Walch, J.-P. | bioRxiv Science

bioRxiv2023

Phyllotaxis as a dynamical system

One of the major puzzles in phyllotaxis is the much higher frequency of Fibonacci spirals compared to other spiral arrangements such as Lucas spirals. We show that spirals are a form of symmetry, in the same way that axial symmetry is a form of symmetry, which explains why they can be the consequence of many different microscopic phenomena. We apply dynamical systems theory to the main types of phyllotaxis. We show that only Fibonacci spirals should exist and that the other spiral modes (including Lucas) are the consequence of developmental errors, such as the dislocation of a pseudo-orthostichy.

developmental biology↗

bioRxiv2021

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.

developmental biology↗