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

Palaeontology - Vol. 63 Part 3 - Cover Image
Publication: Palaeontology
Volume: 63
Part: 3
Publication Date: May 2020
Page(s): 513 524
Author(s): Jennifer F. Hoyal Cuthill, and Aaron W. Hunter
Addition Information

How to Cite

CUTHILL, J.F.H., HUNTER, A.W. 2020. . Palaeontology, 63, 3, 513-524. DOI: /doi/10.1111/pala.12474

Author Information

  • Jennifer F. Hoyal Cuthill - Institute of Analytics & Data Science & School of Life Sciences University of Essex Wivenhoe Park Colchester CO4 3SQ UK
  • Jennifer F. Hoyal Cuthill - Department of Earth Sciences University of Cambridge Downing Street Cambridge CB2 3EQ UK
  • Jennifer F. Hoyal Cuthill - Earth‐Life Science Institute Tokyo Institute of Technology Tokyo 152‐8550 Japan
  • Aaron W. Hunter - Department of Earth Sciences University of Cambridge Downing Street Cambridge CB2 3EQ UK
  • Aaron W. Hunter - School of Earth Sciences The University of Western Australia 35 Stirling Highway Crawley WA 6009 Australia

Publication History

  • Issue published online: 29 April 2020
  • Manuscript Accepted: 21 November 2019
  • Manuscript Received: 10 January 2019

Funded By

John Templeton Foundation

Online Version Hosted By

Wiley Online Library
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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.

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