Computational fluid dynamics (CFD), which involves using computers to simulate fluid flow, is emerging as a powerful approach for elucidating the palaeobiology of ancient organisms. Here, Imran A. Rahman describes its applications for studying fossil echinoderms. When properly configured, CFD simulations can be used to test functional hypotheses in extinct species, informing on aspects such as feeding and stability. They also show great promise for addressing ecological questions related to the interaction between organisms and their environment. CFD has the potential to become an important tool in echinoderm palaeobiology over the coming years.

The principles of stratigraphic paleobiology can be readily applied to the nonmarine fossil record. Consistent spatial and temporal patterns of accommodation and sedimentation in sedimentary basins are an important control on stratigraphic architecture. Temperature and precipitation covary with elevation, causing significant variation in community composition, and changes in base level cause elevation to undergo predictable changes. These principles lead to eight sets of hypotheses about the nonmarine fossil record. Three relate to long-term and cyclical patterns in the preservation of major fossil groups and their taphonomy, as well as the occurrence of fossil concentrations. The remaining hypotheses relate to the widespread occurrence of elevation-correlated gradients in community composition, long-term and cyclical trends in these communities, and the stratigraphic position of abrupt changes in community composition. Testing of these hypotheses makes the stratigraphic paleobiology of nonmarine systems a promising area of investigation.

The study of echinoid evolution, diversity, and ecology has always suffered from the fact that they are represented by taxa showing widely differing architectural designs of their multi-plated skeletons, inhabiting a large range of marine paleoenvironments, which result in highly varying taphonomic biases dictating their presence and recognition. This Element addresses the taphonomy of echinoids and includes: a general introduction to the morphological features of echinoids that play a role in their preservation; a review of processes which play an important role in the differential preservation of both regular and irregular echinoids including predation and transport; a summary of taphonomic pathways included in actualistic studies for recent sea urchins and then reconstructed for fossil taxa; and finally, a case study of the variation of echinoid taphonomy across a shelf gradient using the rich Miocene echinoid fauna of Sardinia.

Imaging and visualizing fossils in three dimensions with tomography is a powerful approach in paleontology. Here, the authors introduce select destructive and non-destructive tomographic techniques that are routinely applied to fossils and review how this work has improved our understanding of the anatomy, function, taphonomy, and phylogeny of fossil echinoderms. Building on this, this Element discusses how new imaging and computational methods have great promise for addressing long-standing paleobiological questions. Future efforts to improve the accessibility of the data underlying this work will be key for realizing the potential of this virtual world of paleontology.

The history of life on earth is largely reconstructed from time-averaged accumulations of fossils. A glimpse at ecologic-time attributes and processes is relatively rare. However, the time-sensitive and predictability of echinoderm disarticulation makes them model organisms to determine post-mortem transportation and allows recognition of ecological-time data within paleocommunity accumulations. Unlike many other fossil groups, this has allowed research on many aspects of echinoderms and their paleocommunities, such as the distribution of soft tissues, assessment of the amount of fossil transportation prior to burial, determination of intraspecific variation, paleocommunity composition, estimation of relative abundance of taxa in paleocommunities, determination of attributes of niche differentiation, etc. Crinoids and echinoids have received the most amount of taphonomic research, and the patterns present in these two groups can be used to develop a more thorough understanding of all echinoderm clades.

Macroevolutionary inference has historically been treated as a two-step process, involving the inference of a tree, and then inference of a macroevolutionary model using that tree. Newer models blend the two steps. These methods make more complete use of fossils than the previous generation of Bayesian phylogenetic models. They also involve many more parameters than prior models, including parameters about which empiricists may have little intuition. In this Element, we set forth a framework for fitting complex, hierarchical models. The authors ultimately fit and use a joint tree and diversification model to estimate a dated phylogeny of the Cincta (Echinodermata), a morphologically distinct group of Cambrian echinoderms that lack the fivefold radial symmetry characteristic of extant members of the phylum. Although the phylogeny of cinctans remains poorly supported in places, this Element shows how models of character change and diversification contribute to understanding patterns of phylogenetic relatedness and testing macroevolutionary hypotheses.

Echinoderms have evolved diverse and disparate morphologies throughout the Phanerozoic. Among them, blastozoans, an extinct group of echinoderms that were an important component of Paleozoic marine ecosystems, are primarily subdivided into groups based on the morphology of respiratory structures. However, systematic and phylogenetic research from the past few decades have shown that respiratory structures in blastozoans are not group-defining and they have re-evolved throughout echinoderm evolution. This Element provides a review of the research involving blastozoan respiratory structures, along with research concerning the morphology, paleoecology, and ontogeny of each of the major groupings of blastozoans as it relates to their corresponding respiratory structures. Areas of future research in these groups are also highlighted.

The quantification of morphology through time is a vital tool in elucidating macroevolutionary patterns. Studies of disparity require intense effort but can provide insights beyond those gained using other methodologies. Over the last several decades, studies of disparity have proliferated, often using echinoderms as a model organism. Echinoderms have been used to study the methodology of disparity analyses and potential biases as well as documenting the morphological patterns observed in clades through time. Combining morphological studies with phylogenetic analyses or other disparate data sets allows for the testing of detailed and far-reaching evolutionary hypotheses.

Recent advances in statistical approaches called phylogenetic comparative methods (PCMs) have provided paleontologists with a powerful set of analytical tools for investigating evolutionary tempo and mode in fossil lineages. However, attempts to integrate PCMs with fossil data often present workers with practical challenges or unfamiliar literature. This Element presents guides to the theory behind and the application of PCMs with fossil taxa. Based on an empirical dataset of Paleozoic crinoids, example analyses are presented to illustrate common applications of PCMs to fossil data, including investigating patterns of correlated trait evolution and macroevolutionary models of morphological change. The authors emphasize the importance of accounting for sources of uncertainty and discuss how to evaluate model fit and adequacy. Finally, the authors discuss several promising methods for modeling heterogeneous evolutionary dynamics with fossil phylogenies. Integrating phylogeny-based approaches with the fossil record provides a rigorous, quantitative perspective on understanding key patterns in the history of life.