Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-18T23:44:41.420Z Has data issue: false hasContentIssue false
  • English
  • Français

CerioShell: a computer program designed to simulate variation in shell form

Published online by Cambridge University Press:  08 February 2016

J. R. Stone
J. R. Stone*
Affiliation:
Department of Zoology, University of Toronto, Toronto, Ontario, Canada M5S 1A1
Get access Rights & Permissions [Opens in a new window]

Abstract

I describe a mathematical model of shells that incorporates simple morphometric measurements, which can be obtained easily from sectioned specimens. The model reconstructs form (size and shape) by describing the path in space traversed by, and the changes in dimensions of, a shell aperture during accretionary growth. The model contains parameters that independently affect components of these two aspects of shell form in directions radially away from (or toward) and along a coiling axis. I also describe a computer program, CerioShell, that uses the mathematical model to graphically simulate shell forms. The program permits the viewing of images from different three-dimensional orientations, using various graphical representations, and provides dimensions of the images it generates. Together, the model and the program allow one to investigate the effects that changes in modes of growth would have on shell form.

Type
Articles
Information
Paleobiology , Volume 21 , Issue 4 , Fall 1995 , pp. 509 - 519
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.)

References

Literature Cited

Ackerly, S. C. 1989. Kinematics of accretionary shell growth, with examples from brachiopods and molluscs. Paleobiology 15:147–164.CrossRefGoogle Scholar
Cortie, M. B. 1989. Models for mollusc shape. South African Journal of Science 85:454–460.Google Scholar
Gould, S. J. 1973. The origin and function of “bizarre” structures: antler size and skull size in the “Irish Elk” Megaloceros giganteus. Evolution 28:191–220.Google Scholar
Gould, S. J. 1984. Morphological channeling by structural constraint: convergence in styles of dwarfing and gigantism in Cerion, with a description of two new fossil species and a report on the discovery of the largest Cerion. Paleobiology 10:172–194.CrossRefGoogle Scholar
Gould, S. J. 1989. A development constraint in Cerion with comments on the definition and interpretation of constraint in evolution. Evolution 43:516–539.Google Scholar
Gould, S. J. 1992. Constraint and the square snail: life at the limits of a covariance set. The normal teratology of Cerion disforme. Biological Journal of the Linnean Society 47:407–437.CrossRefGoogle Scholar
Huxley, J. S. 1932. Problems of relative growth. Dover, New York.Google Scholar
Illert, C. 1982. The mathematics of gnomonic seashells. Mathematical Bioscience 63:21–56.CrossRefGoogle Scholar
Johnston, M. R., Tobachnick, R. E., and Bookstein, F. L. 1991. Landmark-based morphometrics of spiral accretionary growth. Paleobiology 17:19–36.CrossRefGoogle Scholar
Løvtrup, S., and Løvtrup, M. 1988. The morphogenesis of molluscan shells: a mathematical account using biological parameters. Journal of Morphology 197:53–62.CrossRefGoogle ScholarPubMed
Løvtrup, S., and von Sydow, B. 1974. D'Arcy Thompson's theorems and the shape of the molluscan shell. Bulletin of Mathematical Biology 36:567–575.CrossRefGoogle Scholar
Løvtrup, S., and von Sydow, B. 1976. An addendum to “D'Arcy Thompson's theorems and the shape of the molluscan shell.” Bulletin of Mathematical Biology 38:321–322.Google Scholar
McGhee, G. R. Jr. 1980. Shell form in the biconvex articulate Brachiopoda: a geometric analysis. Paleobiology 6:57–76.CrossRefGoogle Scholar
McMahon, T. 1973. Size and shape in biology. Science 179:1201–1204.CrossRefGoogle ScholarPubMed
Morita, R. 1991. Mechanical constraints on aperture form in gastropods. Journal of Morphology 207:93–102.CrossRefGoogle ScholarPubMed
Okamoto, T. 1984. Theoretical morphology of Nipponites (a heteromorph ammonoid). Kaseki (Fossils). Palaeontological Society of Japan 36:37–51. [In Japanese]Google Scholar
Okamoto, T. 1988. Analysis of heteromorph ammonoids by differential geometry. Palaeontology 33:35–52.Google Scholar
Raup, D. M. 1961. The geometry of coiling in gastropods. Proceedings of National Academy of Science, United States of America 47:602–609.CrossRefGoogle ScholarPubMed
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
Raup, D. M., and Graus, R. R. 1972. General equations for volume and surface area of a logarithmically coiled shell. Mathematical Geology 4(4):307–316.CrossRefGoogle Scholar
Savazzi, E. 1985. Shellgen: a BASIC program for the modeling of molluscan shell ontogeny and morphogenesis. Computational Geoscience 11:521–530.CrossRefGoogle Scholar
Schindel, D. E. 1990. Unoccupied morphospace and the coiled geometry of gastropods: architectural constraint or geometric covariation? Pp. 270–304in Ross, R. M. and Allmon, W. D., eds. Causes of evolution: a paleontological perspective. University of Chicago Press.Google Scholar
Sokal, R. R., and Rohlf, F. J. 1981. Biometry. W. H. Freeman, San Francisco.Google Scholar
Stasek, C. R. 1963. Geometrical form and gnomonic growth in the Bivalved Mollusca. Journal of Morphology 112:215–232.CrossRefGoogle Scholar
Stone, J. R. 1995. Computer-simulated shell size and shape variation in the Caribbean land snail genus Cerion: a test of geometrical constraints. Evolution (in press).CrossRefGoogle Scholar
Thompson, D. W. 1961. On growth and form. Cambridge University Press, London.Google Scholar
Vermeij, G. 1980. Gastropod shell growth rate, allometry, and adult size: environmental implications. Pp. 379–394in Rhoads, D. C. and Lutz, R. A., eds. Skeletal growth of aquatic organisms. Plenum Press, New York.CrossRefGoogle Scholar
Wolfram Research, Inc. 1988. Mathematica: a system for doing mathematics by computer. Wolfram Research Inc., Champaign, Ill.Google Scholar