Problems of Relative Growth
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^^—^^—^^^—^m^^—ii in lining—M^^^^M^^M^—^I^M JfniiHHIlillllllllilllilllliilliiiiillililiiiiiiiiiiiiiiiiiniikiiiimiiiiiiiiiiiiiiiiiiiiiiiiiifiiiiiiiiniiniiiiiiiiiiiiiHiiininiiiiiHHiiiiiiiiiHiiiiiiiiHiiiiiii! PROBLEMS OF RELATIVE GROWTH HETEROCIfELY AND REGENERATION IN THE COMMON LOBSTER i. Marine Lobster, Homarus (Gammarus) vulgaris, Normal Left-handed Specimen. 2. The Same Regenerating the Left 'Crusher' Claw after Autotomy. 3. Shed Skin of the Same at the Next Moult. 4. The Same after this Moult, showing Direct Regeneration of Left Crusher. Note the slenderer propus and absolutely longer dactylus in the smaller (' nipper ') claw. PROBLEMS OF RELATIVE GROWTH BY JULIAN S. HUXLEY, M.A. Honorary Lecturer in Experimental Zoology, King's College, London WITH IO5 ILLUSTRATIONS LINCOLN MAC VEAGH THE DIAL PRESS NEW YORK • MCMXXXII PRINTED IN GREAT BRITAIN TO D'ARCY WENTWORTH THOMPSON — ' The morphologist, when comparing one organism with another, describes the differences between them point by point, and " character " by " character." If he is from time to time constrained to admit the existence of " correlation " between characters (as a hundred years ago Cuvier first showed the way), yet all the while he recognizes this fact of correlation somewhat vaguely, as a phenomenon due to causes which, except in rare instances, he cannot hope to trace ; and he falls readily into the habit of thinking and talking of evolution as though it had proceeded on the lines of his own descriptions, point by point, and character by character. But if, on the other hand, diverse and dissimilar fishes can be referred as a whole to identical functions of very different co-ordinate systems, this fact will of itself constitute a proof that a com- prehensive " law of growth " has pervaded the whole structure in its integrity, and that some more or less simple and recog- nizable system of forces has been at work.' D'Arcy Thompson (Growth and Form, p. 727). vn , PREFACE this book I have attempted to give some account of INthe chief results emerging from a study of the relative growth of parts in animals which I have undertaken during the last ten years. I have tried to correlate my own findings and conclusions with those of other workers in the same and related fields, but am well aware of the many gaps that remain. However, it has not been my main intention to produce an exhaustive survey of the subject, but rather to set forth certain new facts and ideas and some of their chief implications. There are, I think, four chief points in the book which are more or less new. One is the quantitative formulation of heterogonic growth (Chapters I and II) ; a second is the dis- covery of the widespread existence of growth-gradients, and their quantitative analysis (Chapters III and IV) ; a third is the recognition that growth of logarithmic spiral type as seen in Molluscan shells, etc., operates with the same growth- mechanisms (growth-centres and growth-gradients) as does growth of ordinary type as seen in a Crustacean antenna or a sheep's leg (Chapter V) ; and the fourth is the application of these results to certain evolutionary problems, as set forth in the final chapter. I owe a great deal to previous work in this field : first and foremost to D'Arcy Thompson's Growth and Form, but also to the books and papers of Champy, Teissier, Schmalhausen and others too numerous to mention. I have to thank Professor L. T. Hogben and Dr. R. A. Fisher, F.R.S., for reading the book in typescript and making various useful suggestions ; and I owe a great deal to Pro- fessor H. Levy for helping me with some of the mathematical problems involved. My thanks are also due to Dr. C. F. A. Pantin and Professor Selig Hecht, whose discussions with me of various problems raised in this book have helped greatly in clarifying my ideas. And especially I would like to thank my pupils and co-workers, Mr. E. B. Ford, Mr. F. N. Rat- cliffe, Miss M. Shaw (Mrs. White), Miss M. A. Tazelaar, Mr. ix x PROBLEMS OF RELATIVE GROWTH S. F. Bush, Professor F. W. Kunkel, Mr. J. A. Robertson, Miss I. Dean, Mr. A. S. Edwards and Mr. F. S. Callow, without whose collaboration I should never have been able to collect and analyse the data on which this treatment of the subject is founded. Finally, I must not forget my secretary, Miss P. Coombs, whose aid has been invaluable in preparing the book for the press. Many of the figures have been drawn for this book. As regards the others, I would like to express my thanks for the willingness of the authors and publishers concerned for allow- ing me to reproduce them. Acknowledgements have been made in the list of illustrations : the citations there made refer to the literature list for fuller details. JULIAN S. HUXLEY King's College, London December, 1931 ERRATUM Page Fig. " 84, 46, legend. For dactylus ; ischium " " read dactylus ; carpus ; ischium "—problems of relative growth. CONTENTS PAGE Preface ......... ix List of Illustrations. ...... xiv CHAPTER I CONSTANT DIFFERENTIAL GROWTH-RATIOS § i. Introductory ........ i § 2. Constant Differential Growth-Ratios ... 4 § 3. Examples of Constant Differential Growth-Ratios. 13 § 4. Inconstancy of Form and Constancy of Form-change 38 CHAPTER II THE COEFFICIENT OF CONSTANT GROWTH- PARTITION ; AND SOME SPECIAL CASES § 1. The Heterogony of Deer Antlers .... 42 § 2. The Coefficient of Constant Growth-partition . 49 § 3. Heterogony in Holometabolous Insects 55 § 4. Heterogony and Polymorphism in Neuter Social Insects ......... 61 § 5. Heterogony, Moulting, and Dimorphism ... 68 CHAPTER III GROWTH-CENTRES AND GROWTH-GRADIENTS §1 Growth-gradients within Single Organs ... 79 §2 Steepness of Growth-gradient within an Organ and Growth-intensity of the Organ as a whole . 83 §3 Reversal of the Sign of the Growth-gradient in Negative Heterogony ...... 87 §4 The Form of Growth-gradients. .90 §5 Growth-gradients in Regions of the Body . 92 §6 Graded Growth-intensity in the Different Planes of Space ......... 95 §7 Gradients in Growth-rate of Epidermal Structures 100 §8 Conclusion ......... 102 xi xii PROBLEMS OF RELATIVE GROWTH PAGE CHAPTER IV GROWTH-GRADIENTS AND THE GENERAL DISTRIBUTION OF GROWTH-POTENTIAL IN THE ANIMAL BODY § i. General Growth-gradients : D'Arcy Thompson's Graphic Method . .104 §2. General Growth-gradients: Quantitative Analysis iio § 3. The Two Phases of Growth . .118 § 4. Growth-changes Correlated with High Local Growth- intensity ........ 120 § 5. Some Cases of Teratological and Abnormal Growth 128 § 6. The Law of Antero-posterior Development and its Effect upon Growth ...... 132 § 7. The Mathematical Formulation of Relative Growth in Embryonic Life ....... 139 § 8. Conclusion ......... 147 CHAPTER V GROWTH-CENTRES AND GROWTH-GRADIENTS IN ACCRETIONARY GROWTH § 1. The Accretionary Method of Growth . 149 § 2. Logarithmic Spirals as the Result of Growth- gradients . .151 § 3. Growth-gradients and the Shells of Molluscs . 154 4. Conclusion 163 § ......... CHAPTER VI HETEROGONY, GROWTH-GRADIENTS AND PHYSIOLOGY § 1. Normal Proportions as Result of a Partition-equili- brium ......... 165 § 2. The Initial Determination and Physiological Basis of Growth-gradients . .167 § 3. Other Gradient Theories . .170 § 4. Heterogony and Hormones . .176 § 5. Heterochely and Relative Growth-rates. 1S9 § 6. Specific Growth-intensities and their Interaction . 191 CONTENTS Xlll page § 7. The Influence of External Conditions 197 § 8. Rhythmical Irregularities of Growth-ratio 203 CHAPTER VII BEARINGS OF THE STUDY OF RELATIVE GROWTH ON OTHER BRANCHES OF BIOLOGY § 1. Heterogony and Taxonomy : Sub-species and Taxo- nomic Forms ........ 204 §2. Heterogony in Groups Higher than the Species . 212 §3- Heterogony and Evolution . .216 §4- Heterogony and Comparative Physiology . 224 §5- Relative Growth and Genetics . .229 §6. Relative Growth, Embryology, and Recapitulation 234 §7- General Approach to the Problem of Qualitative Form-change ........ 240 §8. Conclusion ......... 243 Bibliography ........ 245 Addenda . ... 257 Index of Authors ....... 267 Subject Index ........ 270 Index of Organisms ....... 274 LIST OF ILLUSTRATIONS FIG. PAGE Heterochely AND REGENERATION IN THE LOBSTER Frontispiece (From Przibram, 1931) i. Diagram illustrating some quantitative aspects of heterogony ........ 5 2. Changes in absolute and percentage weight of the large claw during growth in fiddler-crabs . 9 3. heterogony of the large claw in 4oi male fiddler- CRABS ......... IO (From Huxley, 1927k) ' 4. HETEROGONY OF STEM-WEIGHT AGAINST ROOT-WEIGHT IN VARIOUS PLANTS . .13 (From Pearsall, 1927) 5. HETEROGONY OF PETIOLE LENGTH AGAINST LAMINA DIA- METER in Nasturtium leaves . -14 (From Pearsall, 1927) 6. Changes in relative abdomen-breadth during the growth of the shore-crab . .15 7. heterogony of abdomen-breadth in 625 shore-crabs io (After Huxley and Richards, 1931) 8. HETEROGONY OF THE CHELA IN THE PRAWN PALAEMON MAL- COMSONI . 17 g. heterogony of face relative to cranium in sheep- dogs and baboons . 18 10. Baboon skulls of various ages to show change in pro- portions ......... 19 (From Zuckerman, 1926) 11. HETEROGONY OF TAIL-LENGTH IN THE MOUSE PHENACOMYS 22 12. HETEROGONIC RELATION OF DORSAL AND VENTRAL EYE- LOBES IN THE BAR-EYED MUTANTS OF DROSOPHILA . 22 (Modified from Hersh, 1928) 13. HETEROGONY OF INTER-OCULAR DISTANCE IN CRABS . 23 (After Teissier, 1931) 14. Change of proportions in shore-crab ... 24 (From unpublished drawings kindly supplied by Dr. G. Teissier) 15. HETEROGONY OF THORACIC GANGLION IN CRABS . 25 (After Teissier, 1931) 16. HETEROGONY OF WATER-CONTENT IN TENEBRIO LARVAE 26 (After Teissier, 1931) 17. HETEROGONY OF NITROGEN-CONTENT IN TENEBRIO LARVAE 26 (After Teissier, 1931) 18. HETEROGONY OF PHOSPHORUS-CONTENT IN TENEBRIO LARVAE ......... 28 (After Teissier, 1931) xiv LIST OF ILLUSTRATIONS xv FIG. PAGE ig. Heterogonic relation of heat of combustion to body- weight in Tenebrio larvae ..... 28 (After Teissier, 1931) 20. Heterogony of water-content in wax-moth larvae (Galleria) . -3i (After Teissier, 1931) 21. Heterogony of male and female chelae in two species of prawns (palaemon) ...... 33 (A, from Tazelaar, 1931) 22.