Phyllotaxis Models

Foreword ix

Preface xiii

Acknowledgements xvii

Introduction xix

Chapter 1 An Introduction to Phyllotaxis 1

1.1 A game of spirals 1

1.2 Fibonacci phyllotaxis 6

1.3 Lucas phyllotaxis 8

1.4 Whorled phyllotaxis 9

Chapter 2 A History of Theoretical Phyllotaxis 13

Chapter 3 The Static Model 25

3.1 Modeling the sunflower capitulum 25

3.2 Packing density 28

3.3 Optimization of light capture 31

3.4 Discussion 33

3.5 Appendix: the golden angle 34

Chapter 4 The Dynamical Model 39

4.1 Description of the model 39

4.2 Phyllotaxis modes (analytical model) 45

Chapter 5 Molecular or Contact Pressure Origin? 51

5.1 The dynamics of phyllotaxis 51

5.2 The molecular origin of phyllotaxis 52

5.3 The history of the contact pressure model of phyllotaxis 61

5.4 Modeling the floral meristem of Illicium 63

5.5 Mechanical forces in floral development 68

5.6 Physical models 69

Chapter 6 Magnoliales and Laurales 73

6.1 Stability of the Fibonacci spiral 73

6.2 Transient regime 77

6.3 Continuity of the Fibonacci spiral 78

6.4 Magnoliales 81

6.4.1 Magnoliaceae 82

6.4.2 Annonaceae 92

6.5 Laurales 97

6.5.1 Atherospermataceae 98

6.5.2 Monimiaceae 105

6.6 Discussion 107

6.6.1 Regular spirals 109

6.6.2 Permuted spirals 109

6.6.3 Quasi-symmetric spirals 110

6.6.4 Whorls 111

6.6.5 Dedoublement 112

6.6.6 Pseudo-whorls 112

6.6.7 Hemicycles 113

6.6.8 Synorganization 113

Chapter 7 Inflorescences 119

7.1 Bracteole theory 119

7.2 Inflorescences 123

7.2.1 Racemes 126

7.2.2 Cymes 131

7.2.3 Involucra and spathes 154

Conclusion 161

References 183

Index 193