The global fossil record of marine animals has fueled long-standing debates about diversity change through time and the drivers of this change. However, the fossil record is not truly global. It varies considerably in geographic scope and in the sampling of environments among intervals of geological time. We account for this variability using a spatially explicit approach to quantify regional-scale diversity through the Phanerozoic. Among-region variation in diversity is comparable to variation through time, and much of this is explained by environmental factors, particularly the extent of reefs. By contrast, influential hypotheses of diversity change through time, including sustained long-term increases, have little explanatory power. Modeling the spatial structure of the fossil record transforms interpretations of Phanerozoic diversity patterns and their macroevolutionary explanations. This necessitates a refocus of deep-time diversification studies.

Variation in the geographic spread of fossil localities strongly biases inferences about the evolution of biodiversity, due to the ubiquitous scaling of species richness with area. This obscures answers to key questions, such as how tetrapods attained their tremendous extant diversity. Here, we address this problem by applying sampling standardization methods to spatial regions of equal size, within a global Mesozoic-early Palaeogene data set of non-flying terrestrial tetrapods. We recover no significant increase in species richness between the Late Triassic and the Cretaceous/Palaeogene (K/Pg) boundary, strongly supporting bounded diversification in Mesozoic tetrapods. An abrupt tripling of richness in the earliest Palaeogene suggests that this diversity equilibrium was reset following the K/Pg extinction. Spatial heterogeneity in sampling is among the most important biases of fossil data, but has often been overlooked. Our results indicate that controlling for variance in geographic spread in the fossil record significantly impacts inferred patterns of diversity through time.

A series of spectacular discoveries have transformed our understanding of Mesozoic mammals in recent years. These finds reveal hitherto-unsuspected ecomorphological diversity that suggests that mammals experienced a major adaptive radiation during the Middle to Late Jurassic. Patterns of mammalian macroevolution must be reinterpreted in light of these new discoveries, but only taxonomic diversity and limited aspects of morphological disparity have been quantified. We assess rates of morphological evolution and temporal patterns of disparity using large datasets of discrete characters. Rates of morphological evolution were significantly elevated prior to the Late Jurassic, with a pronounced peak occurring during the Early to Middle Jurassic. This intense burst of phenotypic innovation coincided with a stepwise increase in apparent long-term standing diversity and the attainment of maximum disparity, supporting a "short-fuse" model of early mammalian diversification. Rates then declined sharply, and remained significantly low until the end of the Mesozoic, even among therians. This supports the "long-fuse" model of diversification in Mesozoic therians. Our findings demonstrate that sustained morphological innovation in Triassic stem-group mammals culminated in a global adaptive radiation of crown-group members during the Early to Middle Jurassic.

To infer genuine patterns of biodiversity change in the fossil record, we must be able to accurately estimate relative differences in numbers of taxa (richness) despite considerable variation in sampling between time intervals. Popular subsampling (=interpolation) methods aim to standardise diversity samples by rarefying the data to equal sample size or equal sample completeness (=coverage). Standardising by sample size is misleading because it compresses richness ratios, thereby flattening diversity curves. However, standardising by coverage reconstructs relative richness ratios with high accuracy. Asymptotic richness extrapolators are widely used in ecology, but rarely applied to fossil data. However, a recently developed parametric extrapolation method, TRiPS (True Richness estimation using Poisson Sampling), specifically aims to estimate the true richness of fossil assemblages. Here, we examine the suitability of a range of richness estimators (both interpolators and extrapolators) for fossil datasets, using simulations and a novel method for comparing the performance of richness estimators with empirical data. We constructed sampling‐standardised discovery curves (SSDCs) for two datasets, each spanning 150 years of palaeontological research: Mesozoic dinosaurs at global scale, and Mesozoic–early Cenozoic tetrapods from North America. These approaches reveal how each richness estimator responds to both simulated best‐case and empirical real‐world accumulation of fossil occurrences. We find that extrapolators can only truly standardise diversity data once sampling is sufficient for richness estimates to have asymptoted. Below this point, directly comparing extrapolated estimates derived from samples of different sizes may not accurately reconstruct relative richness ratios. When abundance distributions are not perfectly flat and sampling is moderate to good, but not perfect, TRiPS does not extrapolate, because it overestimates binomial sampling probabilities. Coverage‐based interpolators, by contrast, generally yield more stable subsampled diversity estimates, even in the face of dramatic increases in face‐value counts of species richness. Richness estimators that standardise by coverage are among the best currently available methods for reconstructing deep‐time biodiversity patterns. However, we recommend the use of sampling‐standardised discovery curves to understand how biased reporting of fossil occurrences may affect sampling‐standardised diversity estimates.

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