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Pattern Formation on the Shells of Molluscs by Travelling Waves With Unusual Properties

  • Hans Meinhardt
  • Martin Klingler
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Part of the NATO ASI Series book series (NSSB, volume 244)

Abstract

The shells of many molluscs are decorated with either a relief-like or a pigmentation pattern. These patterns are of great diversity and frequently of great beauty. The formation of these patterns proceeds in most species in a strictly linear manner since new pattern elements are added only along a marginal zone, the growing edge of the shell. The second dimension is a protocol of what happens as a function of time. The shell is, so to speak, a space-time plot. The shells provide a unique situation in that the complete history of a very dynamical process is preserved. We have proposed a model for shell patterning based on reaction-diffusion mechanisms. As shown by computer simulations, this model can account for apparently very different shell patterns if small variations of the parameters or minor changes in the underlying mechanism are assumed [5, 8]. Details of computations can be found in [7]. A model based on similar principles but underlining the possible role of the nervous system has been proposed by Ermentrout et al. [1].

Keywords

Pattern Formation Pigment Production Pattern Element Periodic Pattern Oblique Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Ermentrout, B., Campbell, J. & Oster, G. (1986). A model for shell patterns based on neural activity. The Veliger 28, 369–338.Google Scholar
  2. [2]
    Gierer, A. & Meinhardt, H. (1972). A theory of biological pattern formation. Kybernetik 12, 30–39.CrossRefGoogle Scholar
  3. [3]
    Lefever, R. (1968). Dissipative structures in chemical systems. J.Chem.Phys. 49, 4977–4978.ADSCrossRefGoogle Scholar
  4. [4]
    Meinhardt, H. (1982). Models of biological pattern formation. Academic Press: London.Google Scholar
  5. [5]
    Meinhardt, H. (1984). Models for positional signalling, the threefold subdivision of segments and the pigmentation pattern of molluscs. J. Embryol. exp. Morph. 83 (Supplement)’, 289–311.Google Scholar
  6. [6]
    Meinhardt, H. & Gierer, A. (1974). Applications of a theory of biological pattern formation based on lateral inhibition. J. Cell Sci. 15, 321–346.Google Scholar
  7. [7]
    Meinhardt, H. & Klingler, M. (1986). Pattern formation by coupled oscillations: the pigmentation pattern on shells of molluscs. Lecture Notes in Biomath. 71, 184–198.CrossRefMathSciNetGoogle Scholar
  8. [8]
    Meinhardt, H. & Klingler, M. (1987). A model for pattern formation on the shells of molluscs. J. Theor. Biol. 126, 63–69.CrossRefMathSciNetGoogle Scholar
  9. [9]
    Neumann, D. (1958). Morphologische und experimentelle Untersuchungen über die Variabilität der Farbmuster auf der Schale von Theodoxus fluviatilis L. Z. Morph. Ökol. Tiere 48, 349–411.CrossRefGoogle Scholar
  10. [10]
    Prigogine, I. and Lefever, R. (1948). Symmetry breaking instabilities in dissipative systems. II. J. chem. Phys. 48, 1695–1700.ADSCrossRefGoogle Scholar
  11. [11]
    Seilacher, A. (1972). Divaricate patterns in pelecypod shells. Lethaia 5, 325–343.CrossRefGoogle Scholar
  12. [12]
    Seilacher, A. (1973). Fabricational noise in adaptive morphology. Systematic Zool. 22, 451–465.CrossRefGoogle Scholar
  13. [13]
    Turing, A. (1952). The chemical basis of morphogenesis. Phil. Trans. B. 237, 37–72.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Hans Meinhardt
    • 1
  • Martin Klingler
    • 1
  1. 1.Max-Planck-Insitut für EntwicklungsbiologieTübingenGermany

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