Towards a more universal model of phyllotaxis

AbstractAfter a decade of mathematical explanatory modelling of the phenomenon of the spiral patterns seen on plants, that is phyllotaxis, the aim of this symposium is to give further impulses towards a complete solution of the problem. Future developments will come from a better integration of the various aspects of the problem — cellular, epidermic, vascular, anatomical, physiological, mathematical — from a massive introduction of the ideas related to differential growth and allometry, and from the study of aberrant cases by which more or less valid hypotheses can be rejected. For example spiromonostichy is a genuine puzzle: it invalidates Hofmeister's rule on which all the mechanistic theories and models of phyllotaxis are based. This report stresses the importance of higher levels of universality by which the ideas and concepts of the actual theories and models will be generalized, in order to show the limits of their validity, to give more inclusive results, and more logical solutions. This author thinks that a more complete theory of phyllotaxis will be worked out by an interpretative approach by which the phenomenon of phyllotaxis will be interpreted in terms of its ultimate effect. He has made some progress in that direction by assuming that 1) the ultimate effect is the minimization of the entropy of the plants, 2) the primordia form a hierarchical or multilevel system, and 3) the phenomenon of phyllotaxis is first of all an evolutionary problem. It will be shown that the model he developed produces some of the expected generalizations