Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-06-05T10:15:43.443Z Has data issue: false hasContentIssue false
  • English
  • Français

Suture and location of the coiling axis in gastropod shells

Published online by Cambridge University Press:  08 February 2016

Christian Van Osselaer  and
Philippe Grosjean
Christian Van Osselaer
Affiliation:
Laboratory of Bio-Ecology, Université Libre de Bruxelles, 50 avenue F. Roosevelt C.P. 160/14, B-1050 Brussels, Belgium. E-mail: cvanosse@ulb.ac.be
Philippe Grosjean
Affiliation:
Marine Biology Laboratory, Université Libre de Bruxelles, 50 avenue F. Roosevelt C.P. 160/15, B-1050 Brussels, Belgium. E-mail: phgrosje@ulb.ac.be
Get access Rights & Permissions [Opens in a new window]

Abstract

The general allometric equations for the logarithmic helicospiral can fit many extraconical shapes, but the isometric conditions traditionally used limit study only to conical growth. We present evidence to show that in real gastropod shells, the logarithmic helicospiral equations fit the suture. Poor location of the coiling axis and / or an inappropriate pole for the logarithmic helicospiral has often led to the rejection of this model. The differences between the errors associated with measurement or previously available models are discussed. Two methods, based on suture trace measurements, are proposed to locate the coiling axis both in apical and lateral views. The first is a graphical method based on an elementary property of the logarithmic spiral. The second is a computational method based on iterative reprojections of the suture. It is shown that the protoconch and the teleoconch must be treated separately. The precision of the new methods (especially the computing method) enables deviations from logarithmic helicospiral trajectory to be identified and differentiated from irregularities of the shell and sequential growth phases. Application of these methods may be useful not only for other gastropod morphological features, but also for other taxa such as brachiopods and other mollusks.

Type
Articles
Information
Paleobiology , Volume 26 , Issue 2 , Spring 2000 , pp. 238 - 257
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. 1989a. Shell coiling in gastropods: analysis by stereographic projection. Palaios 4:374–378.CrossRefGoogle Scholar
Ackerly, S. C. 1989b. Kinematics of accretionary shell growth, with examples from brachiopods and molluscs. Paleobiology 15:147–164.CrossRefGoogle Scholar
Aldridge, A. E. 1998. Brachiopod outline and the importance of the logarithmic spiral. Paleobiology 24:215–226.CrossRefGoogle Scholar
Bookstein, F. L. 1982. Foundations of morphometrics. Annual Review of Ecology and Systematics 13:451–470.CrossRefGoogle Scholar
Bookstein, F. L. 1993. A brief history of the morphometric synthesis. Pp. 14–40in Marcus, L. F., Bello, E., and Garcia-Valdecasas, A., eds. Contributions to morphometrics. Monografías Museo Nacional de Ciencias Naturales, Madrid.Google Scholar
Bouchet, P. 1987. La protoconque des gastéropodes: aspects biologiques, taxonomiques et évolutifs. Thèse de Doctorat d'Etat. Université Pierre et Marie Curie, Paris.Google Scholar
Boulding, E. G., and Hay, T. K. 1993. Quantitative genetics of shell form of an intertidal snail: constraints on short-term response to selection. Evolution 47:576–592.CrossRefGoogle ScholarPubMed
Chiba, S. 1993. Modern and historical evidence for natural hybridization between sympatric species in Mandarina (Pulmonata: Camaenidae). Evolution 47:1539–1556.CrossRefGoogle ScholarPubMed
Coppois, G., and Glowacki, C. 1982. Bulimulid land snails from the Galapagos. 1. Factor analysis of Santa Cruz Island species. Malacologia 23:209–219.Google Scholar
Cortie, M. B. 1989. Models for mollusc shell shape. South African Journal of Science 85:454–460.Google Scholar
Cox, L. R. 1955. Observations on gastropod descriptive terminology. Proceedings of the Malacological Society of London 31:190–202.Google Scholar
D'Arcy Thompson, W. 1961. On growth and form, 4th ed.Cambridge University Press, Cambridge.Google Scholar
Dawkins, R. 1996. Climbing mount improbable. Penguin, London.Google Scholar
Ekaratne, S.U.K., and Crisp, D. J. 1983. A geometrical analysis of growth in gastropod shells, with particular reference to turbinate forms. Journal of the Marine Biological Association of the United Kingdom 63:777–797.CrossRefGoogle Scholar
Futuyma, D. J. 1986. Evolutionary biology, 2d ed.Sinauer, Sunderland, Mass.Google ScholarPubMed
Galler, L., and Gould, S. J. 1979. The morphology of a “hydrid zone” in Cerion variation, clines and an ontogenic relationship between two “species” in Cuba. Evolution 33:714–727.Google Scholar
Goodfriend, G. A. 1983. Some new methods for morphometric analysis of gastropod shells. Malacological Review 16:79–86.Google Scholar
Gould, S. J. 1966. Allometry and size in ontogeny and phylogeny. Biological Reviews 41:587–640.CrossRefGoogle ScholarPubMed
Goodfriend, G. A. 1989. A developmental constraint in Cerion with comments on the definition and interpretation of constraint in evolution. Evolution 43:516–539.Google Scholar
Goodfriend, G. A. 1992. Constraint and the square snail: life at the limit of a covariance set. The normal teratology of Cerion disform. Biological Journal of the Linnean Society 47:407–437.Google Scholar
Grahame, J., and Mill, P. J. 1989. Shell shape variation in Littorina saxatilis and L. arcana: a case of character displacement?. Journal of the Marine Biological Association of the United Kingdom 69:837–855.CrossRefGoogle Scholar
Harasewych, M. G. 1981. Mathematical modeling of the shells of higher prosobranchs. Bulletin of the American Malacological Union 1981:6–10.Google Scholar
Heath, D. J. 1985. Whorl overlap and the economical construction of the gastropod shell. Biological Journal of the Linnean Society 24:165–174.CrossRefGoogle Scholar
Huxley, J. S., and Teissier, G. 1936. Terminologie et notation dans la description de la croissance relative. Comptes Rendus des Séances de la Société de Biologie et ses filiales 121:934–936.Google Scholar
Illert, C. 1989. Formulation and solution of the classical seashell problem. II. Tubular three-dimensional seashell surfaces. II Nuevo Cimento 11:761–780.CrossRefGoogle Scholar
Janson, K., and Sundberg, P. 1983. Multivariate morphometric analysis of two varieties of Littorina saxatilis from the Swedish west coast. Marine Biology 74:49–53.CrossRefGoogle Scholar
Johannesson, B., and Johannesson, K. 1990. Littorina neglecta Bean, a morphological form within the variable species Littorina saxatilis (Olivi)? Hydrobiologia 193:71–87.CrossRefGoogle Scholar
Johnston, M. R., Tobachnick, R. E., and Bookstein, F. L. 1991. Landmark-based morphometric of spiral accretionary growth. Paleobiology 17:19–36.CrossRefGoogle Scholar
Kohn, A. J., and Riggs, A. C. 1975. Morphometry of the Conus shell. Systematic Zoology 24:346–359.CrossRefGoogle Scholar
Kristensen, T. K., and Christensen, A. G. 1989. Bulinus africanus-group species in West Africa differentiated by morphometric analysis (Gastropoda, Planorbidae). Journal of Molluscan Studies 55:103–110.CrossRefGoogle Scholar
Lawrence, E. 1995. Henderson's dictionary of biological terms, 11th ed. Longman, Harlow, England.Google Scholar
Lison, L. 1949. Recherches sur la forme et la mécanique de développement des coquilles des Lamellibranches. Mémoires de l'Institut Royal des Sciences Naturelles de Belgique 2:3–87.Google 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
Mayr, E., and Aschlock, P. D. 1991. Principles of systematic zoology, 2d ed.McGraw-Hill, Singapore.Google Scholar
McGhee, G. R. Jr. 1978. Analysis of shell torsion phenomenon in the Bivalvia. Lethaia 11:315–329.CrossRefGoogle Scholar
McGhee, G. R. Jr. 1980. Shell form in the biconvex articulate Brachiopoda: a geometric analysis. Paleobiology 6:57–76.CrossRefGoogle Scholar
McGhee, G. R. Jr. 1991. Theoretical morphology: the concept and its applications. Analytical Paleobiology 4:87–102.Google Scholar
Murray, T. 1982. Morphological characterization of the Littorina scutulata species complex. Veliger 24:233–238.Google Scholar
Nemeschkal, H. L. 1990. Uber die form der Schneckenschale: Morphometrische Grundlagen und Vorbereitungen für ein statistisches Taxonmodell. Zoologische Jahrbüch für Systematik 117:491–534.Google Scholar
Nemeschkal, H. L., and Kothbauer, H. 1989. Zur Spirale der Schneckenschale: Eine Varianz-Kovarianzuntersuchung bei Arianta (Gastropoda, Helicidae). Zoologische Jahrbüch für Systematik 116:391–409.Google Scholar
Okamoto, T. 1988. Analysis of heteromorph ammonoids by differential geometry. Paleontology 33:35–52.Google Scholar
Prusinkiewicz, P., and Fowler, D. R. 1995. Shells models in three dimensions. Pp. 163–181in Meinhart, H., ed. The algorithmic beauty of sea shells. Springer, Berlin.CrossRefGoogle Scholar
Raup, D. M. 1961. The geometry of coiling in gastropods. Proceedings of the National Academy of Sciences USA 47:602–609.CrossRefGoogle ScholarPubMed
Raup, D. M. 1962. Computer as aid in describing form in gastropods shells. Science 138:150–152.CrossRefGoogle ScholarPubMed
Raup, D. M. 1966. Geometric analysis of shell coiling: general problems. Journal of Paleontology 40:1178–1190.Google Scholar
Raup, D. M., and Michelson, A. 1965. Theoretical morphology of the coiled shell. Science 147:1294–1295.CrossRefGoogle ScholarPubMed
Robertson, R. 1974. Marine prosobranch gastropods: larval studies and systematics. Thalassia Yugoslavia 10:213–238.Google Scholar
Rohlf, F. J. 1990. Morphometrics. Annual Review of Ecology and Systematics 21:299–316.CrossRefGoogle Scholar
Savazzi, E. 1990. Biological aspects of theoretical shell morphology. Lethaia 23:195–212.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, Chicago.Google Scholar
Sedgewick, R. 1988. Algorithms, 2d ed.Addison Wesley, Reading, Mass.Google Scholar
Sen, A., and Srivastava, M. 1990. Regression analysis. Theory methods and applications. Springer, New York.Google Scholar
Sheldon, P. 1993. The evolution of form. Pp. 668–742in Skelton, P., ed. Evolution: a biological and paleontological approach. Open University Press, Wokingham, England.Google Scholar
Skelton, P. 1993. The fossil record of evolution in species. Pp. 445–508in Skelton, P., ed. Evolution: a biological and paleontological approach. Open University Press, Wokingham, England.Google Scholar
Stepczak, K. 1988. Correlation between measurable features of Helix pomatia L. (Gastropoda), useful in the investigation of the snail. Bulletin de la Société des Amis des Sciences et des Lettres de Poznan 26:115–124.Google Scholar
Stone, J. R. 1995. Cerioshell: a computer program designed to simulate variation in shell form. Paleobiology 21:509–519.CrossRefGoogle Scholar
Stone, J. R. 1996a. Computer-simulated shell size and shape variation in the Caribbean land snail genus Cerion: a test of geometrical constraints. Evolution 50:341–347.Google ScholarPubMed
Stone, J. R. 1996b. The evolution of ideas: a phylogeny of shell models. American Naturalist 148:904–929.CrossRefGoogle Scholar
Stone, J. R. 1997. Using shell parameters as complementary data in phylogenetic systematic analyses: evolution of form in five species of littorinids (Mollusca: Gastropoda). Veliger 40:12–22.Google Scholar
Tursch, B. 1997. Spiral growth: “The Museum of All Shells” revisited. Journal of Molluscan Studies 63:581–588.CrossRefGoogle Scholar
Tursch, B. 1998. A simple shell model: applications and implications. Apex 13:161–176.Google Scholar
Van Osselaer, C., and Tursch, B. 1994. Studies on Olividae. XIX. Where is the suture of Oliva shells? Apex 9:47–50.Google Scholar
Verduin, A. 1982. How complete are diagnoses of coiled shells of regular build? A mathematical approach. Basteria 45:127–142.Google Scholar
Vermeij, G. J. 1971. Gastropod evolution and morphological diversity in relation to shell geometry. Journal of Zoology 163:15–23.CrossRefGoogle Scholar
Vermeij, G. J. 1993. A natural history of shells. Princeton University Press, Princeton, N.J.Google Scholar
Wagner, P. J. 1996. Morphologic diversification of early Paleozoic “archaeogastropods.“ Pp. 161–169in Taylor, J. D., ed. Origin and evolutionary radiation of the Mollusca. Oxford University Press, Oxford.Google Scholar