Hostname: page-component-6bb9c88b65-6scc2 Total loading time: 0 Render date: 2025-07-26T13:18:05.861Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinematics of accretionary shell growth, with examples from brachiopods and molluscs

Published online by Cambridge University Press:  08 April 2016

Spafford C. Ackerly
Spafford C. Ackerly*
Affiliation:
Department of Geological Sciences, Cornell University, Ithaca, New York 14853
Get access Rights & Permissions [Opens in a new window]

Abstract

A moving reference frame is introduced for the analysis of accretionary shell growth. Simple principles of motion and stepwise growth define the model. At each growth step, the aperture migrates from its present position to a new position, according to locally defined rules. The aperture becomes the focus of the analysis, mathematically and conceptually, in conformity with biological reality. Kinematic principles provide the analytical framework for describing the aperture's trajectory (kinematics is the study of motion). The aperture “translates,” “rotates,” and “dilates.” The model offers exceptional flexibility in the analysis of accretionary growth forms and is particularly well-suited to analysis of conical and loosely coiled shell geometries. Computer simulations illustrate the principles of a moving reference model. The inverse problem of finding the aperture motions from actual shell data is rigorously specified, for both planispiralled and helicospiralled shell forms.

Information

Type
Articles
Information
Paleobiology , Volume 15 , Issue 2 , Spring 1989 , pp. 147 - 164
Copyright
Copyright © The Paleontological Society 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Literature Cited

Ackerly, S. C. 1987. Using “local” coordinates to analyze shell form in molluscs (abstract). Geological Society of America abstracts with Programs 19:566.Google Scholar
Ackerly, S. C.In press. Shell coiling in gastropods: analysis by stereographic projection. Palaios.Google Scholar
Bayer, U. 1977. Cephalopoden-Septen. Teil 2: Regelmechanismen im Gehäuse- und Septenbau der Ammoniten. Neues Jahrbuch für Geologie und Paläontologie, Abhandlungen 155:162–215.Google Scholar
Bayer, U. 1978. Morphogenetic programs, instabilities, and evolution—a theoretical study. Neues Jahrbuch für Geologie und Paläontologie, Abhandlungen 156:226–261.Google Scholar
Bayer, U. 1979. II. Projektbereich D “Konstruktions-Morphologie,” A. Structure and morphogenesis. Neues Jahrbuch für Geologie und Paläontologie, Abhandlungen 157:57–69.Google Scholar
Bookstein, F. L., Chernoff, B., Elder, R. L., Humphries, J. M. Jr., Smith, G. R., and Strauss, R. E. 1985. Morphometrics in evolutionary biology: the geometry of size and shape change with examples from fishes. Academy of Natural Sciences of Philadelphia, Special Publication 15.Google Scholar
Carter, R. M. 1967. On Lison's model of bivalve shell form, and its biological interpretation. Proceedings of the Malacological Society, London 37:265–278.Google Scholar
Condon, E. U. 1958. Kinematics. In Condon, E. U., and Odishaw, H. (eds.), Handbook of Physics. McGraw-Hill; New York.Google Scholar
Ekaratne, S. U. K., and Crisp, D. J. 1983. A geometric analysis of growth in gastropod shells, with particular reference to turbinate forms. Journal of the Marine Biological Association of the UK 63:777–797.Google Scholar
Hall, J. 1867. Devonian Brachiopods. Paleontology of New York 4.Google Scholar
Hayami, I., and Matsukuma, A. 1970. Variation of bivariate characters from the standpoint of allometry. Palaeontology 13:588–605.Google Scholar
Kohn, A. J., and Riggs, A. C. 1975. Morphometry of the Conus shell. Systematic Zoology 24:346–359.CrossRefGoogle Scholar
Illert, C. 1982. The mathematics of gnomonic seashells. Mathematical Biosciences 63:21–56.CrossRefGoogle Scholar
Illert, C. 1987. Formulation and solution of the classical sea-shell problem. II Nuovo Cimento 9:791–814.Google Scholar
Linsley, R. M., and Javidpour, M. 1980. Episodic growth in Gastropoda. Malacologia 20:153–160.Google Scholar
Lison, L. 1942. Charactéristiques géometriques naturelles des coquilles de Lamellibranches. Bulletin de l'Académie Royale, Classe des Sciences 28:377–390.Google Scholar
Lison, L. 1949. Récherches sur la forme et la mécanique de développement des coquilles des Lamellibranches. Mémoires de l'Institut royale des Sciences naturelles Belgique, 2e série 34:3–87.Google Scholar
McGhee, G. R. 1978. Analysis of the shell torsion phenomenon in the Bivalvia. Lethaia 11:315–329.Google Scholar
McGhee, G. R. 1980. Shell form in the biconvex articulate Brachiopoda: a geometric analysis. Paleobiology 6:57–76.Google Scholar
Moseley, H. 1838. On the geometrical forms of turbinated and discoid shells. Philosophical Transactions of the Royal Society of London 128:351–370.Google Scholar
Okamoto, T. 1984. Theoretical morphology of Nipponites (a heteromorph ammonoid) (in Japanese). Kaseki 36:37–51.Google Scholar
Okamoto, T. 1988. Analysis of heteromorph ammonoids by differential geometry. Palaeontology 31:35–52.Google Scholar
Raup, D. M. 1966. Geometric analysis of shell coiling: general problems. Journal of Paleontology 40:1178–1190.Google Scholar
Raup, D. M. 1967. Geometric analysis of shell coiling: coiling in ammonoids. Journal of Paleontology 41:43–65.Google Scholar
Savazzi, E. 1985. SHELLGEN: a BASIC program for the modeling of molluscan shell ontogeny and morphogenesis. Computers and Geosciences 11:521–530.Google Scholar
Savazzi, E. 1987. Geometric and functional constrains on bivalve shell morphology. Lethaia 20:293–306.Google Scholar
Schindel, D. E.In press. Architectural constraint on the coiled geometry of gastropod molluscs. In Ross, R. M., and Allmon, W. D. (eds.), Biotic and Abiotic Factors in Evolution: A Paleontological Perspective. University of Chicago Press; Chicago.Google Scholar
Vermeij, G. J. 1987. Evolution and Escalation: An Ecological History of Life. Princeton University Press; Princeton.Google Scholar
Whitworth, W. A. 1862. The equiangular spiral, its chief properties proved geometrically. Messenger of Mathematics 1:5–13.Google Scholar