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The Whitehorse Group and Quartermaster Formation are extensive red-bed terrestrial sequences representing the final episode of sedimentation in the Palo Duro Basin in north-central Texas, U.S.A. Regionally, these strata record the culmination of a long-term regression sequence beginning in the middle to late Permian. The Whitehorse Group includes beds of abundant laminated to massive red quartz siltstone to fine sandstone and rare dolomite, laminated to massive gypsum, and claystones, as well as diagenetic gypsum. The Quartermaster Formation exhibits a change from nearly equal amounts of thin planar and lenticular fine sandstone and laminated to massive mudstone in its lower half to overlying strata with coarser-grained, cross-bedded sandstones indicative of meandering channels up to 7 m deep and rare overbank mudstones. Paleosols are absent in the Upper Whitehorse Group and only poorly developed in the Quartermaster Formation. Volcanic ash-fall deposits (tuffs) present in uppermost Whitehorse Group and lower Quartermaster Formation strata permit correlation among five stratigraphic sections distributed over ∼150 km and provide geochronologic age information for these rocks. Both the Whitehorse Group and Quartermaster Formation have traditionally been assigned to the late Permian Ochoan (Changhsingian) stage, and workers assumed that the Permian-Triassic boundary is characterized by a regionally significant unconformity. Chemostratigraphic or biostratigraphic evidence for this age assignment, however, have been lacking to date. Single zircon U-Pb CA-TIMS analyses from at least two distinct volcanic ash fall layers in the lower Quartermaster Formation, which were identified and collected from five different localities across the Palo Duro Basin, yield interpreted depositional ages ranging from 252.19 ± 0.30 to 251.74 ± 0.28 Ma. Single zircon U-Pb CA-TIMS analyses of detrital zircons from sandstones located only a few meters beneath the top of the Quartermaster Formation yield a range of dates from Mesoproterozoic (1418 Ma) to Middle Triassic (244.5 Ma; Anisian), the latter of which is interpreted as a maximum depositional age, which is no older than Anisian, thus indicating the Permian-Triassic boundary to lie somewhere within the lower Quartermaster Formation/upper Whitehorse Group succession. Stable carbon isotope data from 180 samples of early-burial dolomicrite cements preserve a chemostratigraphic signal that is similar among sections, with a large ∼−8‰ negative isotope excursion ∼20 m beneath the Whitehorse Group-Quartermaster Formation boundary. This large negative carbon isotope excursion is interpreted to be the same excursion associated with the end-Permian extinction and this is in concert with the new high precision radioisotopic age data presented and the fact that the excursion lies within a normal polarity stratigraphic magnetozone. Dolomite cement δ 13 C values remain less negative (between about −5 and −8 permil) into the lower part of the Quartermaster Formation before becoming more positive toward the top of the section. This long interval of negative δ 13 C values in the Quartermaster Formation is interpreted to represent the earliest Triassic (Induan) inception of biotic and ecosystem “recovery.” Oxygen isotope values of dolomicrite cements show a progressive trend toward more positive values through the boundary interval, suggesting substantially warmer conditions around the end-Permian extinction event and a trend toward cooler conditions after the earliest Triassic. Our observations on these strata show that the paleoenvironment and paleoclimate across the Permian-Triassic boundary in western, sub-equatorial Pangea was characterized by depositional systems that were not conducive to plant preservation. 

Urban scaling analysis, the study of how aggregated urban features vary with the population of an urban area, provides a promising framework for discovering commonalities across cities and uncovering dynamics shared by cities across time and space. Here, we use the urban scaling framework to study an important, but under-explored feature in this community—income inequality. We propose a new method to study the scaling of income distributions by analysing total income scaling in population percentiles. We show that income in the least wealthy decile (10%) scales close to linearly with city population, while income in the most wealthy decile scale with a significantly superlinear exponent. In contrast to the superlinear scaling of total income with city population, this decile scaling illustrates that the benefits of larger cities are increasingly unequally distributed. For the poorest income deciles, cities have no positive effect over the null expectation of a linear increase. We repeat our analysis after adjusting income by housing cost, and find similar results. We then further analyse the shapes of income distributions. First, we find that mean, variance, skewness and kurtosis of income distributions all increase with city size. Second, the Kullback–Leibler divergence between a city’s income distribution and that of the largest city decreases with city population, suggesting the overall shape of income distribution shifts with city population. As most urban scaling theories consider densifying interactions within cities as the fundamental process leading to the superlinear increase of many features, our results suggest this effect is only seen in the upper deciles of the cities. Our finding encourages future work to consider heterogeneous models of interactions to form a more coherent understanding of urban scaling.