Abstract
While self-organization has been studied for some time and is now a familiar concept in science, there is as yet no general theory nor even a generally accepted definition. Much of what has been done has been within the context of dissipative structures, so much so that for many people the two ideas have become totally conflated. But the concept of self-organization is much broader; it encompasses systems described by catastrophe theory, for example. Here we draw on the experience of catastrophe theory to suggest features that a theory of self-organization should have, and we illustrate this by the problem of segmentation. We point out that self-organization provides an alternative to natural selection as an explanation of order and organization in biological systems.
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References
Arcuri, P. & Murray, J.D. (1986). Pattern sensitivity to boundary and initial conditions in reaction-diffusion models. J. math. Biol. 24, 141–165.
Bazin, M.J. & Saunders, P.T. (1979). Determination of critical variables in a microbial predator prey system by catastrophe theory. Nature 275 (1978) 52–54.
Berry, M.V. & Upstill, C. (1980). Catastrophe optics: morphologies of caustics and their diffraction patterns. In Progress in Optics 18 (E. Wolfe, ed.). North Holland, Amsterdam, pp. 256–346.
Gierer, A. & Meinhardt, H. (1972). A theory of biological pattern formation. Kybernetik 12, 30–39.
Ho, M.W. (1984). Heredity and environment in development and evolution. In Beyond Neo-Darwinism: An Introduction to the New Evolutionary Paradigm (M.W. Ho & P.T. Saunders, eds). Academic Press, London, pp. 267–288.
Ho, M.W. (1990). An exercise in rational taxonomy. J. theor. Biol. 141, 43–57.
Hunding, A., Kauffman, S.A. and Goodwin, B.C. (1990). Drosophila segmentation: Supercomputer simulation of prepattern hierarchy. J. theor. Biol. 145, 369–384.
Lacalli, T.C. (1981). Dissipative structures and morphogenetic pattern in unicelluar algae. Phil. Trans. R. Soc. Lond. B294, 547–588.
Lacalli, T.C., Wilkinson, D.A. and Harrison, L.G. (1988). Development 104, 105–113.
Le Guyader, H. & Hyver, C. (1990). Modelling of the duplication of cortical units along a kinety of Paramecium using reaction-diffusion equations. J. theor. Biol. 143, 233–250.
Lovelock, J.E. (1979). Gaia: A New Look at Life on Earth. Oxford, Oxford University Press.
Lovelock, J.E. (1988). The Ages of Gaia. Oxford, Oxford University Press.
Maynard Smith, J. (1988). Evolutionary progress and levels of selection. In Evolutionary Progress (M.H. Nitecki, ed.) Chicago, University of Chicago Press, pp. 219–230
Meinhardt, H. (1982). Models of Biological Pattern Formation. London, Academic Press.
Meinhardt, H. (1988). Models for maternally supplied positional information and the activation of segmentation genes in Drosophila embryogenesis. Development 104 (Suppl) 95-110.
Murray, J.D. (1981). A pre-pattern mechanism for animal coat markings. J. theor. Biol. 88, 161–199.
Murray, J.D. (1989). Mathematical Biology, Springer-Verlag, Berlin.
Oster, G.F., Murray, J.D. and Harris, A.K. (1983). J. Embryol. exp. Morph. 18, 83.
Pan, P. and Wurster, B. (1979). Inactivation of the chemoattractant folic acid by cellular slime molds and identification of the reaction product. J. Bacteriol. 136, 955–959.
Sander, K. (1984). Embryonic pattern formation in insects: basic concepts and their experimental foundations. In Pattern Formation (G. Malacinski and S. Bryant, eds.), Macmillan, New York.
Saunders, P.T. (1980). An Introduction to Catastrophe Theory. Cambridge University Press, Cambridge.
Saunders, P.T. (1989). Mathematics, Structuralism and the Formal Cause in Biology. In Dynamic Structures in Biology (B.C. Goodwin, G.C. Webster & A. Sibatani, eds). Edinburgh University Press, Edinburgh, pp 107–120.
Saunders, P.T. (1993a). The Organism as a Dynamical System. In Thinking about Biology SFI Studies in the Sciences of Complexity, Lecture Notes Vol. III (F. Varela & W. Stein, eds). Addison Wesley, New York.
Saunders, P.T. (1993b). Evolution without natural selection: Further implications of the Daisy world parable. J. theor. Biol. (in press).
Saunders, P.T. and Ho, M.W. (1985). Primary and Secondary Waves in Prepattern Formation. J. Theor. Biol., 114 (1985) 491–504.
Saunders, P.T. and Ho, M.W. (1992). Successive bifurcations and the stability of segmentation. (to be submitted)
Smale, S. (1966). Structurally stable systems are not dense. Amer. J. Math. 88, 491–496.
Thorn, R. (1972). Stabilité Structurelle et Morphogénèse. Benjamin, Reading.
Thompson, D’A.W. (1917). On Growth and Form. Cambridge University Press, Cambridge.
Turing, A.M. (1952). The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B237, 37–72.
Watson, A.J. & Lovelock, J.E. (1983). Biological homeostasis of the global environment: the parable of Daisy world. Tellus (1983), 35B, 284–289.
Xu, Y., Vest, C. & Murray, J.D. (1983). Holographic interferometry used to demonstrate a theory of pattern formation in animal coats. Appl. Optics 22, 3479–3483.
Zeeman, E.C. (1974). Primary and secondary waves in developmental biology. In Some Mathematical Questions in Biology VIII: Lectures in Mathematics in the Life Sciences, Vol. 7, (S.A. Levin, ed.). Providence, American Mathematical Society, pp. 69–161.
Zeeman, E.C. (1978). A dialogue between a mathematician and a biologist. Biosci. Commun. 4, 225–240.
Zeeman, E.C. (1989). A new concept of stability. In Theoretical Biology: Epigenetic and Evolutionary Order from Complex Systems (B.C. Goodwin & P.T. Saunders, eds) Edinburgh, Edinburgh University Press, pp. 8–15.
Zuckerkandl, E. & Villet, R. (1988). Concentration affinity equivalence in gene regulation: Convergence of genetic and environmental effects. Proc. Natl. Acad. Sci. USA 85, 4784–4788.
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Saunders, P.T., Ho, M.W. (1994). Self-Organization, Catastrophe Theory and the Problem of Segmentation. In: Mishra, R.K., Maaß, D., Zwierlein, E. (eds) On Self-Organization. Springer Series in Synergetics, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45726-5_10
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DOI: https://doi.org/10.1007/978-3-642-45726-5_10
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