Variation in observed global generic richness over the Phanerozoic must be partly explained by changes in the numbers of fossils and their geographic spread over time. The influence of sampling intensity (i.e., the number of samples) has been well addressed, but the extent to which the geographic distribution of samples might influence recovered biodiversity is comparatively unknown. To investigate this question, we create models of genus richness through time by resampling the same occurrence dataset of modern global biodiversity using spatially explicit sampling intensities defined by the paleo-coordinates of fossil occurrences from successive time intervals. Our steady-state null model explains about half of observed change in uncorrected fossil diversity and a quarter of variation in sampling-standardized diversity estimates. The inclusion in linear models of two additional explanatory variables associated with the spatial array of fossil data (absolute latitudinal range of occurrences, percentage of occurrences from shallow environments) and a Cenozoic step increases the accuracy of steady-state models, accounting for 67% of variation in sampling-standardized estimates and more than one-third of the variation in first differences. Our results make clear that the spatial distribution of samples is at least as important as numerical sampling intensity in determining the trajectory of recovered fossil biodiversity through time and caution against the overinterpretation of both the variation and the trend that emerge from analyses of global Phanerozoic diversity.

Apicobasal ridges are longitudinal ridges of enamel that are particularly common in several clades of aquatic-feeding predatory amniotes, including Plesiosauria, Ichthyosauria, Mosasauridae, Crocodylia, and Spinosauridae, as well as some early members of Cetacea. Although the repeated evolution of these dental ridges in unrelated clades suggests an adaptive benefit, their primary function in feeding is debated. Hypothesized functions range from increasing tooth strength to improving prey puncture or removal efficiency, but these have never been quantitatively tested. This study utilizes finite element analysis (FEA) to assess the impact of apicobasal ridges upon tooth crown strength in aquatic-feeding amniotes. Drawing on morphometric data from fossilized tooth crowns, a set of digital models was constructed to calculate the performance of smooth and ridged tooth variants under simulated bite force loadings. The similarities in overall stress distribution patterns across models of the same tooth shape, regardless of the presence or morphology of ridges, indicate that apicobasal ridges have little impact on stress reduction within the tooth crown. Ultimately, these findings suggest that apicobasal ridges have a minimal role in improving crown strength and form a framework for future research into the remaining hypotheses.

Body size has a long history of study in paleobiology and underlies many important phenomena in macroevolution. Body-size patterns in the fossil record are often examined by utilizing size data alone, which hinders our ability to describe the biological meaning behind size change on macroevolutionary timescales. Without data reflecting the biological and geologic factors that drive size change, we cannot assess its mechanistic underpinnings.

Existing frameworks for studying ontogeny and phylogeny can remedy this problem, particularly the classic age–size–“shape” space originally developed for studies of heterochrony. When evaluated based on metrics for age, size, and phenotype in populations, proposed mechanisms for size change can be outlined theoretically and tested empirically in the record. Using this framework, we can compare ontogenetic trajectories within and between species and determine how changes in size emerge. Here, we outline ontogenetic mechanisms for evolutionary size change, such as heterochrony, as well as how geologic factors can drive apparent, non-biological size change (e.g., taphonomic size sorting).

To demonstrate the utility of this framework in actual paleobiological problems, we apply it to the Lilliput effect, a compelling and widely documented pattern of size decrease during extinction events. However, little is known about the mechanisms underlying this pattern. We provide a brief history of the Lilliput effect and refine its definition in a framework that can be mechanistically tested. Processes that likely produce Lilliput effects include allometric and sequence repatterning (including heterochrony) and evolutionary size-selective sorting. We describe these mechanisms and highlight relevant examples of the Lilliput effect for which feasible empirical tests are possible.

During the late Miocene and early Pliocene (latest Hemphillian, Hh4 interval, 5.7 to 4.75 Ma) a distinctive suite of four species of extinct horses (Family Equidae) were widespread in North America. This includes Nannippus aztecus, Neohipparion eurystyle, Astrohippus stocki, and Dinohippus mexicanus. In Florida, two additional equid species, Pseudhipparion simpsoni and Cormohipparion emsliei, are also typically found at Hh4 localities. Here we compare horses from four Hh4 Florida fossil sites, including three from the Bone Valley mines and a fourth from the recently discovered Montbrook site. Two of these sites have all six expected species, one has five species, and one has only four species present. To explain these differences, we used species counts from research databases and rarefaction simulation to clarify the relative abundances, species richness, and occurrences of these horses from these four sites. The Palmetto Mine (Agrico) site, with five equid species, appears to lack the sixth species owing to ecological reasons. This is different from Montbrook, the site with only four of the six species. Results indicate that Montbrook is likely lacking two missing equid species for a couple of reasons: sampling bias and biological/ecological causes. Our results demonstrate that sampling biases can account for observed equid species richness when the overall abundance of certain equid species is low. Nevertheless, other factors, including ecology and with sufficient resolution, perhaps also time, may also explain the distribution and occurrences of individual species at these and other fossil sites. In a broader perspective, analyses such as this example provide an opportunity to address a persistent challenge in paleontology, that is, how do we explain absences of extinct taxa from the fossil record?

Scaling fluctuation analyses of marine animal diversity and extinction and origination rates based on the Paleobiology Database occurrence data have opened new perspectives on macroevolution, supporting the hypothesis that the environment (climate proxies) and life (extinction and origination rates) are scaling over the “megaclimate” biogeological regime (from ≈1 Myr to at least 400 Myr). In the emerging picture, biodiversity is a scaling “crossover” phenomenon being dominated by the environment at short timescales and by life at long timescales with a crossover at ≈40 Myr. These findings provide the empirical basis for constructing the Fractional MacroEvolution Model (FMEM), a simple stochastic model combining destabilizing and stabilizing tendencies in macroevolutionary dynamics, driven by two scaling processes: temperature and turnover rates.

Macroevolution models are typically deterministic (albeit sometimes perturbed by random noises) and are based on integer-ordered differential equations. In contrast, the FMEM is stochastic and based on fractional-ordered equations. Stochastic models are natural for systems with large numbers of degrees of freedom, and fractional equations naturally give rise to scaling processes.

The basic FMEM drivers are fractional Brownian motions (temperature, T) and fractional Gaussian noises (turnover rates, E+) and the responses (solutions), are fractionally integrated fractional relaxation noises (diversity [D], extinction [E], origination [O], and E− = O − E). We discuss the impulse response (itself representing the model response to a bolide impact) and derive the model's full statistical properties. By numerically solving the model, we verified the mathematical analysis and compared both uniformly and irregularly sampled model outputs with paleobiology series.

Strata of the Ediacaran Period (635–538.8 Ma) yield the oldest known fossils of complex, macroscopic organisms in the geologic record. These “Ediacaran-type” macrofossils (known as the Ediacaran biota) first appear in mid-Ediacaran strata, experience an apparent decline through the terminal Ediacaran, and directly precede the Cambrian (538.8–485.4 Ma) radiation of animals. Existing hypotheses for the origin and demise of the Ediacaran biota include: changing oceanic redox states, biotic replacement by succeeding Cambrian-type fauna, and mass extinction driven by environmental change. Few studies frame trends in Ediacaran and Cambrian macroevolution from the perspective of the sedimentary rock record, despite well-documented Phanerozoic covariation of macroevolutionary patterns and sedimentary rock quantity. Here we present a quantitative analysis of North American Ediacaran–Cambrian rock and fossil records from Macrostrat and the Paleobiology Database. Marine sedimentary rock quantity increases nearly monotonically and by more than a factor of five from the latest Ediacaran to the late Cambrian. Ediacaran–Cambrian fossil quantities exhibit a comparable trajectory and have strong (rs > 0.8) positive correlations with marine sedimentary area and volume flux at multiple temporal resolutions. Even so, Ediacaran fossil quantities are dramatically reduced in comparison to the Cambrian when normalized by the quantity of preserved marine rock. Although aspects of these results are consistent with the expectations of a simple fossil preservation–induced sampling bias, together they suggest that transgression–regression and a large expansion of marine shelf environments coincided with the diversification of animals during a dramatic transition that is starkly evident in both the sedimentary rock and fossil records.