Phyllotaxis Models: from the Inhibition Potential to the Real Plant

Previous phyllotaxis models allowed the initiation of new primordia when a threshold of inhibition potential is reached on the meristem front: their adequacy to botanical reality is only qualitative. We formulated the hypothesis that it is not the value of the inhibition threshold that remains constant as the meristem develops, but the difference of the inhibition thresholds during the initiation of two successive primordia. We were thus able to model with accuracy the sequence of plastochron ratios observed by Williams (1975) on the leaf meristem of flax: an outstanding result. More generally, we have shown that the evolution trajectories of the phyllotaxis modes as a function of the plastochron ratios follow the minima of the potential under decreasing plastochron ratios constraint and bifurcate when the number of these minima increases, thus giving physicochemical foundations to the famous van Iterson diagram. This historical representation of rising phyllotaxis shows the trajectories, but doesnt give the velocity of the movement: our plastochron ratio sequence adds this major dynamical information.