Including autapomorphies is important for paleontological tip-dating with clocklike data, but not with non-clock data

Tip-dating, where fossils are included as dated terminal taxa in Bayesian dating inference, is an increasingly popular method. Data for these studies often come from morphological character matrices originally developed for non-dated, and usually parsimony, analyses. In parsimony, only shared derived characters (synapomorphies) provide grouping information, so many character matrices have an ascertainment bias: they omit autapomorphies (unique derived character states), which are considered uninformative. There has been no study of the effect of this ascertainment bias in tip-dating, but autapomorphies can be informative in model-based inference. We expected that excluding autapomorphies would shorten the morphological branchlengths of terminal branches, and thus bias downwards the time branchlengths inferred in tip-dating. We tested for this effect using a matrix for Carboniferous-Permian eureptiles where all autapomorphies had been deliberately coded. Surprisingly, date estimates are virtually unchanged when autapomorphies are excluded, although we find large changes in morphological rate estimates and small effects on topological and dating confidence. We hypothesized that the puzzling lack of effect on dating was caused by the non-clock nature of the eureptile data. We confirm this explanation by simulating strict clock and non-clock datasets, showing that autapomorphy exclusion biases dating only for the clocklike case. A theoretical solution to ascertainment bias is computing the ascertainment bias correction (Mkparsinf), but we explore this correction in detail, and show that it is computationally impractical for typical datasets with many character states and taxa. Therefore we recommend that palaeontologists collect autapomorphies whenever possible when assembling character matrices.Discovery Early Career Researcher Award (DECRA): DE150101773. National Institute for Mathematical and Biological Synthesis (NIMBioS). Institute sponsored by the National Science Foundation. US Department of Homeland Security. US Department of Agriculture through NSF: EFJ0832858, DBI-1300426. The University of Tennessee, Knoxville. NESCent. The University of Utah

A new southern Laramidian ankylosaurid, Akainacephalus johnsoni gen. et sp. nov., from the upper Campanian Kaiparowits Formation of southern Utah, USA

A partial ankylosaurid skeleton from the upper Campanian Kaiparowits Formation of southern Utah is recognized as a new taxon, Akainacephalus johnsoni, gen. et sp. nov. The new taxon documents the first record of an associated ankylosaurid skull and postcranial skeleton from the Kaiparowits Formation. Preserved material includes a complete skull, much of the vertebral column, including a complete tail club, a nearly complete synsacrum, several fore- and hind limb elements, and a suite of postcranial osteoderms, making Akainacephalus johnsoni the most complete ankylosaurid from the Late Cretaceous of southern Laramidia. Arrangement and morphology of cranial ornamentation in Akainacephalus johnsoni is strikingly similar to Nodocephalosaurus kirtlandensis and some Asian ankylosaurids (e.g., Saichania chulsanensis, Pinacosaurus grangeri, and Minotaurasaurus ramachandrani); the cranium is densely ornamented with symmetrically arranged and distinctly raised ossified caputegulae which are predominantly distributed across the dorsal and dorsolateral regions of the nasals, frontals, and orbitals. Cranial caputegulae display smooth surface textures with minor pitting and possess a distinct conical to pyramidal morphology which terminates in a sharp apex. Character analysis suggests a close phylogenetic relationship with N. kirtlandensis, M. ramachandrani, Tarchia teresae, and S. chulsanensis, rather than with Late Cretaceous northern Laramidian ankylosaurids (e.g., Euoplocephalus tutus, Anodontosaurus lambei, and Ankylosaurus magniventris). These new data are consistent with evidence for distinct northern and southern biogeographic provinces in Laramidia during the late Campanian. The addition of this new ankylosaurid taxon from southern Utah enhances our understanding of ankylosaurid diversity and evolutionary relationships. Potential implications for the geographical distribution of Late Cretaceous ankylosaurid dinosaurs throughout the Western Interior suggest multiple time-transgressive biogeographic dispersal events from Asia into Laramidia

Numerical approximation of statistical solutions of scalar conservation laws

We propose efficient numerical algorithms for approximating statistical solutions of scalar conservation laws. The proposed algorithms combine finite volume spatio-temporal approximations with Monte Carlo and multi-level Monte Carlo discretizations of the probability space. Both sets of methods are proved to converge to the entropy statistical solution. We also prove that there is a considerable gain in efficiency resulting from the multi-level Monte Carlo method over the standard Monte Carlo method. Numerical experiments illustrating the ability of both methods to accurately compute multi-point statistical quantities of interest are also presented

Magnetochronology of the Entire Chinle Formation (Norian Age) in a Scientific Drill Core From Petrified Forest National Park (Arizona, USA) and Implications for Regional and Global Correlations in the Late Triassic

Building on an earlier study that confirmed the stability of the 405‐kyr eccentricity climate cycle and the timing of the Newark‐Hartford astrochronostratigraphic polarity time scale back to 215 Ma, we extend the magnetochronology of the Late Triassic Chinle Formation to its basal unconformity in scientific drill core PFNP‐1A from Petrified Forest National Park (Arizona, USA). The 335‐m‐thick Chinle section is imprinted with paleomagnetic polarity zones PF1r to PF10n, which we correlate to chrons E17r to E9n (~209 to 224 Ma) of the Newark‐Hartford astrochronostratigraphic polarity time scale. A sediment accumulation rate of ~34 m/Myr can be extended down to ~270 m, close to the base of the Sonsela Member and the base of magnetozone PF5n, which we correlate to chron E14n that onsets at 216.16 Ma. Magnetozones PF5r to PF10n in the underlying 65‐m‐thick section of the mudstone‐dominated Blue Mesa and Mesa Redondo members plausibly correlate to chrons E13r to E9n, indicating a sediment accumulation rate of only ~10 m/Myr. Published high‐precision U‐Pb detrital zircon dates from the lower Chinle tend to be several million years older than the magnetochronological age model. The source of this discrepancy is unclear but may be due to sporadic introduction of juvenile zircons that get recycled. The new magnetochronological constraint on the base of the Sonsela Member brings the apparent timing of the included Adamanian‐ Revueltian land vertebrate faunal zone boundary and the Zone II to Zone III palynofloral transition closer to the temporal range of the ~215 Ma Manicouagan impact structure in Canada

Integrating gross morphology and bone histology to assess skeletal maturity in early dinosauromorphs: new insights from Dromomeron (Archosauria: Dinosauromorpha)

Understanding growth patterns is central to properly interpreting paleobiological signals in tetrapods, but assessing skeletal maturity in some extinct clades may be difficult when growth patterns are poorly constrained by a lack of ontogenetic series. To overcome this difficulty in assessing the maturity of extinct archosaurian reptiles—crocodylians, birds and their extinct relatives—many studies employ bone histology to observe indicators of the developmental stage reached by a given individual. However, the relationship between gross morphological and histological indicators of maturity has not been examined in most archosaurian groups. In this study, we examined the gross morphology of a hypothesized growth series of Dromomeron romeri femora (96.6–144.4 mm long), the first series of a non-dinosauriform dinosauromorph available for such a study. We also histologically sampled several individuals in this growth series. Previous studies reported that D. romeri lacks well-developed rugose muscle scars that appear during ontogeny in closely related dinosauromorph taxa, so integrating gross morphology and histological signal is needed to determine reliable maturity indicators for early bird-line archosaurs. We found that, although there are small, linear scars indicating muscle attachment sites across the femur, the only rugose muscle scar that appears during ontogeny is the attachment of the M. caudofemoralis longus, and only in the largest-sampled individual. This individual is also the only femur with histological indicators that asymptotic size had been reached, although smaller individuals possess some signal of decreasing growth rates (e.g., decreasing vascular density). The overall femoral bone histology of D. romeri is similar to that of other early bird-line archosaurs (e.g., woven-bone tissue, moderately to well-vascularized, longitudinal vascular canals). All these data indicate that the lack of well-developed femoral scars is autapomorphic for this species, not simply an indication of skeletal immaturity. We found no evidence of the high intraspecific variation present in early dinosaurs and other dinosauriforms, but a limited sample size of other early bird-line archosaur growth series make this tentative. The evolutionary history and phylogenetic signal of gross morphological features must be considered when assessing maturity in extinct archosaurs and their close relatives, and in some groups corroboration with bone histology or with better-known morphological characters is necessary

LA-ICPMS U-Pb geochronology of detrital zircon grains from the Coconino, Moenkopi, and Chinle Formations in the Petrified Forest National Park (Arizona)

Uranium–lead (U–Pb) geochronology was conducted by laser ablation – inductively coupled plasma mass spectrometry (LA-ICPMS) on 7175 detrital zircon grains from 29 samples from the Coconino Sandstone, Moenkopi Formation, and Chinle Formation. These samples were recovered from ∼ 520 m of drill core that was acquired during the Colorado Plateau Coring Project (CPCP), located in Petrified Forest National Park (Arizona). A sample from the lower Permian Coconino Sandstone yields a broad distribution of Proterozoic and Paleozoic ages that are consistent with derivation from the Appalachian and Ouachita orogens, with little input from local basement or Ancestral Rocky Mountain sources. Four samples from the Holbrook Member of the Moenkopi Formation yield a different set of Precambrian and Paleozoic age groups, indicating derivation from the Ouachita orogen, the East Mexico arc, and the Permo-Triassic arc built along the Cordilleran margin. A total of 23 samples from the Chinle Formation contain variable proportions of Proterozoic and Paleozoic zircon grains but are dominated by Late Triassic grains. LA-ICPMS ages of these grains belong to five main groups that correspond to the Mesa Redondo Member, Blue Mesa Member and lower part of the Sonsela Member, upper part of the Sonsela Member, middle part of the Petrified Forest Member, and upper part of the Petrified Forest Member. The ages of pre-Triassic grains also correspond to these chronostratigraphic units and are interpreted to reflect varying contributions from the Appalachian orogen to the east, Ouachita orogen to the southeast, Precambrian basement exposed in the ancestral Mogollon Highlands to the south, East Mexico arc, and Permian–Triassic arc built along the southern Cordilleran margin. Triassic grains in each chronostratigraphic unit also have distinct U and thorium (Th) concentrations, which are interpreted to reflect temporal changes in the chemistry of arc magmatism. Comparison of our LA-ICPMS ages with available chemical abrasion thermal ionization mass spectrometry (CA-TIMS) ages and new magnetostratigraphic data provides new insights into the depositional history of the Chinle Formation, as well as methods utilized to determine depositional ages of fluvial strata. For parts of the Chinle Formation that are dominated by fine-grained clastic strata (e.g., mudstone and siltstone), such as the Blue Mesa Member and Petrified Forest Member, all three chronometers agree (to within ∼ 1 Myr), and robust depositional chronologies have been determined. In contrast, for stratigraphic intervals dominated by coarse-grained clastic strata (e.g., sandstone), such as most of the Sonsela Member, the three chronologic records disagree due to recycling of older zircon grains and variable dilution of syn-depositional-age grains. This results in LA-ICPMS ages that significantly predate deposition and CA-TIMS ages that range between the other two chronometers. These complications challenge attempts to establish a well-defined chronostratigraphic age model for the Chinle Formation

U-Pb zircon geochronology and depositional age models for the Upper Triassic Chinle Formation (Petrified Forest National Park, Arizona, USA): implications for Late Triassic paleoecological and paleoenvironmental change

The Upper Triassic Chinle Formation is a critical non-marine archive of low-paleolatitude biotic and environmental change in southwestern North America. The well-studied and highly fossiliferous Chinle strata at Petrified Forest National Park (PFNP), Arizona, preserve a biotic turnover event recorded by vertebrate and palynomorph fossils, which has been alternatively hypothesized to coincide with tectonically driven climate change or with the Manicouagan impact event at ca. 215.5 Ma. Previous outcrop-based geochronologic age constraints are difficult to put in an accurate stratigraphic framework because lateral facies changes and discontinuous outcrops allow for multiple interpretations. A major goal of the Colorado Plateau Coring Project (CPCP) was to retrieve a continuous record in unambiguous superposition designed to remedy this situation. We sampled the 520-m-long core 1A of the CPCP to develop an accurate age model in unquestionable superposition by combining U-Pb zircon ages and magnetostratigraphy. From 13 horizons of volcanic detritus-rich siltstone and sandstone, we screened up to ∼300 zircon crystals per sample using laser ablation−inductively coupled plasma−mass spectrometry and subsequently analyzed up to 19 crystals of the youngest age population using the chemical abrasion−isotope dilution−thermal ionization mass (CA-ID-TIMS) spectrometry method. These data provide new maximum depositional ages for the top of the Moenkopi Formation (ca. 241 Ma), the lower Blue Mesa Member (ca. 222 Ma), and the lower (ca. 218 to 217 Ma) and upper (ca. 213.5 Ma) Sonsela Member. The maximum depositional ages obtained for the upper Chinle Formation fall well within previously proposed age constraints, whereas the maximum depositional ages for the lower Chinle Formation are relatively younger than previously proposed ages from outcrop; however, core to outcrop stratigraphic correlations remain uncertain. By correlating our new ages with the magnetostratigraphy of the core, two feasible age model solutions can be proposed. Model 1 assumes that the youngest, coherent U-Pb age clusters of each sample are representative of the maximum depositional ages and are close to (227 Ma) in age, and hence the biotic turnover event cannot be correlated to the Carnian−Norian boundary but is rather a mid-Norian event. Our age models demonstrate the powers, but also the challenges, of integrating detrital CA-ID-TIMS ages with magnetostratigraphic data to properly interpret complex sedimentary sequences

The Fossil Calibration Database—A New Resource for Divergence Dating

Fossils provide the principal basis for temporal calibrations, which are critical to the accuracy of divergence dating analyses. Translating fossil data into minimum and maximum bounds for calibrations is the most important—often least appreciated—step of divergence dating. Properly justified calibrations require the synthesis of phylogenetic, paleontological, and geological evidence and can be difficult for nonspecialists to formulate. The dynamic nature of the fossil record (e.g., new discoveries, taxonomic revisions, updates of global or local stratigraphy) requires that calibration data be updated continually lest they become obsolete. Here, we announce the Fossil Calibration Database (http://fossilcalibrations.org), a new open-access resource providing vetted fossil calibrations to the scientific community. Calibrations accessioned into this database are based on individual fossil specimens and follow best practices for phylogenetic justification and geochronological constraint. The associated Fossil Calibration Series, a calibration-themed publication series at Palaeontologia Electronica, will serve as a key pipeline for peer-reviewed calibrations to enter the databas

The Fossil Calibration Database, A New Resource for Divergence Dating

Fossils provide the principal basis for temporal calibrations, which are critical to the accuracy of divergence dating analyses. Translating fossil data into minimum and maximum bounds for calibrations is the most important, and often least appreciated, step of divergence dating. Properly justified calibrations require the synthesis of phylogenetic, paleontological, and geological evidence and can be difficult for non- specialists to formulate. The dynamic nature of the fossil record (e.g., new discoveries, taxonomic revisions, updates of global or local stratigraphy) requires that calibration data be updated continually lest they become obsolete. Here, we announce the Fossil Calibration Database (http://fossilcalibrations.org), a new open- access resource providing vetted fossil calibrations to the scientific community. Calibrations accessioned into this database are based on individual fossil specimens and follow best practices for phylogenetic justification and geochronological constraint. The associated Fossil Calibration Series, a calibration-themed publication series at Palaeontologia Electronica, will serve as one key pipeline for peer-reviewed calibrations to enter the database