Time- probabilistic approach to the late Miocene Messinian salinity crisis: Implications for a disconnected Paratethys

The late Miocene Messinian salinity crisis was an evaporitic episode that occurred throughout the Mediterranean; it concluded with a transition from hypersaline to fresher- water “lake sea” (Lago Mare) conditions prior to the Pliocene. Whereas numer ous researchers propose that Lago Mare sediments accumulated in a Mediterranean-wide lake filled with Paratethyan waters, other workers reject this hypothesis. Here, to test this Paratethyan- overflow model, we develop a novel time- probabilistic approach to evaluate the distribution of precession- related deposits. We apply our methodol ogy to 24 circum- Mediterranean sites, focusing on two previously untested param -eters: the probability of preserving intrabasin precession cycles; and the similarities in interbasin preservation. Our results, which show an increase in preservation and similarity in successively younger cycles, display a trend opposite to what is expected from a flooded Mediterranean. Consequently, we conclude that Lago Mare accumula tions were


| INTRODUC TI ON
The late Miocene Messinian salinity crisis (MSC) was a pan-Mediterranean episode (5.97-5.33 Ma; Gautier et al., 1994;Krijgsman et al., 1999;Manzi et al., 2013) responsible for the emplacement of >1 × 10 6 km 3 of halite, gypsum, and anhydrite as well as overlying siliciclastics and mixed-lithology sediments (Figure 1a; Ryan, 1973;Haq et al., 2020). Whereas the crisis is interpreted to have begun with the onset of evaporitic conditions caused by shoaling across the Betic and Rifian corridors (Duggen et al., 2003;Simon and Meijer, 2015), it is thought to have concluded during "lake sea" (Lago Mare-LM) conditions caused by Paratethyan overspill, which introduced endemic fauna (Cita, 1973;Hsü et al., 1977). Though many topics in MSC research are debated widely, the subject of a Paratethyan spillover is among the most contentious (see Andreetto et al., 2021).
To date, two well-established models have been proposed to explain the detailed chronology of the MSC. Although both models invoke Paratethyan overflow, they differ in the number of purported connections. For example, in the first hypothesis, termed the "consensus model" (Figure 1b; CIESM, 2008 andRoveri et al., 2014), one LM interval is used to infer a single Paratethyan invasion. In the second hypothesis, herein termed the "alternative model" (Figure 1c), three LM intervals are recognised, two of which are interpreted to represent episodes of Paratethyan supply (Clauzon et al., 2005;Do Couto et al., 2014;Popescu et al., 2015). While both the consensus model and alternative model use biota to draw conclusions regarding a Paratethyan overspill, neither hypothesis evaluates the host sediments independently of the organisms contained within them. Consequently, we test the concept of Paratethyan flooding using only LM accumulations. Our results, which provide new insight into the dynamics of the terminal MSC, propose not only an updated framework for the latest Messinian deposits but also an evaluation of formerly unconsidered parameters.

| DATA AND ME THODS
To test the hypothesis of a Paratethyan spillover, previously published data were compiled from 24 circum-Mediterranean locations spanning the following countries (from west to east): Spain; Morocco; Algeria; Italy; Tunisia; Libya; Greece; Egypt; Cyprus; Lebanon; Israel; and Turkey. Of the 24 locales assessed, 16 were situated onshore, while the remaining eight were positioned offshore. Using these publicly available data, a new analytical approach, herein termed "time probability", was created to evaluate objectively the preservation of individual MSC precession cycles (21.7 kyr/cycle with approximately 29 cycles spanning the  Ma]; Krijgsman et al., 1999). Although we applied our methodology to precession-paced sedimentation, it can be employed on any age-constrained accumulations where knowledge exists of a specified temporal range of deposition. In addition to the creation of a time-probabilistic framework, similarities between interbasin preservation and rates of precession-scaled sedimentation were calculated. While we compared our results to those expected from the consensus model, we were unable to test the alternative model due to a lack of temporal consistency among workers (compare Clauzon et al., 2005, Do Couto et al., 2014, and Popescu et al., 2015.

| Facies
Previous work was compiled to better understand the temporal distribution of MSC facies throughout the Mediterranean; consequently, depositional interpretations were kept consistent with original publications. Because our study focused on evaluating the events leading up to and including a purported Paratethyan water source, particular attention was given to cycles spanning 5.60-5.33 Ma ("stage 2" and "stage 3" of the consensus model).

| Probability of intra basin preservation
Restoring MSC accumulations to the time domain is complicated by variable uncertainties in age control; this is particularly the case for resolving deposits to the precession scale. To address this variability, cyclic accumulations were dealt with in terms of independent probabilities. Whereas our methodology treats repetitive deposits as having been driven by precession (the current view of the MSC; see Krijgsman et al., 1999), this may be invalid locally as accumulations could have been controlled by auto-cyclic processes (avulsion).

Figure 2a
presents a summary of our approach, whereby uncertainties in age drive the probability of occurrence for individual deposits. As such, we introduce the following equation: where p is the probability of occurrence of an individual accumulation within a given precession cycle; d is the number of cyclic deposits; and c is the number of precession cycles. For example, if one accumulation (d = 1) is well constrained to one precession cycle (c = 1), the probability of occurrence for that interval is 1.0 (1/1 or 100%). Yet, if one deposit (d = 1) has poorly constrained age control limiting it to three potential precession cycles (c = 3), the probability of occurrence for each of the three intervals is 0.33 (1/3 or 33%). Therefore, because it is not possible to know the exact temporal position of such an accumulation, it can be deduced that there is a 1/3 chance that the deposit will occupy any one of the three precessional intervals. This same logic applies to multiple, stacked, accumulations which compose the stratigraphic architecture of post-evaporitic facies.

| Difference in interbasin preservation
In addition to calculating the probability that precession cycles are recorded in a single basin, interbasin differences were also calculated. Figure 2b shows a summary of this approach whereby the probability of a given precession cycle (at a specific location) was subtracted from all other sites (over the same time). This methodology yielded a result where all precession deposits were scaled to one another. For example, over a given 21.7 kyr interval, if two locations each yield a probability of 0.5 (50% chance cycles would accumulate), the difference (0.0), suggests that they are 100% similar. Yet, if a 0.9 probability exists at one location, which is compared to another site with a 0.1 probability, their difference suggests that sites differ by 0.8 (80%), indicating that they are dissimilar. This methodology was applied to the final 13 precession cycles of the MSC, which were plotted as matrices and reduced to single average values of variance.

| Rates of precession-scaled sedimentation
Along with the probability of preserving precession deposits, sedimentation rates were approached probabilistically. Consequently,

Statement of significance
This study presents a test of the prevailing palaeoenvironmental hypothesis for the late Miocene Messinian salinity crisis (5.97-5.33 Ma) that prior to the earliest Pliocene, there existed a single Mediterranean-wide lake filled with Paratethyan waters. Using a new methodology, which draws on independent probabilities, we constructed a pan-Mediterranean, time-stratigraphic framework to test this Paratethyan-spillover model. Our study shows that there exists no compelling stratigraphic evidence for an interconnection, supports the notion of regional non-marine conditions, and therefore challenges the widely accepted assumption of a major Paratethyan water source.
averages taken over longer durations are driven downward ("Sadler effect"; Sadler, 1981). For example, if a 10 m-thick accumulation is constrained to one precession cycle (21.7 kyr), the average sedimentation rate for that interval is 0.046 cm/yr. Yet, given a 10 m-thick deposit with age control constrained to three precession cycles (65.1 kyr), the average sedimentation rate is 0.015 cm/yr (1/3 of 0.046 cm/yr).

| RE SULTS
Based on data from previous publications and the analyses reported here, post-evaporitic facies are interpreted to have formed in non-marine settings during the latest Messinian. Although the number of precession cycles is not consistent among locations, there exists an average tendency towards both increased preservation and similarity in successively younger sediments. Taken together, rates of precession-scaled sedimentation show a marked west-to-east increase, with the highest values in the eastern Mediterranean.

| Facies
Post-evaporitic accumulations throughout the Mediterranean comprise mixed-lithology sediments, siliciclastics, carbonates, and          Hsü et al. (1978c)    Boundaries separating pulses appear to coincide generally with low values of eccentricity.

| Difference between interbasin preservation
Along with probabilities, similarities in interbasin preservation show a marked increase in successively younger intervals (temporal reduction in

| DISCUSS ION
To test the Paratethyan-overflow hypothesis, the chronology from the consensus model was used to calculate expected values for the aforementioned statistical parameters; divergences among these attributes and those reported above were then used to gauge the predictive fidelity of the consensus model. Because highstand exchange is the inferred mechanism of Paratethyan supply (see Andreetto et al., 2021), the ensuing analysis is necessarily a test of the effect of base-level change on controlling time-dependent trends in facies, probabilities, and similarities.  (Roveri et al., 2014). This water mass exchange is interpreted primarily from biota (Grossi et al., 2008), which are thought to have been introduced during Paratethyan spillover.
Although no direct estimates of palaeo-water depth are given for such a Mediterranean-wide lake filled with Paratethyan waters, hun- from sediment sources and by the onshore capture of sedimentation. Figure 8b shows the resultant stratigraphic architecture of these purported processes at three pseudo-wells (analogous to To correct for spatial and temporal inconsistencies in the consensus model, we propose an updated hypothesis that better explains observed trends in facies, similarities, and probabilities. Figure 9 summarises this model, in which depositional patterns are controlled by in-filling of alluvial, fluvial, and lacustrine systems after significant drawdown ("stage 2"). Such in-filling is marked by three depositional pulses (1-3, with relatively static sedimentation rates) that produced increasing trends in probabilities and similarities.
Although local patterns in backstepping and basinward shifts in facies are observed, they have been explained by both basin-centred, load-induced subsidence (driving basin-margin uplift and erosion; Duggen et al., 2003;Norman and Chase, 1986;Ryan, 2008) and by increased fluvial runoff (Madof et al., 2019). These mechanisms therefore imply that biota were delivered by an unknown source (potentially avian; Benson, 1978) and that organisms may have been introduced early in "stage 3". A trend towards increased biodiversity F I G U R E 8 Conceptual spatial-temporal reconstruction of the MSC using the chronology of the "consensus model" (see CIESM, 2008 andRoveri et al., 2014). (a) The Paratethyan spillover from 5.42 to 5.33 Ma results in the burial of antecedent non-marine deposits and the landward migration of depositional systems. (b) Three pseudo-wells show the implied stratigraphic architecture (left) and temporal relationships (right). Decreased preservation probability in successively younger sediments is caused by regional flooding, which is also responsible for an overlying basinwardexpanding hiatus [Colour figure can be viewed at wileyonlinelibrary. com] in successively younger intervals, which parallels patterns in probability and similarity, indicates that biota flourished under late "stage 3" conditions (Grossi et al., 2008).

| CON CLUS ION
A compilation of 24 pan-Mediterranean locations has led to the construction of a time-stratigraphic framework for the MSC (5.97-5.33 Ma). We find that terminal Messinian deposits ("stage 3") accumulated in alluvial, fluvial, and lacustrine settings and exhibit a time-dependent increase in probability and similarity. Although numerous workers invoke a Paratethyan source (brackish to freshwater) to explain Mediterranean post-evaporitic facies and biota, we argue instead that the accumulations themselves provide no compelling evidence for such an overflow. Our conclusions, which propose a more plausible non-marine scenario, provide a new model for the demise of the most misunderstood evaporitic episode in Earth history.

ACK N OWLED G EM ENTS
A.S. Madof thanks Chevron and B.S. Cabote for allowing publication, D. Cosentino and E. Gliozzi for significant contributions to an earlier version of the manuscript, and L. Li for assistance with statistical analyses. C. Bertoni thanks the Leverhulme Trust (Neptune grant) for support. We thank J.-P. Suc, F. Raad, and an anonymous reviewer for thoughtful remarks.

CO N FLI C T O F I NTE R E S T
The authors declare that they have no conflict of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data sharing is not applicable to this article as no new data were created or analyzed in this study.