What has the potential to tie these disparate approaches together is the widespread recognition that phyllotaxis displays some truly remarkable and quite seductive mathematical properties. By contrast, those favouring empirical approaches, including comparative morphologists and molecular geneticists such as Hofmeister, Kaplan, Meyerowitz and Kuhlemeier, have studied phyllotactic patterns in a range of different plants or genetic variants in the hope that this comparative approach might reveal fundamental principles or underlying mechanisms. Those scientists interested in theoretical approaches, including idealistic morphologists and theoretical biophysicists such as Goethe, Braun, Thompson and Green, have attempted to construct an appealing synthetic theory for explaining phyllotactic patterning, and then search for compelling botanical examples to support that theory. lateral determinate organs) on shoot axes, has perhaps attracted wider attention than most other botanical subjects in part because it appeals to the proponents and practitioners of both traditions. Phyllotaxis, which is broadly defined as the arrangement of leaf homologues (i.e. Western philosophy has two major complementary intellectual traditions: (1) Platonic idealism, in which an overarching theory is used to integrate existing observations and to predict new observations, and (2) Aristotelian empiricism, in which individual observations are used to construct a unifying theory. Instead, the consensus starting to emerge from different subdisciplines in the phyllotaxis literature supports the alternative perspective that phyllotactic patterns arise from local inhibitory interactions among the existing primordia already positioned at the shoot apex, as opposed to the imposition of a global imperative of optimal packing.Īuxin, golden ratio, number sequence, optimal packing, spiral phyllotaxis, whorled phyllotaxis INTRODUCTION Nonetheless, a simple modelling exercise argues that the most common spiral phyllotaxes do not exhibit optimal packing. Insofar as developmental transitions in spiral phyllotaxis follow discernible Fibonacci formulae, phyllotactic spirals are therefore interpreted as being arranged in genuine Fibonacci patterns. The evidence presented here shows that phyllotactic whorls of leaf homologues are not positioned in Fibonacci patterns. This paper reviews the fundamental properties of number sequences, and discusses the under-appreciated limitations of the Fibonacci sequence for describing phyllotactic patterns. It is frequently alleged that leaf primordia adopt Fibonacci-related patterns in response to a universal geometrical imperative for optimal packing that is supposedly inherent in most animate and inanimate structures. the arrangements of leaf homologues such as foliage leaves and floral organs on shoot axes) and the intriguing Fibonacci number sequence (1, 2, 3, 5, 8, 13 …). A favourite botanical example is the apparent relationship between phyllotaxis (i.e. Complex biological patterns are often governed by simple mathematical rules.
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