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Disruption of ideal geometry in the growth of receptaculitids: a natural experiment in theoretical morphology

Published online by Cambridge University Press:  08 April 2016

Stephen Jay Gould  and
Michael Katz
Stephen Jay Gould
Affiliation:
Museum of Comparative Zoology, Harvard University, Cambridge, Massachusetts 02138
Michael Katz
Affiliation:
Museum of Comparative Zoology, Harvard University, Cambridge, Massachusetts 02138
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Abstract

Facets of the Silurian receptaculitid Ischadites barrandei are arranged in circlets about a nucleus. They form a set of spirals, originally eight in number, but increasing by the intercalation of new facets (initiating new spirals) in later circlets. We have simulated the surficial geometry of this alga by assuming, as much evidence indicates, that facets are limited in final size and that new spirals must therefore be intercalated in order to cover the surface with a fully tesselated pattern. We use only five parameters in our simulation: nature of the surface (radius of a sphere), tightness of the spirals (assumed to be logarithmic) and rate of increase in facet width (three parameters of an equation fitted to actual data). The program draws facets in circlets and intercalates new ones whenever the sum of facet diameters is at least a facet less than the circumference of the circlet. By holding all but one parameter constant, we can test the influence of single factors upon the pattern of intercalation. We compare these figures with actual patterns of intercalation for eight specimens. Variation in tightness of the spiral seems to affect the pattern most radically—tight spirals intercalate fewer facets because new circlets stay near the pole of the sphere. The morphology of intercalation supports the interpretation of Rietschel (1969, contra Nitecki, 1972 and Byrnes, 1968) that the nuclear circlets are the oldest part of the plant and that new circlets are generated at the opposite pole. Our simulation represents a basic pattern in nature, not a specific feature of receptaculitids. All structures that fill space with spirals and impose limits upon the size of individual units must add new spirals. Bryozoans subject to similar constraints but growing in a completely different way (peripheral growth in radial rows) display the same final pattern.

Type
Research Article
Information
Paleobiology , Volume 1 , Issue 1 , Winter 1975 , pp. 1 - 20
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Bourret, J. A., Lincoln, R. G., and Carpenter, B. H. 1969. Fungal endogenous rhythms expressed by spiral figures. Science 166:763–764.CrossRefGoogle ScholarPubMed
Byrnes, J. G. 1968. Notes on the nature and environmental significance of the Receptaculitaceae. Lethaia. 1:368–381.CrossRefGoogle Scholar
Church, A. H. 1895. The structure of the thallus of Neomeris dumetosa Lamour. Ann. Botany. 9:581–608.Google Scholar
Church, A. H. 1904. The principles of phyllotaxis. Ann. Botany:227–243.Google Scholar
Cook, P. L. 1965. Notes on the Cupuladriidae (Polyzoa, Anasca). Bull. Brit. Mus. (Nat. Hist.) Zoology. 13(5):151–187.Google Scholar
Cook, T. A. 1914. The Curves of Life. 479 pp. Constable and Co. London.Google Scholar
Egerod, L. E. 1952. An analysis, of the siphonous chlorophycophyta. Pubs. Botany Univ. Calif. 25:325–454.Google Scholar
Foster, M. 1973. Ordovician receptaculitids from California and their significance. Lethaia. 6:35–65.Google Scholar
Hinde, G. J. 1884. On the structure and affinities of the family of the Receptaculitidae. Quart. J. Geol. Soc. London. 40:795–849.CrossRefGoogle Scholar
Kesling, R. V., and Graham, A. 1962. Ischadites is a dasycladacean alga. J. Paleontology. 36:943–952.Google Scholar
Moseley, H. 1838. On the geometrical forms of turbinated and discoid shells. Phil. Trans. Roy. Soc. London. 128:351–370.Google Scholar
Murchison, R. I. 1839. The Silurian System. 768 pp. John Murray. London.Google Scholar
Nitecki, M. H. 1969. Redescription of Ischadites koenigi Murchison, 1839. Fieldiana Geology. 16:341–359.Google Scholar
Nitecki, M. H. 1970. North American cyclocrinitid algae. Fieldiana Geology. 21:1–182.Google Scholar
Nitecki, M. H. 1971. Ischadites abbottae, a new North American Silurian species. Phycologia. 10:263–275.Google Scholar
Nitecki, M. H. 1972. North American Silurian receptaculitid algae. Fieldiana Geology. 28:1–108.Google Scholar
Rauff, H. 1892. Untersuchungen über die Organisation und systematische Stellung der Receptaculitiden. Abh. bayr.-Akad. Wiss. math-phys. Cl. 17:645–722.Google Scholar
Raup, D. M. 1966. Geometric analysis of shell coiling: general problems. J. Paleontology. 40:1178–1190.Google Scholar
Raup, D. M. 1968. Theoretical morphology of echinoid growth. In, Macurda, D. B. Jr., ed. Paleobiological aspects of growth and development. Paleont. Soc. Mem. 2 (J. Paleont.). 42 (No. 5 suppl.):50–63.Google Scholar
Rietschel, S. 1969. Die Receptaculiten. Eine Studie zur Morphologie, Organisation, Ökologie und Überlieferung einer problematischen Fossil-Gruppe und die Deutung ihrer Stellung im System. Senckenbergiana Lethaea. 50:465–517.Google Scholar
Rudwick, M. J. S. 1968. Some analytic methods in the study of ontogeny in fossils with accretionary skeletons. In, Macurda, D. B. Jr., ed. Paleobiological aspects of growth and development. Paleont. Soc. Mem. 2 (J. Paleont.). 42(No. 5 suppl.):35–49.Google Scholar
Silén, L. 1942. On the spiral growth of the zoaria of Bryozoa. Arkiv för Zoologi. 34A, 2:1–22.Google Scholar
Stevens, P. S. 1973. Space, architecture, and biology. Syst. Zool. 22:405–408.CrossRefGoogle Scholar
Stevens, P. S. 1974. Patterns in Nature. 240 pp. Atlantic Monthly Press. Boston.Google Scholar
Thompson, D'Arcy. 1917. On Growth and Form. 793 pp. Cambridge Univ. Press.CrossRefGoogle Scholar
Vermeij, G. J. 1973. Adaptation, versatility and evolution. Syst. Zool. 22:466–477.Google Scholar

Reference

Campbell, K. S. W., Holloway, O. J., and Smith, W. D. 1974. A new receptaculitid genus Hexabactron, and the relationships of the Receptaculitaceae. Palaeontographica. 146:52–77.Google Scholar