Jean-Paul Walch & Solange Blaise 
Phyllotaxis Models 
A Tool for Evolutionary Biologists

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.

Inhaltsverzeichnis

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 Dédoublement 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

Über den Autor

Jean-Paul Walch is a former computer scientist for large French companies in the oil and electricity distribution sectors.

Solange Blaise is a former Associate Professor at Université Paris-Sud, Laboratoire Écologie, Systématique et Évolution, France.