Initial transitions, order and disorder in phyllotactic patterns: the ontogeny of Helianthus annuus: a case study

The variability of the phyllotactic organization of Helianthus annuus L. is investigated. Specimens exhibiting the various possible phyllotactic modes (Fibonacci spirals, Lucas spirals, bijugate spirals etc...) were selected. The transitions from the initial decussate growth to these organizations, were characterized and shown to correspond to only a few archetypes. The possible transients from a decussate mode were then investigated in the model of self organization introduced by Douady and Couder (1996a, b, c). They are shown to exhibit the same phenomenology as the observed ones. These various transients have a very different probability of ccurrence which explains the difference of their frequency in plants. Finally the imperfections of the observed dispositions, which affect mainly the plastochron, are also investigated. The model provides an interpretation of this apparent disorder: after a transition the system optimizes the regularity of the parastichies but in doing so it disturbs the plastochron and the divergence. It is only when very large external disturbances affect the system that a real disorder is generated. In these latter cases the parastichies themselves disappear