Abstract
Phyllotaxis studies published in German in the 1930s have reported intriguing regularity in the arrangement of incipient leaves on shoot apices of a wide variety of plant species. However, these studies have received little attention today, even though they provide a crucial evidence base for understanding this mathematical phenomena. Here I recapitulate the essential point by means of illustrative examples. It is emphasized that accurate control of apical divergence angle is at the heart of the numerical riddle of spiral phyllotaxis. The accurate patterning at the shoot apex has an unexpected evolutionary benefit of being optimally adaptive in the subsequent events of phyllotactic change to occur on an elongating shoot.
Highlights
Fibonacci numbers 1, 2, 3, 5, 8, 13, 21, 34, etc., manifested in the disposition of various organs of higher plants have been a long-standing source of wonder
A curved spiral connecting contiguous organs is called a contact parastichy. This observation attracts people’s attention first and foremost, the aim of this paper is to show that the occurrence of Fibonacci numbers in contact parastichies is nothing but the tip of the iceberg of the truly intriguing phenomena of phyllotaxis
The phyllotaxis literature in the nineteenth century has expressed the arrangement of adult leaves on a stem by means of a Schimper–Braun fraction like 1/2, 1/3, 2/5, 3/8, 5/13, 8/21, etc., which signifies the angle of divergence between consecutive leaves expressed in terms of a fraction of a full turn
Summary
Fibonacci numbers 1, 2, 3, 5, 8, 13, 21, 34, etc., manifested in the disposition of various organs of higher plants have been a long-standing source of wonder. By the 1930s, it was recognized and established gradually and presumably independently that, instead of Schimper–Braun fractions, divergence angles of leaf primordia are fixed at a constant value intriguingly close to the mathematical limit of the above sequence, that is, 137.508° (Fig. 1) [1,2,3,4]. The most comprehensive monograph of 386 pages with 898 references by Jean [5] makes no reference to this series of studies [6,7,8,9,10,11] In view of this situation, I come to realize that most researchers are unaware that theoretical models including modern variants have
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