Phyllotaxis Models E-Book

Jean-Paul Walch

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 232

Veröffentlichungsjahr: 2023

Beschreibung

The equations of phyllotaxis were discovered by Douady and Couder: these describe the inhibition "force" generated by an incipient primordium, preventing the initiation of other primordia in its vicinity: the method that was lacking was to take into account the distance of primordia to the meristem apex over the course of its development. With these parameters, our model integrates both biochemical "forces" (inhibition due to auxin) and mechanical forces (contact pressure). This powerful tool allows us to revisit many important notions of plant biology. For example, we model auxin concentrations at the plant apex, as well as the development of vegetative and reproductive meristems. We also explain why the whorls of monocots are trimerous and those of plants with quincuncial perianths are pentamerous. We design a geometric method for reconstructing inflorescences from their building blocks, i.e. floral meristems. We also show that phyllotaxic spirals are only the application of a general property of symmetry, the advantages of which have been exploited by natural selection.

Leseprobe

Series EditorMarie-Christine Maurel

Phyllotaxis Models

A Tool for Evolutionary Biologists

Jean-Paul WalchSolange Blaise

First published 2023 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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© ISTE Ltd 2023The rights of Jean-Paul Walch and Solange Blaise to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.

Library of Congress Control Number: 2023933897

British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-78630-913-6

Foreword

I could not think of any better circumscription of the concept of phyllotaxis than the one provided by Adler et al. (1997) in their article entitled “A history of the study of phyllotaxis”:

Phyllotaxis, a subdivision of plant morphology, is the study of the arrangement of repeated units such as leaves around a stem, scales on a pine cone or on a pineapple, florets in the head of a daisy, and seeds in a sunflower. Remarkably, these units often form systems of spirals or helices. As a study of the self-organization of repeated units, it somewhat resembles the study of crystallography. In fact, the objects studied may be thought of as living crystals. However, the fact that they are living and growing adds a further dimension to the subject, making it necessary to take into account such things as growth rates, heredity, interaction with the environment, and evolution. Trying to explain the regularity of the arrangements of petals, leaves, etc. has led research workers to incorporate molecular biology, general comparative morphology, and evolutionary theory into their thinking.

Studying phyllotaxis – its causes, its establishment during development and its functions – is a challenge that several scientists and brilliant minds have faced in the past. Historically, Theophrastus, Pliny the Elder, Leonardo Da Vinci, Johannes Kepler and Johann Wolfgang von Goethe are among the most influential figures who played a pioneering role in the study of phyllotaxis, paving the way to modern studies. Numerous hypotheses have been tested, and many articles have been published in the 19th and 20th centuries, trying to bring forward our knowledge about the mechanisms underlying the different phyllotactic types. This book from Walch and Blaise is a summary of the research conducted so far on the topic, and it also introduces an elegant model for reproducing (accurately) and predicting (quite satisfactorily) phyllotactic patterns.

I assume there will be at least three ways of reading this book, depending on how we can handle the profuse information presented in the seven chapters. While some will be curious about the mathematical and theoretical modeling aspects that are indicative of crucial properties of plant structure and development, others will be interested in the history of paradigm shifts that have characterized the evolution of plant morphology. A third kind of reader will use a taxonomical map to circulate through the landscape of this book and use particular species or supraspecific lineages as magnifying lenses.

Jean-Paul Walch is not a trained botanist. Far from being a drawback, this is what probably allowed him to assertively overcome the supposedly daunting task of modeling phyllotaxis in (mostly) angiosperm lineages, focusing on (mostly) reproductive units, to explain adult (with a static model) and developing (with a dynamical model) structures, relying on concepts from the fields of mathematics, physics, mechanics, evo-devo and molecular biology.

Although the initial project of Jean-Paul Walch and the botanist Solange Blaise was indisputably ambitious, they succeeded in formalizing their ideas and opinions in a book that will for sure inspire researchers from the above-mentioned disciplines and give grist to the mill of anyone who wants to discuss their model and propose adjustments, albeit improvements.

This book will find its place in the library of botanists interested in the theoretical aspects of plant shape and organization, and more broadly of scientists who are keen on deciphering and understanding natural forms and the phenotypes realized in the course of evolution, compared to those that are theoretically possible.

Florian JABBOURAssociate Professor,Muséum National d’Histoire Naturelle,Paris, France

Preface

“What theory is there in botany that is vast enough to embrace all the facts, and a formula that is flexible enough to counter all objections?”

“Some may thank us for attempting something so foolhardy, without concealing from us the pitfalls of this perilous enterprise.”

“The plant kingdom loses itself like an atom in the vast plane of possible systems, but it displays nonetheless a unicity of form in its origin and infinite variation in its details.”

– Bravais and Bravais (1830)“Essai sur la disposition générale des feuilles rectirisées”(Essay on the general arrangement of whorled leaves).

Phyllotaxis, as a discipline, uses a mathematical approach to understand plant structure. Its conceptual level was already advanced in the early 19th century, notably with the contribution of Auguste Bravais. The time has now come for this concept to become a real tool for biologists. The few equations that describe in a general, and thus simplified manner the biochemical and physical mechanisms underlying the development of each species can only be solved with numerical calculations, that is, using computational means.

This approach may be offputting for biologists. We therefore suggest they draw information from this book in the following manner:

Chapter 1

presents the main concepts of phyllotaxis: parastichies, divergence angles, plastochron ratios, etc., which are systematically illustrated with examples from the botanical world.

Chapter 2

retraces the history of this discipline without going into any mathematical detail, allowing the reader to understand the evolution of the theoretical aspects of phyllotaxis, and highlights the turning point that was Douady and Couder’s “standard model” in 1996.

Chapter 3

presents the model of the classic sunflower capitulum (the “static model”), showing that Fibonacci spirals optimize organ packing even though they are not the only configuration to do so. Although this idea is met with some resistance by those who see it as a finalist approach, Fibonacci spirals minimize the self-shading of leaves. Biologists may limit themselves to the discussion, and perhaps read the section on the golden ratio, which was based on a high school project.

Chapters 4

and

5

are essentially mathematical: they present the equations of Douady and Couder describing the arrangement of organs in developing meristems, as well as the parametrization we used and with which we were able to model the diversity of the arrangements found in plants. Indeed, our predecessors who developed this model relied on too few parameters, like meteorologists who only have data from a few recording stations over an area as large as France. Biologists can nevertheless read our presentation of the model of molecular phenomena underlying plant phyllotaxis. On request, the authors can provide a simple Excel spreadsheet where the initial position of two to four primordia can be set, and the positions of the following six primordia can be calculated

1

.

Chapter 6

presents the evolution of Magnoliales and Laurales in a new light. Botanists can simply read the discussion and refer to the main text for details of how the results were obtained. If the model described at the start of the chapter allows a new interpretation of particular arrangements in members of these orders, its most significant result is the concept of pseudo-whorls. Although flowers in basal angiosperms are either completely spiraled or whorled, flowers in Magnoliales and especially Laurales evolved the spiral organization to acquire qualities that were unique to the whorls. This explains why the numbers of organs in these pseudo-whorls, i.e. 3, 5, etc. belong to the Fibonacci sequence!

Chapter 7

presents the organization of inflorescences. It does not rely on mathematics, but is based on the elementary geometrical construction of inflorescences, namely, the assembly of “bricks” consisting of floral meristems and their bracts and bracteoles.

The conclusion is purely textual.

Our model has been published in the Journal of Theoretical Biology, its application in basal angiosperms in Botany Letters and the demonstration of the influence of bracteoles on sepal arrangement (initially intuited by Eichler in 1875) in Flora.

February 2023

Note

1

To request the Eichler.xls spreadsheet please contact Jean-Paul Walch at

[email protected]

.

Acknowledgments

We would like to thank Florian Jabbour, Associate professor, Muséum National d’Histoire Naturelle, Paris, for his encouragement, Hélène Citerne for her review of the manuscript and Line Walch for her superb drawings.