DYNAMICS OF THE LATE TRIASSIC ADAMANIAN-REVUELTIAN EXTINCTION, PETRIFIED FOREST NATIONAL PARK, AZ

In the Late Triassic of Petrified Forest National Park (PEFO), AZ, the coincidence of high-precision geochronology and robust lithostratigraphy allows an adaption of the Bayesian statistical approaches of Haslett and Parnell (2008) and Alroy (2014) to quantify the dynamics of a Late Triassic vertebrate extinction and replacement, the Adamanian-Revueltian (A-R) faunal turnover. This analysis indicates negligible probability of synchroneity of Adamanian extinctions and Revueltian originations. This protracted reconstruction of the A-R turnover decouples the event from the geologically instantaneous Manicouagan impact (215.4 + 0.20 Ma; Québec, Canada), previously implicated as a causal mechanism.


LIST OF TABLES
Pink and blue densities respectively refer to extinction and origination. Dark-colored, opaque densities are obtained under assumption of "undersampling"; light, translucent densities are not (see Methods). Chinle mean annual precipitation (MAP) record of  shown above. Also above are posterior probability densities of floral turnover (green; Reichgelt et al., 2013;Baranyi et al., 2017) and Manicouagan impact

INTRODUCTION
Extinction dynamics are difficult to quantify because the last appearance of an organism does not likely signify its ultimate extinction (Signor and Lipps, 1982).
The Adamanian-Revueltian turnover is now regarded as a transition between two single-taxon biozones, defined by the first appearance datums of species of the pseudopalatine phytosaur Machaeroprosopus . This definition supersedes the earlier designation "land vertebrate faunachrons," characterized by successive faunal assemblages at their type localities in the Chinle Formation (Lucas, 1993;Lucas and Hunt, 1993;Lucas and Heckert, 1996;Lucas, 1998;Heckert and Lucas, 2006). Because these assemblages appear distinct within the confines of PEFO (Long and Ballew, 1985; Revueltosaurus callenderi defines the Revueltian origination. These are quantitatively expressed as: The hypothesis test is as follows:   Martz and Parker, 2010) in the Sonsela Member (Reichgelt et al., 2013;Baranyi et al., 2017). Also included were fossils from two additional localities: the nearby Placerias Quarry (Camp and Welles, 1956), dated with a zircon sample collected from the fossiliferous bed , and the Hayden Quarry (Irmis et al., 2011). A single date from the Hayden Quarry with significant analytical uncertainty (+ 0.7 Ma) accommodated a broad range of possible ages for fossils, likely encompassing the complete depositional age of the Quarry.
Analytical error came from three sources: the geochronological precision of the dates (Ma), the stratigraphic positions of the zircon samples (m), and the correlations of dates with fossil localities (m). The geochronological precision of the dates is described by the "X" error of Ramezani et al. (2011, Supplement, Table S1), because they represent the work of a single lab (MIT's EarthTime laboratory) in a single isotopic system (U-Pb). This uncertainty is generally < 0.1%. Because the precision of each fossil position varied with the robustness of its correlation to the dated beds (see Table 2.7), the age-depth model estimates ages more conservatively for less precisely correlated fossil localities.

Quantifying extinctions and replacements in time using Bayesian arguments
Alroy (2014) proposed Bayesian arguments to estimate extinction times (as distinct from last appearance times), stated as a conditional (posterior) probability: what is the chance that a species has gone extinct conditional on the fact that it has not been observed after a certain time?
Following his method, a sequence of 0.1 Ma time "bins" was first constructed in which to evaluate extinction probability. These bins were populated with fossils according to the age-depth models; data for each taxon thus consisted of 1000 sequences of successes or failures to observe that taxon through the full succession of bins.
The Alroy (2014) method ultimately produces a posterior probability distribution of extinction for each taxon. This first requires (1) a sampling probability, or the frequency of findings over the observation range, and (2) a prior probability. Sampling probability was defined with four components, for which gives the time where a taxon is present, and gives the time where that taxon is absent: 1. The probability of observing a certain taxon if the taxon is not extinct is given by the frequency over the observed range minus the first and last sighting:

The probability of not observing a certain taxon if the taxon is not extinct is
3. The probability of observing a certain taxon if the taxon is extinct is 4. The probability of not observing a certain taxon if the taxon is extinct is Definition of the prior probability ( ), or probability of extinction at any point in time, followed the assumptions of Alroy (2014): (a) that the probability of an organism having gone extinct can be modeled exponentially (i.e. longer the elapsed time beyond the last fossil, the greater the chance that the extinction has already occurred), and (b) because it cannot be known whether the organism is better considered extinct or extant at the time of the last fossil, the chance of extinction there is best considered 50%. Indicating with the observed range of a given taxon, the prior ( ) was thus specified as follows: To accommodate the possibility of strong dissonance between the observed and true range of a taxon (dubbed "undersampling" by Alroy [2014]), analyses were also run in which the denominator of ( ) was doubled to make the algorithm more conservative.
Posterior extinction probability, or probability that a taxon is extinct given that a sighting is not recorded, was next calculated using Bayes' Theorem. Because the goal was to assess the probability of extinction at different points in time, the posterior probability at time t became part of the prior for the next time interval t+1. Let: The iterative, posterior-dependent formula to evaluate the probability of extinction was thus as follows: This operation was repeated to calculate, for each taxon, posterior extinction probability for each sequence of probabilistic age-depth relationships. Because the relative ages of fossil localities varied across each sequence, calculations accommodate the possibility that fossil ages do not strictly adhere to stratigraphic superposition, as might occur in a fluvial system.

Testing for synchroneity of extinctions and originations
To test that extinctions were synchronous, an average posterior extinction probability of each taxon in each bin was calculated from all 1000 sequences. Because the analysis assumed that the extinction of each Adamanian taxon occurred at some point within the analytical time series, a posterior extinction probability density was defined for each taxon by scaling per-bin probabilities such that ∑ ( | ̅ ) 153 =1 = 1.
The joint probability that n taxa went extinct at any time t is the intersection of their posterior extinction probability densities at that time. The overall probability that these n taxa went extinct synchronously at any time t was therefore defined as the summation of these joint taxic probabilities: This operation assumed conditional independence of taxon extinctions. This assumption is practical, as hypothetical dependencies can be neither demonstrated nor falsified.
Analytical treatment of Revueltian originations mirrored that of extinctions: following Alroy (2014), all of the operations above were performed in reverse from the first fossil occurrence of a taxon to calculate posterior origination probability.

RESULTS
Based on all available evidence, model support for a synchronous A-R turnover is negligible (Table 1.1). Regarded individually, the probabilities of a synchronous Adamanian extinction and Revueltian origination are also slim. However, pairwise comparisons between taxon extinctions and originations (Table 1.2) indicate modest support for synchroneity of some biotic events.

DISCUSSION AND CONCLUSIONS
Two possible causes of the A-R turnover have been proposed in the literature.
Many authors (Dunlavey et al., 2009;Olsen et al., 2011;Onoue et al., 2012;Olsen et al., 2014;Rampino and Caldeira, 2017;Olsen et al., 2018)  confounds these extinction mechanisms a priori. The essential question is therefore whether the pattern of extinctions and originations conforms to classes of extinction mechanisms, operating on disparate time scales, plausibly associated with each event.
Since the Alvarez et al. (1980) attribution of the Cretaceous-Paleogene (K-Pg) mass extinction to an asteroid impact, it has been universally recognized that impactdriven extinctions must be synchronous and abrupt (i.e. the "short, sharp, shock" of      Pink and blue densities respectively refer to extinction and origination. Dark-colored, opaque densities are obtained under assumption of "undersampling"; light, translucent densities are not (see Methods). Chinle mean annual precipitation (MAP) record of  shown above. Also above are posterior probability densities of floral turnover (green; Reichgelt et al., 2013;Baranyi et al., 2017) and Manicouagan impact (orange); vertically-oriented green and orange fields (below) delineate respective 95% highest posterior density regions.
Chapter 2 of this thesis will serve as a Supplement to Chapter 1 when that manuscript is submitted to Geology. It will not be published independently of Chapter 1 elsewhere.
Park, the Placerias Quarry, and the Hayden Quarry). Age constraints based on fossils or lithology, often established at those Chinle localities where geochronologic dates are unavailable, did not rise to the level of temporal precision permissible for the analysis.
2. The Alroy (2014) algorithm requires that each taxon have at least three fossil occurrences of different ages: two to define a temporal range, and at least one between them to define a frequency within that range. All taxa known from fewer than three total fossil occurrences at PEFO, the Placerias Quarry, and the Hayden Quarry were therefore excluded: these included Tecovasuchus (PFV 211), Acallosuchus (PFV 124), Crosbysaurus (PFV 122), and Maleriasuchus (PFV 161). Rioarribasuchus (PFV 075, PFV 366, and the Hayden Quarry) was also excluded on these grounds because the Bchron models frequently reconstructed two or more of these localities as contemporaneous, pushing the taxon below the analytical threshold.
3. Fossils must occur in localities correlable to U-Pb dated beds via continuouslyexposed outcrop. Seventy-one PEFO fossil localities were included in this analysis, but fifteen additional localities that did not meet this criterion were excluded. General stratigraphic positions can be established for these additional localities per the stratigraphy of Martz and Parker (2010;see Parker and Martz, 2011); however, the uncertainty associated with those correlations-information required to integrate a locality into an age-depth model-cannot be tallied into a non-arbitrary cumulative term, as can those associated with correlations constructed along continuous outcrop.
Accordingly, Scutarx deltatylus (occurrences at PFV 224, PFV 169, PFV 304, and PFV 355, but the latter three cannot be correlated to dated beds with sufficient stratigraphic precision) and Poposaurus (occurrences at the Placerias Quarry, PFV 161, and PFV 336, but the last of these cannot be correlated with sufficient precision) were excluded from the analysis.
The Adamanian extinction was therefore defined as the intersection of the Typothorax and Paratypothorax were excluded from this analytical definition of the Revueltian origination because Adamanian-aged fossils belonging to these taxa exist. Table 2.7 lists voucher numbers for all fossils included in the analysis.

AGE-DEPTH MODELING IN BCHRON
A distribution of plausible ages was constructed for each PEFO fossil locality through age-depth modelling implemented in the R package Bchron (v. 4.3.0, Haslett and Parnell, 2008). Separate models for northern (Figure 2.1) and southern ( Figure   2.2) PEFO were defined for practicality, as stratigraphic correlations can be most precisely drawn between U-Pb dates and those fossils situated closest geographically. and "ageSds" arguments) are scaled down by 10 3 , but Bchronology scales them to their true magnitude as the ageScaleVal argument of the function defaults to 1000.
Stratigraphic inputs ("position" and "thickness") are derived from the original field notes supporting the correlations of Ramezani et al. (2011), in addition to the positions  and  report for the dates SS-7 and P57-C.
Because all ages are derived from a U-Pb isotopic system, the calibration curves ("calCurves") argument was set to "normal" following the instruction of Bchron BchronCalibrate was run with all arguments set to their default values, and sampleAges with the "n_sample" argument set to provide 1000 age estimates.