Phyllotaxis

Abstract

Phyllotaxis, the study of the patterns exhibited by leaves and other organs of plants, raises some of the deepest questions of plant morphogenesis. What principles of biological organisation produce these dynamical geometric systems? The constant occurrence of the Fibonacci sequence in such systems is a phenomenon that has fascinated botanists and mathematicians for centuries. In this book, first published in 1994, the many facets of phyllotaxis are dealt with in an integrated manner for the first time. The author describes a unified concept of phyllotaxis based on experimental, anatomical, cellular, physiological and paleontological observations. The book provides a framework for formal analyses of botanical data and emphasises the relevance of the phyllotactic paradigm in the study of other structures, such as crystals and proteins. It is of interest to cystallographers and physicists as well as to botanists and mathematicians.

Aberrant phyllotactic patterns in cones of some conifers: a quantitative study

“…Roger V. Jean's entropy-based model in turn may be sorely contradicted by the existence of the 7:10 and 8:11 patterns found at first in balsam fir's vegetative shoots [7], later in magnolia flowers [2] and now also in the cones of Pinus nigra analyzed in the present study. According to the model these patterns shouldn't exist [1], but otherwise, the order of frequency of cone patterns corresponds quite well with it. Roger Jean's model and this study have the following identical results: (i) the three most frequent aberrant patterns are (in descending order) the sequences 2, 4, 6, … (bijugy), 1, 3, 4, ... (first accessory) and 3, 6, 9, … (trijugy); (ii) multijugate patterns are found in descending frequency from bijugy down to trijugy down to tetrajugy patterns (Fig.…”

“…Again, his most frequent aberrant sequences were bijugy and first accessory, found in 71 cones. In 1994, Roger Jean [1] pooled the data from 12 750 observations on more than 650 species, not all of them conifers, and found bijugy the most frequent aberrant sequence, followed by the first accessory. In 1998, Iliya Vakarelow [8] studied both vegetative shoots and cones of conifers.…”

“…The aim of this study was to find as many different aberrant patterns as possible in cones from one single conifer, and to compare the yield of one single genet with the existing theories [1] or with the results of Beata Zagórska-Marek's large quantitative study based upon pooled genetic material from Abies balsamea shoots [7]. With a single tree one can study neither intra-or interspecific differences nor environmental influences.…”

“…It is a much simpler mathematical description of phyllotactic diversity than Roger Jean's entropy model [1]. It might be an interesting alternative: for Fibonacci phyllotaxis, it has its important majority of results in common but does not forbid certain patterns to exist (e.g.…”

“…However, there are exceptions to the rule: in most species of conifers, always quite rarely but in different frequency, aberrant patterns of cones show different parastichy numbers. They belong to the "Fibonacci-type" sequences [1]; as in the main Fibonacci sequence, each number is the sum of the previous two (Fig. 2).…”