka Formation deposits, traditionally classified as Inoceramian Beds, due to the presence of horizons locally abundant in these fossils (Uhlig, 1885). The Skole Unit represents the sediments of a former basin extending along the northeastern shore of the Tethys Ocean, and the area of Inoceramian Beds occurrence is called inoceramian facies in the Polish Outer Carpathians for this reason. The marginal part of the Skole Unit bears the characteristics of shelf-prone facies, but in the inner, offshore part, the inoceramian facies bears the characteristics of basinal facies, in which suspension current sediments, or turbidites, occur (Kędzierski & Leszczyński, 2013).

F I G U R E 1
The most significant astronomical and geophysical (short term) rhythms on the Earth dictated by the Moon and the Sun influence. (a) Lunidian rhythm -the period between two next highest point of the Moon in the sky (meridian transit); Tidal rhythm -the water level rising and falling twice each day (lunar day) due to combination of the Earth's rotation and the Moon orbiting around it. (b) Synodic month -the Moon completes one revolution around the Earth relative to the Sun and tidal variations following this: spring tides cycle -during Full Moon (FM) and New Moon (NM) phases, neap (solar) tides cycle -during First Quarter Moon (FQM) and Last Quarter Moon (LQM) phases. (c) Tropical month -the clockwise rotation of the Earth axis creates declination of the Moon trajectory. (d) Anomalistic month -the elliptical orbit of the Moon results in different distance between the Earth and it's satellite. Because of no significant changes in periodicity between Upper Cretaceous and recent lunar-related rhythms lengths are given the same as in present (modified after Kvale et al., 1995).
In the north, the Skole basin was connected to the epicontinental sea of the boreal province by a seaway between the passive margin of the Central European Land and the Ukrainian Shield; in the south, the basin was open towards the inner part of the (Neo-)Tethys Ocean (Golonka et al., 2000;Remin et al., 2022) (Figure 2a). The Late Cretaceous seafloor evolution, the thermal structure of water column (Pucéat et al., 2003;Walliser & Schöne, 2020) and water circulation (Ladant et al., 2020) show significant changes in the Tethys Ocean.
During the Maastrichtian, the deep-water connection, between the North Atlantic and Indian Ocean throughout the Tethys Ocean, was limited or did not exist at all. Hence, the deep circulation in the Tethys Ocean decreased by that time, and shallow/intermediate-water exchange was more likely to be connected to the North Atlantic rather than to northern parts of the Indian Ocean. Poor water-mixing results in warmer, more saline water masses and may indicate stronger water column stratification in the basin (Figure 2c). Moreover, significant influence of shallow-water shelf waters from boreal zone conditions was limited and is inferred only for winter seasons (Ladant et al., 2020). Therefore, the studied section was most likely prone to equable open-marine conditions ( Figure 2a).

Rock samples and shell fragments of Inoceramus (Platyceramus)
salisburgensis were collected from a natural exposure outcropping along the Wiar riverbank, close to the village of Rybotycze, (city of Przemyśl vicinity, SE Poland). The analysed section consists of distal fine-grained flysch deposits, i.e. turbidites intercalated with pelagic sediments, with clay-marlstones interbedded occasionally by finegrained thin-medium sandstone turbidites. A dozen of inoceramidbearing horizons were identified, and in every case the hosting rock represents interturbiditic (pelagic) sedimentation (T e Bouma division) (Leszczyński et al., 1995). The in situ accumulation of the inoceramid fauna in the studied section embraces part of the Inoceramian Beds (or Ropianka Formation) of the late early Maastrichtian age (Leszczyński et al., 1995; Figure 2b).

| Sample preparation and microscope examination
Analyses were performed on I. (P.) salisbugrensis medium-sized (up to 7 × 6 cm), well-preserved shell fragments (without discoloration or visible fractures). Bivalve shells were embedded in epoxy resin to avoid fracturing during cross-sectioning. Each of these specimens was cut in half, perpendicular to the growth lines, along the maximum axis of growth straight through the centre of the shell fragments with a low-speed precision lapidary saw equipped with a 0.5-mm-thin, diamond-coated blade. One half of each specimen was used to prepare, standard (~30 μm thick) thin sections. The other half, dedicated for geochemical analysis, was ground and polished subsequently with 500, 1000, 2000 and 4000 grit SiC sandpapers at the cut-line surface. Every change of paper grain size was proceeded using ultrasonically cleaning samples in deionized water (~5 min/20°C). Possible diagenetic alterations were examined on thin sections by cathodoluminescence (CL) analysis with polarization light microscope (Nikon Eclipse 50i) and the Cambridge Image Technology (CITL) 8200 Mk three cold cathode sets under standard carbonate operating conditions (electron beam voltage: ~12 kV, electric current: ~500 mA). The shell slabs remains from thinsection preparation were analysed for preservations understand a HITACHI S-4700 Field Emission Scanning Electron Microscope (FE-SEM) at the Institute of Geological Sciences (Jagiellonian University, Poland). Before FE-SEM analyses fresh cut samples were rinsed with deionized water in an ultrasonic bath (~10 min/20°C), then dried (24 h/~60°C) and afterwards coated in a Cressington Turbo Carbon Coater 208carbon. FE-SEM analysis was performed to investigate diagenetic alteration and detect microboring. Additionally, a simple method of microboring detection was applied (Golubic et al., 1970) that includes preparation using low-viscosity Araldite2020 epoxy resin casting, hydrochloric acid etching technique and coatings by carbon.

| Geochemical screening
For each shell fragment, stable isotope ratios (δ 13 C and δ 18 O) were determined at the Institute of Geological Sciences of the Polish Academy of Sciences in Warsaw to assess diagenetic alteration in more detail. For that purpose, micro-drilled powders from three locations of the shells (inner, middle and outer part) per each specimen, using a DREMEL3000 drilling tool with a flexible arm equipped with a 300 μm-diameter spherical SiC Mesinger dental drill bit, were obtained. The drilling tool was fixed to a binocular microscope, and the surrounding bulk rock matrix (mudstone with calcium carbonate content ranging from 16.85% to 49.13%) was collected for measurements then. Sampled carbonate phase (20 in total) was reacted with oversaturated 100% orthophosphoric acid at 70°C in a Thermo KIEL IV Carbonate Device automated reaction system and measured with a Finnigan Delta Plus dual system isotope-ratio mass spectrometer. The reproducibility of replicate analysis for standards (NBS 19 and IAEA CO8) and samples was better than ±0.03‰ for

| Time series analysis
The influence of environmental parameters on bivalve shell chemistry can be very complex, as it is likely related to both environmental conditions and controlled by the organism itself. Sometimes a small population in the same habitat can exhibit different accumulation strategies because biological control of the shell composition often prevails over the environmental control (Rainbow et al., 2000). The left side of the model is related to Earth-Moon interplay, i.e. a strong influence on shallow water basin parts (creation of tidal zone) hence control in rhythmically distribution nutrients to deeper parts or frequency of shelf remobilization (turbidites slides). The right side of the model refers to Earth-Sun interaction, i.e. the interplay of sun height at the horizon (day length) and oceanic primary production in the open-marine zone, control of mean water temperature or most obvious light availability in the water column. The Earth-Moon-Sun relation, despite influence on the tidal force, may imply marine biota activity, i.e. spawning events due to lunar reflected light during the full moon. Because of no significant changes in periodicity between Late Cretaceous and recent lunar-related rhythms lengths are given the same as in present. The Late Cretaceous solar year and day length (year -372 days; day -23.5 h) calculated by de Winter et al. (2020).
Ca elemental ratios has been carried out with time-series spectral analysis using PAST: Paleontological statistical software (Hammer et al., 2001). The "astrochron" package built in the open-source computational software package R was used to investigate the spectral density of timeseries of geochemical signals in inoceramid specimens (Meyers, 2012(Meyers, , 2014R Core Team, 2021). To identify potential spectral peaks in Mg/Ca, Mn/Ca and Sr/Ca series, we applied the "Locally-Weighed Regression Spectral Background Estimation" ("LOWSPEC") method. Power spectra are estimated by the multitaper method (Thomson, 1982), and additionally harmonic F-test estimates the significance of the multitaper spectrogram. The analysis lists spectral peaks that fulfil all requirements and achieve the required threshold, in this paper a confidence interval (CI) of 95%.
If necessary, data were interpolated using piecewise interpolation.
The LOWSPEC analysis applied a time bandwith of 3, the span for lowess smoothing was set to 5 (term "lowspan"), and the data series was prewhitened and zero-padded adding 2 × n (where n is the total length of the dataset, see Meyers, 2014).
Despite the presence of nonperiodic signals that are likely linked to local events or analytical noise, the number of stacked peaks at similar frequencies relies on the numbers of different environmentally controlled parameters (e.g. water temperature, availability of nutrients) as variants recorded from the biologically controlled rhythms (circa-tidal or lunidian, circa-semilunar, circalunar; Figure 4b). Additionally, the peaks bundling strongly depends on the amount of recorded time of shell growth. Naturally, a longer record implies a higher chance of noting more event patterns and their aftermath. An interplay of the overlapping environmental cycles, i.e.
anomalistic month -Perigee with synodic month -new moon (NM) or full moon (FM) or seasonal conducted primary oceanic production dependent on day length during the summer/winter season, needs to be considered in the low repetitive peaks interpretations as well.
Moreover, a variety in growth rates can also influence these peaks; however, we assume that in the studied specimens of I. (P.) salisburgensis, there is a continuous accretion of shells resulting from an essentially unchanging year-round habitat (the bottom of a sea body at the foot of the continental slope, below the photic zone and storm wave base). Moreover, the ability to mixtrophic way of feeding is an additional argument supporting an almost stable accretion of shell material (e.g. Hawkins & Klumpp, 1995), thus a stable time/distance relation in the geochemical record.

| I. (P.) salisburgensis specimens' observations
The inoceramid shells macroscopically reveal mostly well-preserved material and almost untouched internal structure. Despite the absence of the aragonite nacre layer and organic periostracum, typical for bivalve fossil material, the specimens were collected having the left and right shells. It should be mentioned here that the predominant low-magnesium calcite in the prismatic layer in the fossils of Platyceramus and related inoceramides is relatively diagenetically resistant (e.g. Walliser et al., 2018). Cracks that occur throughout the collected shells are related to fracturing due to compaction over time rather than eventual damage during postmortem transportation. Additionally, accumulation of the investigated shells in interturbidites only and the extraordinary shell size, partly exceeding 1 metre in length (characteristic for the Platyceramus group, see Kauffman et al., 2007), also indicate in situ occurrence of the shells.
Considering their overall dimensions and slightly convex shape, the shells would not have been able to be transported for long distances without intense fragmentation or disarticulation. Moreover, the surrounding mudstone represents pelagic sedimentation (T e Bouma Division), and some inoceramid specimens occurred directly at the pelagic-turbidite interface, covered by thin distal turbidite beds, which further supports this interpretation. Therefore, we assume that the collected shells can be considered as biogeoarchives from an off-shore pelagic, slope-to-basin deep-marine site ( ranges from ~125 to ~70 μm (av. ~90 μm). Moreover, the boundary between darker organic-rich and lighter inorganic, as well as distinguishing increment couplets, is impeded. Nevertheless, the age (seasonal) interpretation based on these blurry visual laminae becomes less reliable than using geochemical data. Based on the observations of a perfectly preserved paratype and specimens partially exposed during field work providing the morphological structure of the outer shell surface, the growth ratio seems to be very regular and follows examined. Specimens partially exposed in analysed outcrop reveal analogous trend in furrow/ridges regular and continuous distribution. for bulk rock, and for δ 13 C ranged between 2.15‰ and 3.14‰ for bivalve and 1.60‰ and 1.84‰ for clay-marlstone. In every case, δ 18 O stable isotope ratios of the inoceramid shells were more positive than those of the hosting bulk rock samples. A similar trend is generally observed for δ 13 C stable isotope ratios, where records of I.

| Time-series analysis
High-resolution line-scan LA-ICP-MS analysis allows us to obtain a few thousand geochemical data points of time record in each bivalve shell sample (Table 1) (Table 1).

| DISCUSS ION
Fossil shell material exposed for almost 70 Ma to various diagenetic processes may provide a biased geochemical record. Factors that can significantly preserve the original elemental composition of the shells include the type of rock and its permeability. Post-depositional fluid migration at our study site was strongly limited thanks to the TA B L E 1 The general outlook of LA-ICP-MS data from all specimens provided by spectral analysis. The paleoecology of I. (P.) salisburgensis represents extraordinary environmental conditions, inhabiting deeper aphotic parts of ocean basins in considerable distance from the shelf and the tidal zone (Figure 2). This may be interpreted as an evolutionary niche of survival due to avoidance of predatory encounters, that is, as a response to stress by predators and/or food competitors (Langerhans, 2007). Additionally, some of the inoceramid species, especially in the Platyceramus group, likely harboured symbionts related to the inferred dual feeding strategy (mixtrophic thioautotrophic) imprinting significantly on their stable isotope ratios Anderson and Arthur (1983) formula with a correction to VSMOW and VPDB scales given by Coplen et al. (1983), and they vary in the range of ~17.4-23.4°C -see the Appendix S1. Also, relatively high δ 13 C stable isotope values, low-diversity faunal assemblages and above-average shell size corroborate with I. (P.) salisburgensis ability to mixtrophic chemosymbiotic behaviour under oxygendepleted conditions. Most of the time, these kinds of ecological properties are typically linked to hydrothermal vents or methane seeps fuelled by tectonic or volcanic activity (Levin et al., 2016). In addition, the lack of evidence of predator attack, i.e. damage on the shell surface, promoted rapid growth and construction of new calcium carbonate, which did not need to be transferred to shell repair (Nedoncelle et al., 2013). This feature, as well as the lack of indicators for a periodic significant slowdown in the rate of crustal growth, indicates a quiescent environment, inaccessible to other organisms (see also Harries & Schopf, 2003 (Kennedy et al., 1996) or mature/old stage -decline (Harzhauser et al., 2010). Moreover, indistinct internal laminae structure and micro-growth increments visibility in thin sections cause problems with estimating the ontogenetic age of analysed material by visual counting. Typically, the pattern of bivalve shell growth increments is explicitly observed in modern (Schöne & Giere, 2005) as well as fossil bivalves (Walliser & Schöne, 2020). The growth is marked by alternating light and dark lamina created, respectively, during fast and slow biomineralization,

Number of data points (LA-ICP-MS)
where the width of increments is controlled by environmental conditions (Schöne, 2008). In I. (P.) salisburgensis, we relate this feature to small variations of paleoecological changes and uninterrupted growth powered by jointly support of suspension and symbiontsrelated way of feeding. By almost continuously providing the demand on energy, due to the most possible ability to mixotrophy, in more-or-less stable paleoecological conditions, the lamination may be characterized by blurred small-width variation along cross section and regular outer shell architecture. We also suggest a constant level of bottom oxygenation during the inoceram life, and lack of influence of methane releases documented by relatively high δ 13 C values. However, recent research on the Platyceramus group indicates an ontogenetic age to a few years (Walliser et al., 2018), and consequently, we assumed a similar age range in our studied material. The origin of microgrowth increments in (deep-water) Platyceramus platinus was considered to reflect lunar daily shell accretion (Walliser et al., 2018) in contrast to the solar-related daily growth of one light and dark laminae couplet, dominated by day-night cycles, observed, for example, in the Campanian shallow-water rudist bivalve (de Winter et al., 2020).
The shell specimens analysed show clearly marked concentric growth lines which regularly and continuously occur at a similar interval across entire surface of the shell fragment examined.
Therefore, it may reflect almost continuously and undisturbed growth over ontogeny. Assuming that the maximum shell length of an adult specimen (see Kauffman et al., 2007)  Nevertheless, the origin of increments is not well understood, and just relying on counting of them may strongly overestimate the lifespan; therefore, we focused on geochemical laminae counting estimating the ontogenetic age of each analysed shell specimen.
On the other hand, shell growth in a tidal rhythm generally occurs as a semi-diurnal increment, that is, two pairs of organic and inorganic laminae are formed during a day at a rate of one pair every ~12.4 h or half a lunar day (Pannella, 1976).
Meanwhile, the average number of small-scale fundamental cycles calculated by time-series analysis, forming one set of dark and light layers visible to the naked eye, is about 31-33 cycles per set.
It suggests the formation of one pair of increments per lunar day, rather than two. The calculation is because in the case of the formation of two pairs in a daily rhythm, the growth rate of the analysed crust would be unnaturally fast. Therefore, given the similarities of the genus Platyceramus, the aphotic and deep-sea habitat, we hypothesize that tide-induced shell biomineralization of I. (P.) salisburgensis follows a circadian rhythm, most likely resulting in one increment per lunar day.
To obtain more precise age estimates and further investigate into the origin of increments, we have used the geochemical fluctuations and results of spectral analysis. The visibility of lamina may be disturbed due to diagenetic alteration such as recrystallization, although the geochemical signals of analysed material still indicate significant regular fluctuations in element content ( Figure 4a).
Moreover, strontium concentrations above 1000 μg/g were observed in all samples, attesting as additional marker for a good state of preservation (Ullmann & Korte, 2015). However, high concentrations of manganese were detected, whereas typical diagenetically unaltered Cretaceous low-magnesium carbonates are assumed to have manganese concentrations below the threshold of 100 μg/g (Huck et al., 2011). Elevated Mn input to the oceans during the Late Cretaceous may be related to increased, wildfire-driven supply from terrestrial sources (Brown et al., 2012) and/or hydrothermal activity (Ingram et al., 2016) during tectonic rearrangement of the Tethys seafloor and evolution of the Carpathian orogenic belt. Mechanisms of this type are indicated as the main source of Mn in seawater (van Hulten et al., 2016). The increased Mn content recorded in inoceramid shells may be related to the above events (Ingram et al., 2016).
Particularly in the case of hydrothermal activity, however, other indicators such as highly negative stable carbon isotope ratios or other faunal elements associated with hydrothermal events are lacking (Hammer et al., 2011). Therefore, there is no clear evidence in the material studied that I. (P.) salisburgensis inhabited a hydrothermal or methane leakage-controlled environment. Also, we rule Mn content out as a marker of diagenetic alteration in our material.
Direct element thresholds, described as a diagenetic screening tool, must be carefully considered due to differences in species' environmental preferences, taxa physiology or burial history ( Reeder, 1983). Therefore, these elements reveal the most visible rhythmical/cycle patterns periodically incorporated during lifespan.
The dominant biological inner clock, the circadian clock, controls bivalve body functioning and is mostly related to the intertidal zone, where multiple environmental factors drive the (cyclic) behaviour such as temperature, sunlight, moonlight and tides (Connor & Gracey, 2011). However, even in tidal-related environments, circadian clock genes can run at tidal frequencies -the strong tidal rhythm combined with a daily rhythm -and it may be sufficient to entrain behavioural patterns at daily and tidal frequencies (Tran et al., 2020). Therefore, organization of biological processes, although circadian and circatidal, in varied marine environments, may be present, in different amounts, run by single or more clocks (Mat et al., 2020). Furthermore, oscillations observed in I. (P.) salisburgensis could be driven either by one or more endogenous biological clocks or a direct environmental stimulus. In this case, these zeitgeber may be attributed solely to hydrodynamic changes in physicochemical conditions at seafloor, i.e. pressure and temperature, linked to tidal-related cycles. Considering limited environmental cues, the ecological preferences of I. (P.) salisburgensis evidence a major lunarrelated (circatidal) inner-clock strategy combined with or without a circadian timing mechanism. The record of persistence modulations, preserved in shell geochemical composition, may be explained by the time-keeping mechanism, which is constantly reset by lunar cycles acting as a peacemaker in this biological process, underlying the influence of biological clocks (Schöne, 2008;Schöne & Giere, 2005).
Therefore, to identify the main origin of lunar frequencies, we considered two possible periodicity models as being recorded in the analysed shells ( Figure 5). The most distinctive pattern peaks are present at a frequency of ~180 cycles/mm; therefore, it is interpreted to follow the most significant stimuli of the biological cycle record.

| Model A -ca. 14.8d semilunar cycle
According to the deep-water habitat, far below the wave base and the photic zone, the main environmental factor is barotropic tides, which achieve their highest gravitational influence (extra high tide) when the Earth, Moon and Sun are aligned, at FM or NM phase ( Figure 5). Hence, we assume that these peaks at a frequency of ~180 cycles/mm may be controlled by the ca. 14.8-day semilunar cycle. Due to that assumption, half of these frequencies (~90 cycles/ mm), which is also recognizable in some cases, indicates the full lunar cycle at ~29.5 days. Thence, basic rhythms record such as tidal and lunidian will be assigned to peaks recorded at lower frequencies (occurring more often However, the analysed shell slabs from middle to close-to umbo shell parts represent only parts of the fossil's full age, and our reconstructed geochemical age estimates need to be raised by unknown missing time -the most complete record of bivalve would be present at the hinge. Additionally, in this case, the estimated growth accretion rate reaches ~0.013 cm in shell thickness per lunar year, which seems very slow even considering the energy demand needed to exceed the enormous shell size.
Moreover, the almost horizontal arrangement of laminae in the cross section suggests a much faster growth rate likewise in P.
platinus (Walliser et al., 2018) or oysters Crassostrea gryphoides (Harzhauser et al., 2016). Moreover, mixtrophy ability and absence of food-competitors correspond to more intensive calcium carbonate production. Nevertheless, the biological behaviour that may follow lunar cycles in molluscs could be related to the spawning rhythm. The stable cycle stimulus provided by the Moon allows to synchronize reproduction even across widespread populations (Tessmar- Raible et al., 2011). Bivalve spawning events may mark signals in the shell structure arranged as a result of slowing down growth rate due to the energy allocation from biomineralization to gametogenesis (Nedoncelle et al., 2013). Reproduction events in case of I. (P.) salisburgensis from the one hand could occur during entire year because of the little seasonal variability (Dalton & Menzel, 1983) and be presented in irregular timing that is not significantly reflected in high-frequency spectra peaks because of low repetitively. On the other hand, regular spawning in temperate zone species is known but occurs twice per year (Rand, 1973), and it is unlikely that bivalve reproduction would be proceed every semi-/lunar cycle through the entire year without highly increased population and referring it to dominant peak pattern. Therefore, we infer that I. (P.) salisburgensis had a continuous (year-round) spawning season ability with unknown periodicity.

| Model B -ca. 12.4 h tidal cycle
Alternatively, due to blurry visual laminae age estimation, the peak patterns at a frequency of ~180 cycles/mm might be considered to be run by a basic marine environmentally driven ~12.4-h tidal cycle ( Figure 5). Thereby, recorded patterns at ca. ~90 cycles/mm would correspond to the effect of the ~24.8-h lunidian cycle. Tidecontrolled shell growth patterns are typically observed in many bivalves (Schöne & Giere, 2005). Therefore, the daily influence of hydrodynamic changes may have had enough impact to stimulate I.
(P.) salisburgensis to follow a circatidal rhythm. The Late Cretaceous shelf and shallow-sea water areas were much more widespread (Ladant et al., 2020), thus tidal gravitational force had to mobilize much higher water mass, resulting in significant daily (every ~12.4 h) water pressure changes on the seafloor. Even today, under presumably less forceful conditions, in situ measurements of physical parameters in a deep-sea environment confirm a signal following periodic variability and tidal frequencies (Barreyre et al., 2014).
Several recent studies substantiate the occurrence of tidal rhythms in deep-sea organisms' behaviour (Cuvelier et al., 2017;Lelièvre et al., 2017). The high tidal dynamics provided the necessary amount of shelf nutrients income to a deeper part of the basins, resulting in achieving higher growth accretion rates of ~0.4 cm in shell thickness per lunar year, comparable with the rate noted in fossil giant clam Tridacna gigas (Watanabe et al., 2004). Moreover, elevated food supply and higher temperature of the waters fostered intensive shell biomineralization (Marali & Schöne, 2015). Such excessive growth in a relatively small time period is known from a large fossil bivalve such Crassostrea gryphoides (Harzhauser et al., 2016) and should have also been a major feature characterizing the biology of I. (P.) salisburgensis.
Additionally, estimation of I. (P.) salisburgensis age by the number of recorded tidal cycles in shell sample compared with the counted visible seasonal laminae gives convergent results (Table 2) Nevertheless, the process of direct 'color' laminae biomineralization appears to be complicated in our pelagic deeper-water environment and may have resulted more likely from lunar-periodicity cycle influencing oceanic primary production as a main export source (Gliwicz, 1986) rather than only shelf tidal-related nutrient income.
Moreover, as frequency slightly changes at dominant peaks range frequency of ca. 15 (Table 1) This tidal dominant cycle -model B seems to fit better in the light of I. (P.) salisburgensis biological behaviour. Therefore, as circatidal and partially lunidian are the lowest rank biological rhythms which occur at frequencies of ~180 cycles/mm and ~90 cycles/mm, respectively, we are able to identify ultra-high-resolution subdaily changes, even up to ~2 h ( Figure 5).
The putative presence of symbionts in I. (P.) salisburgensis and its influence on circatidal rhythms should also be mentioned. A wealth of confirmed data proves the influence of host behaviour rhythms by symbionts such as photosynthetic algae (Sorek et al., 2018) or bacteria (Heath-Heckman et al., 2013). The host-symbiont interaction and the potential of microbial symbionts may manipulate host rhythms (Heath-Heckman, 2016). Nevertheless, a mutually related interaction of symbionts generally follows rhythms of the host, and it has already been proposed for recent deep-sea bivalves (Mat et al., 2020).
Therefore, taking into consideration the most significant peak period pattern, we assume that even in the presence of chemo-symbiotic bacteria, the rhythms had to correlate to the inoceramid inner-clock and/or tidal-driven cycle without strong asynchronism in physiological processes. Noteworthy, in the analysed record, there are minor, non-periodic interruptions in growth, which can be linked to a variable and irregular supply of methane/sulfides for the symbionts or to changes in the oxygenation of the bottom where the studied inocerams lived.
The shells of I. (P.) salisburgensis provide unique biogeoarchives from still poorly known aphotic fossil deep-marine environments of the Late Cretaceous. Besides the indicated unusual, inhabited niche of these bivalve fossils (i.e. dysoxic/anoxic conditions) and peculiar physiology (i.e. dual-feeding strategy), the geochemical record reveals to be significantly characterized by environmental/ biological cycles. According to spectral analysis results, the single leading spectral power at close-related frequencies (~180 cycles/ mm) is clearly marked in all specimens. All data collected suggest that the I. (P.) salisburgensis inner clock had to correlate to the Earth-Moon system periodicity, independently from the sunlight/ solar-related cycle. Moreover, the only possible stimulating factor (zeitgeber) in this circumstance considers barotropic tides regulating and affecting major biological behaviour. Therefore, this study confirms the presence of circatidal biological rhythms and allows distinguishing and strongly correlating astronomically driven cycles recorded as a visible shell banding to semilunar influence.
Additionally, results indicate that single shell increments couplet in I. (P.) salisburgensis formed every lunar day specifying an ultra-highresolution data set record, determining it even up to a few hours.
Undoubtably, extended knowledge about the physiological properties of organisms and their remains (i.e. shells, bones, tusks) has played a key role in paleontological research for decades and is still developing into wider and more sophisticated analysis. However, the major and most meaningful force controlling life on Earth depends on the repetitiveness of molecular-cellular processes designing biological behaviour. Therefore, the recognition of the major biological clocks followed (circadian or circalunar) should be considered in every single fossil-based paleoenvironment reconstruction, especially nowadays, where progressing analytical advances bring more detailed data achievement possibilities. Moreover, a closer look at deep marine biota from the past may solve desirable questions about life-controlling forces and its evolution, with benefits for future research in many fields.

ACK N OWLED G M ENTS
The authors gratefully acknowledge editors and reviewers for their helpful and constructive comments that improved the quality of grant from the Facul ty Geo graphy and Geology unde r t he S tra teg i c P rog r amm e E xelle nce In itia tiv e a t J agiellonian University.

CO N FLI C T O F I NTE R E S T S TATE M E NT
The authors declare no competing interests.

DATA AVA I L A B I L I T Y S TAT E M E N T
All data are available in the main text or the supplementary materials.