[MS12] Mathematical and Computational Perspectives of Phyllotaxis and Growth of Plants

[MS12-03] Common mathematical structures underlying developmental constraints and light capture optimization in phyllotaxis

*Takaaki Yonekura¹, Munetaka Sugiyama¹ (1. University of Tokyo (Japan))

Keywords:

phyllotaxis

Phyllotaxis is an arrangement of leaves around the stem in plants. Spiral phyllotaxis has long attracted particular interest due to its special relationship with Fibonacci sequence and the dominant occurrence of the golden angle (about 137.5°) in its divergence angle between successive leaves (such spirals are referred to as Fibonacci spiral). As a mechanism of phyllotactic pattern formation, inhibitory field models are widely accepted, which posit that a new leaf arises at the position on the periphery of the shoot apical meristem (SAM) where the effect of existing leaves to inhibit new leaf formation is lowest. Computer simulations with these models have shown that Fibonacci spiral is produced as a stable pattern across many parameter settings, yet theoretically it remains unclear why it is so robust under various conditions. Here, we developed a simplest version of the inhibitory field model in which particles representing leaves are placed at a constant divergence angle on the circle representing the SAM periphery. By theoretical analysis, we successfully demonstrated that only four divergence angles can keep the inhibitory field strength at the position of new leaf formation below a certain value for any number of existing leaves and that the best one among these angles is the golden angle. Furthermore, using a simple rosette plant model treating leaves as annulus sectors, we found that similar theoretical analysis can be applied to the problem of leaf overlapping and the resultant light capture efficiency because mathematical structures are shared by the inhibitory field mechanism and the leaf overlapping problem. That is, for the same theoretical reason, only four angles including the golden angle can keep the light capture efficiency above a certain value. Our findings have bridged two perspectives of phyllotaxis often considered separately: the developmental constraint operating via the inhibitory field mechanism and the natural selection through the optimization of leaf arrangement for light capture. Finally, we have concluded that the dominance of Fibonacci spiral is theoretically and purely attributable to the developmental constraint and does not need assuming the presence of the natural selection for light capture optimization. The advantage of Fibonacci spiral in the light capture might be a “by-product” of the common mathematical structures underlying the developmental constraint and the light capture optimization.