Conodont fossils are highly valuable for Paleozoic biostratigraphy and for interpreting evolutionary change, but identifying and describing conodont morphologies, and characterizing gradual shape variation remain challenging. We used geometric morphometric (GM) analysis to conduct the first landmark-based morphometric analysis of the biostratigraphically useful conodont genus Neognathodus. Our objective is to assess whether previously defined morphotype groups are reliably distinct from one another. As such, we reevaluate patterns of morphologic change in Neognathodus P1elements, perform maximum-likelihood tests of evolutionary modes, and construct novel, GM-based biozonations through a Desmoinesian (Middle Pennsylvanian) section in the Illinois Basin. Our GM results record the entire spectrum of shape variability among Neognathodus morphotypes, thus alleviating the problem of documenting and classifying gradual morphologic transitions between morphotypes. Statistically distinct GM groups support previously established classifications of N. bassleri, N. bothrops, and N. roundyi. Statistically indistinct pairs of GM groups do not support literature designations of N. medadultimus and N. medexultimus, and N. dilatus and N. metanodosus, and we synonymize each pair. Maximum-likelihood tests of evolutionary modes provide the first statistical assessment of Neognathodus evolutionary models in the Desmoinesian. The most likely evolutionary models are an unbiased random walk or a general random walk. We name four distinct biozones through the Desmoinesian using GM results, and these align with previous biozonation structure based on the Neognathodus Index (NI), illustrating that Neognathodus-based biostratigraphic correlations would not change between GM or NI methods. The structural similarity between both biozonations showcases that determining GM-based biozones is not redundant, as this comparison validates using landmark-based GM work to construct viable biozonations for subsequent stratigraphic correlations. Although this study is limited to the Illinois Basin, our quantitative methodology can be applied broadly to test taxonomic designations of additional genera, interpret statistically robust evolutionary patterns, and construct valid biozones for this significant chordate group.

The Neognathodus Index (NI) is developed as a primary biostratigraphic indicator for the Desmoinesian Series of the Illinois Basin in Indiana, Illinois, and Kentucky. It is based on the gradual evolutionary morphotypic variations of P1 elements of named species of Neognathodus Dunn, 1970. The NI analyses and zonations presented herein are constructed from 472 productive conodont samples from 105 different localities. NIs for the Illinois Basin show morphologic drift in Indiana from the Perth Limestone Member of the Staunton Formation (NI = 2.03) to the Velpen Limestone and Mecca Quarry Shale members of the Linton Formation (NI = 5.04) followed by stability through the Alum Cave (NI = 4.83). Further morphologic drift then occurred through the Providence Limestone Member of the Dugger Formation (NI = 5.43) and continued through the West Franklin Limestone Member of the Shelburn Formation (NI = 6.32) until the extinction of Neognathodus at the end of Desmoinesian. The patterns of drift and stability translate to Neognathodus biozones and are supported by Kolmogorov-Smirnov tests of standardized Neognathodus morphotype distributions. Localized NI variations are due to morphologic shifts and differential evolution in response to localized environmental conditions. Examination of the NI differences in the states of Illinois, Kentucky, and Indiana reflect similar morphologic simplification of the P1 element from Perth to Velpen and Mecca Quarry in Indiana (NI = 2.03–5.04) and from Seville to Brereton in Illinois and Kentucky (NI = 2.80–5.00). Post-Brereton in Illinois and Kentucky (NI = 5.00–5.65) and post-Providence in Indiana (NI = 5.43–6.32) saw progressive P1 simplification, but it was much more pronounced in Indiana.

Work of J. Rickard proves that the derived module categories of two rings A and B are equivalent as triangulated categories if and only if there is a particular object T, a so-called tilting complex, in the derived category of A such that B is the endomorphism ring of T. The functor inducing the equivalence, however, is not explicit by the knowledge of T. Suppose the derived categories of A and B are equivalent. If A and B are R-algebras and projective of finite type over the commutative ring R, then Rickard proves the existence of a so-called two-sided tilting complex X, which is an object in the derived category of bimodules. The left derived tensor product by X is then an equivalence between the desired categories of A and B.

This study provides the first focused investigation of rudist bivalves from the Upper Cretaceous of the Gulf Coastal Plain (GCP) in the southern US and previously undescribed specimens from the Flor de Alba Limestone Member of the Pozas Formation in Puerto Rico. Identified rudists from the GCP comprise the Monopleuridae, including Gyropleura, as well as Radiolitidae, including Biradiolites cardenasensi, Durania maxima, Guanacastea jamaicensis, Radiolites acutocostata, and Sauvagesia. Integrating rudist occurrences within well-established GCP biostratigraphy allows for extension of upper ranges of D. maxima and R. acutocostata into the late Campanian, and extension of the lower ranges of B. cardenasensis and G. jamaicensis into the early Campanian. Identified rudists from Puerto Rico comprise the Hippuritidae and include Barrettia monilifera, which supports the age of the Flor de Alba Limestone Member of the Pozas Formation as middle Campanian. Combined taxonomic, biostratigraphic, and paleobiogeographic analyses indicate there is no rudist fauna endemic to the GCP, and the region marks the northeastern range of the Caribbean genera Biradiolites, Durania, Guanacastea, Gyropleura, Radiolites, and Sauvagesia during the Campanian and Maastrichtian. The new occurrences help inform future updates of Late Cretaceous sea surface-current reconstructions for the Caribbean and Western Interior Seaway, USA.

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