The significance of γ-and λ-dislocations in transient states of phyllotaxis: how to get more from less – sometimes!

In some plants, developmental changes of phyllotaxis are so frequent that the whole spectrum of phyllotactic patterns becomes available for investigation and thus many unknown subtleties of phyllotaxis come to light. Among these, Magnolia acuminata is the most prominent. In a series of experiments performed in silico with application of a simple geometric model of phyllotaxis, we were able to confront the empirical data on phyllotactic transitions occurring in magnolia flowers with the results of computer simulations. They revealed that in addition to the ratio between the sizes of plant organs, the history of developing pattern was also important, especially for the direction of ontogenetic changes. The parameters of size tolerance and vertical tolerance in positioning a new element in the first available space, brought the effects of simulations closer to the real patterns. They helped especially to resolve the enigma of multiplication of parastichies (γ-dislocations) observed sometimes during determined growth of magnolia floral axes. We conclude that ontogenetic changes in phyllotaxis result mainly from changing sizes of organs in the course of development and that the changes do not always occur with mathematical accuracy