The Shoot Apex and Leaf Growth s* The Shoot Apex and Leaf Growth A Study in Quantitative Biology R. F. WILLIAMS Division of Plant Industry C.S.I.R.O., Canberra CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, Delhi Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521112871 © Cambridge University Press 1975 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1975 This digitally printed version 2009 A catalogue record for this publication is available from the British Library Library of Congress Catalogue Card Number: 74—21716 ISBN 978-0-521-20453-8 hardback ISBN 978-0-521-11287-1 paperback Contents Acknowledgements page vii 1 Introductory 1 2 The quantitative description of growth 9 3 Phyllotaxis 27 3.1 Spiral and other systems of phyllotaxis 28 3.2 The parameters of phyllotaxis 35 3.3 The Fibonacci angle - irrational or inevitable? 42 4 Shoot-apical systems 56 4.1 Flax, Linum usitatissimum L. 56 4.2 Tobacco, Nicotiana tabacum L. 81 4.3 Cauliflower, Brassica oleracea L. 91 4.4 Blue lupin, Lupinus angiistifolius L. 97 4.5 Subterranean clover, Trifolium subterraneum L. 100 4.6 Eucalyptus, Eucalyptus grandis Hill and Maiden, and 116 Eucalyptus bicostata Maiden, Blakely and Simmonds 4.7 Wheat, Triticum aestivum L. 131 4.8 Fig, Ficus elastica Roxb. ex Hornem. 146 4.9 Yellow serradella, Ornithopus compressus L. 157 Dianella sp. (Liliaceae) Narrow-leaf wattle, Acacia mucronata Willd. ex H. Wendl Sunflower, Helianthus annuus L. 5 The dynamics of leaf growth 163 5.1 Subterranean clover 163 5.2 Wheat 172 5.3 Relative rates of change, R and G \11 6 The growth of an inflorescence 183 7 The growth of wheat tillers 199 8 Plant growth as integration 207 8.1 Physical constraint as a determinant of growth rate 207 Contents 8.2 Constraint and the genesis of form page 212 8.3 Organization of the shoot apex 214 Appendix 223 A.I Three-dimensional reconstruction 223 A.2 Volume estimation by serial reconstruction 227 A.3 Phyllotaxis 230 A.4 Age equivalence and covariance 236 A. 5 Data processing and presentation 239 A.6 Cell counting 243 A.7 Conversion table 244 References 245 Indexes 251 VI Acknowledgements The author is happy to record his indebtedness to immediate colleagues of the Division of Plant Industry, and to others who have contributed in many ways to the preparation of this book. My personal assistant Miss R. A. Metcalf is especially deserving of my thanks, not only for dedicated technical assistance over the last five years, but for the pre- paration of nearly all the text figures in this volume. Her predecessor, too, Mrs T. C. Wallace is deserving of my warmest thanks. My colleague, Dr A. H. G. C. Rijven, ever my sternest critic, has helped more than he is aware by his unfailing enthusiasm and interest. He and Professor F. L. Milthorpe made many valued suggestions for the improvement of the text. In matters mathematical and statistical I owe much to Mr G. A. Mclntyre, and more recently to Mr W. J. Muller of the Division of Mathematical Statistics. They do not necessarily concur in all the procedures that have been adopted by the author. Mr C. J. Totterdell and Mr H. G. Baas Becking, leaders of the Photography and Illustration Sections of the Division have been generous with help and advice, and Mrs A. J. Simpson and Mr E. Brunoro have done all the routine photography relating to the text figures, both half-tone and line drawings. In particular, Mrs S. C. Mclntosh and Mrs Joan Simpson are warmly thanked for the dust cover design. Mrs V. J. Ronning and several members of the Divisional Typing Pool have been very patient with my reiterated requests for typing, and I thank them. Miss Fumei Lin was involved for a time, as a post-graduate student, in the study of Eucalyptus seedling growth. I acknowledge her work and regret that she was unable to complete it under my guidance. I am especially grateful to the Australian journals of scientific research for permission to reproduce seven plates and 38 text figures previously published by them. They are specifically acknowledged in the legends and References. A few other diagrams have been modified from the originals in the literature, and due acknowledgement is made. In conclusion, I wish to thank my wife, Ethel, for her forbearance and support throughout the project. vii 1 Introductory '. . . if arithmetic, mensuration, and weighing be taken away from any art, that which remains will not be much'. PLATO, Philebus (Jowett's translation, iv, 104 (1875)) \ . . the growth and development of an organism is the result of a number of ontogenetic processes, among which complex interrelations exist. The interpretation of these interrelations, and of the manner in which the processes are integrated to produce the living plant, is the fundamental problem in the study of growth'. A. H. K. PETRIE (1937) At the time of his death, Petrie had completed early drafts of two or three chapters of a book which was to have been called 'The Develop- mental Physiology of Plants', and the above quotation from Plato had been placed at the beginning of Chapter 2, 'The Change in Dry Weight and Leaf Area, and First Steps in the Analysis of Growth Rate'. Unfortunately the book had not reached a stage from which it could have been completed by any of his colleagues, and we had to content ourselves with placing the quotation on the title page of a bound volume of Petrie's papers in plant physiology for the Library of the Waite Institute, Adelaide. The second quotation is from one of Petrie's published papers, and epitomizes his thinking and general approach to the study of growth, though more extended statements along the same lines had in fact appeared a year earlier (Ballard and Petrie, 1936). Although his research ouput was quite remarkable in quantity and quality, Petrie did not live long enough to bring this kind of thinking to its full fruition, but he did succeed in transmitting some of his enthusiasm and outlook to his rather few research students and those who became his junior colleagues. This book is intended as a very belated tribute from one who was privileged to be associated with him for almost nine years. Petrie was the son of Dr James M. Petrie, who was for many years Macleay Research Fellow of the Linnean Society of New South Wales. After holding junior academic posts in Sydney and Melbourne he was awarded an 1851 Exhibition Scholarship, and this enabled him to study
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