The unified rule of phyllotaxis explaining both spiral and non-spiral arrangements.

Takuya Okabe,Atsushi Ishida,Jin Yoshimura

doi:10.1098/rsif.2018.0850

Abstract

Leaf-like appendages of different plant groups are arranged in common phyllotaxis patterns categorized into two types: spiral and non-spiral arrangements. The adaptive reason for this morphological convergence is unknown. In the non-spiral arrangement, the divergence angle between successive leaves is a simple fraction of 360°, e.g. distichy, decussate and whorled phyllotaxis. In the spiral arrangement, the divergence angle of nascent leaves at the shoot apex is fixed at the golden angle 137.5°, whereas those of the developed leaves varies within a sequence of Fibonacci fractions, such as 1/3, 2/5, 3/8, 5/13, etc. The optimality of the golden angle has been shown recently by assuming that the pattern of developed leaves varies during growth in a manner depending on the divergence angle of nascent leaves. Here we propose a unified rule of phyllotaxis to explain both types of arrangement: the developed leaves form vertical rows along the stem. In the non-spiral arrangement, nascent to developed leaves always follow this rule, so that the number of leaf rows is kept constant irrespective of stem growth. In the spiral arrangement, developed leaves attain this rule by adjusting the divergence angle from the golden angle. The spiral arrangement is adaptive in that the number of leaf rows varies during growth depending on shoot thickness.

Highlights

Leaf-like organs of most seed plants, ferns, mosses and even brown algae are arranged according to common rules, phyllotaxis [1,2,3,4]
The phyllotaxis phenomenon is a remarkable case of convergent evolution [30], the independent evolution of similar features in species of different lineages, e.g. seed plants, ferns, mosses, algae
It is important to distinguish the phyllotaxis of the shoot apex and that of the mature shoot [14]

Summary

Introduction

Leaf-like organs of most seed plants, ferns, mosses and even brown algae are arranged according to common rules, phyllotaxis [1,2,3,4]. These facts have not been regarded as of special importance so far, because the longitudinal arrangement obviously conforms to the anatomical architecture In accord with this empirical rule, this study puts forward a general view that the two major types of phyllotaxis originate from a common rule, i.e. mature organs are arranged in rows along the axis. Spiral phyllotaxis is a non-trivial case of non-zero cost, where the initiated leaves are not arranged radially so that there are multiple ways of forming rows (e.g. 2/5 and 3/8 derive from 137.58, figure 1e,g) In this case, the optimal arrangement of nascent leaves becomes uniquely non-radial, so to speak, as an average of 3 the multiple row patterns to which it leads (the average of 2/5 and 3/8 is about the same as 137.58). Higher-order patterns with more than five rows are neglected by assuming wM 1⁄4 0 for M . 5

Constant phyllotaxis

Variable phyllotaxis

Discussion