Fullerene‐like structures of Cretaceous crinoids reveal topologically limited skeletal possibilities

There are few cases where numbers or types of possible phenotypes are known, although vast state spaces have been postulated. Rarely applied in this context, graph theory and topology enable enumeration of possible phenotypes and evolutionary transitions. Here, we generate polyhedral calyx graphs for the Late Cretaceous, stemless crinoids Marsupites testudinarius and Uintacrinus socialis (Uintacrinoidea Zittel) revealing structural similarities to carbon fullerene and fulleroid molecules (respectively). The U. socialis calyx incorporates numerous plates (e.g. graph vertices |V| ≥ 197), which are small, light, low‐density and have four to eight sides. Therefore, the corresponding number of possible plate arrangements (number of polyhedral graphs) is large (≫1 × 1014). Graph vertices representing plates with sides >6 introduce negative Gaussian curvature (surface saddle points) and topological instability, increasing buckling risk. However, observed numbers of vertices for Uintacrinus do not allow more stable pentaradial configurations. In contrast, the Marsupites calyx dual graph has 17 faces that are pentagonal or hexagonal. Therefore, it is structurally identical to a carbon fullerene, specifically C30‐D5h. Corresponding graph restrictions result in constraint to only three structural options (fullerene structures C30‐C2v 1, C30‐C2v 2 and C30‐D5h). Further restriction to pentaradial symmetry allows only one possibility: the Marsupites phenotype. This robust, stable topology is consistent with adaptation to predation pressures of the Mesozoic marine revolution. Consequently, the most plausible evolutionary pathway between unitacrinoid phenotypes was a mixed heterochronic trade‐off to fewer, larger calyx plates. Therefore, topological limitations radically constrained uintacrinoid skeletal possibilities but thereby aided evolution of a novel adaptive phenotype

A Re‐Interpretation of the Ambulacral System of Eumorphocystis (Blastozoa, Echinodermata) and its Bearing on the Evolution of Early Crinoids

Recent debates over the evolutionary relationships of early echinoderms have relied heavily on morphological evidence from the feeding ambulacral system. Eumorphocystis, a Late Ordovician diploporitan, has been a focus in these debates because it bears ambulacral features that show strong morphological similarity to early crinoid arms. Undescribed and well‐preserved specimens of Eumorphocystis from the Bromide Formation (Oklahoma, USA) provide new data illustrating that composite arms supported by a radial plate that bear a triserial arrangement of axial and extraxial components encasing a coelomic extension can also be found in blastozoans. Previous reports have considered these arm structures to be restricted to crinoids; these combined features have not been previously observed in blastozoan echinoderms. Phylogenetic analyses suggest that Eumorphocystis and crinoids are sister taxa and that shared derived features of these taxa are homologous. The evidence from the arms of Eumorphocystis suggests that crinoid arms were derived from a specialized blastozoan ambulacral system that lost feeding brachioles and strongly suggests that crinoids are nested within blastozoans

Palaeobiogeography of Ordovician echinoderms

The palaeobiogeographical distribution of the six major clades of Ordovician echinoderms (asterozoans, blastozoans, crinoids, echinozoans, edrioasteroids and stylophorans) is analysed based on a comprehensive and up-to-date database compiling 3701 occurrences (1938 species recorded from 331 localities) of both complete specimens and isolated ossicles. Although historically biased towards a limited number of regions (Europe, North America, Russia), the resulting dataset makes it possible to identify six main palaeobiogeographical provinces for Ordovician echinoderms: Laurentia, Baltica, West Gondwana, East Gondwana, Avalonia and Siberia. At a global scale, the high endemicity of echinoderms during the Early to Middle Ordovician coincides with the time of maximum dispersal of continental masses. Late Ordovician faunas tend to become more cosmopolitan, possibly as a consequence of changing palaeogeography and/or relatively higher sea-levels in the Sandbian–Katian interval. Regional biodiversity patterns of Ordovician echinoderms confirm that their major diversification during the Ordovician is not a single, universal evolutionary event, but rather results from the complex addition of contrasted local evolutionary trends

The Nonprofit Business Model: Empirical Evidence From the Magazine Industry

This article seeks to shed some light on the nonprofit business model by considering empirical data from one area of the media industry where nonprofits make up a sizable segment: periodical publishing. The primary context for this study is the body of economic research into the effects of organizational structure on firm behavior, which is used to propose hypotheses about nonprofit periodicals. The results highlight management challenges that nonprofits face.