Phyllotaxis: A Systemic Study in Plant Morphogenesis

Cover......Page 1
About......Page 2
Phyllotaxis: A Systemic Study in Plant Morphogenesis......Page 4
9780521104692......Page 5
Contents......Page 8
Acknowledgments......Page 15
1. Subject and aims of the book......Page 16
2. The problem of origins of phyllotactic patterns......Page 18
3. The level of presentation......Page 19
4. Related works in the field......Page 20
Introduction......Page 23
1.1.1. Patterns in plants......Page 26
1.1.2. Whorled and spiral patterns......Page 27
1.1.3. Contact parastichies......Page 28
1.2.1. Visible opposed parastichy pairs......Page 31
1.2.2. Genetic spiral and the Bravais-Bravais theorem......Page 34
1.3.1. Fibonacci and Lucas sequences......Page 35
1.3.2. The golden ratio r......Page 37
1.3.3. Relationships between the constants......Page 38
1.4.1. Geometry of the spiral lattice......Page 39
1.4.2. A mathematical puzzle......Page 41
1.5. Problems......Page 43
2.1. A cornerstone in phyllotaxis - insight into history......Page 46
2.2.1. Visible opposed parastichy pairs for the Fibonacci angle......Page 48
2.2.2. Phyllotactic fractions associated with the Fibonacci angle......Page 50
2.3.1. Various forms......Page 51
2.3.2. Useful algorithms relating d and (m, n)......Page 53
2.4. Interpretation of spiromonostichy in Costus and Tapeinochilus......Page 56
2.5.1. The cylindrical lattice......Page 58
2.5.2. Derivation of the formula......Page 60
2.6. Problems......Page 61
3.1. Lestiboudois-Bolle theory of duplications......Page 63
3.2.1. Ancestral land plants......Page 67
3.2.2. Algal ancestors......Page 68
3.2.3. Vascular phyllotaxis......Page 72
3.3. Translocation of substances in plants......Page 74
3.4.1. Van der Linden model......Page 76
3.4.2. The fractal nature of phyllotaxis......Page 78
3.5.1. Hierarchies with only simple and double nodes......Page 82
3.5.2. Growth matrices, L-systems, and Fibonacci hierarchies......Page 84
3.6. Problems......Page 88
4.1. Differential growth in the plant apex......Page 91
4.2.1. Derivation of the model......Page 92
4.2.2. Interpretation of the model......Page 95
4.3. Generalized Coxeter formula......Page 97
4.4. Derivation of the Richards phyllotaxis index......Page 98
4.5. The Pattern Determination Table......Page 100
4.6.1. Church bulk ratio......Page 102
4.6.2. Richards area ratio......Page 105
4.6.3. The plastochrone P......Page 107
4.7. Problems......Page 108
5.1. The necessity of theoretical frameworks......Page 111
5.2.1. Linear relations in an expanding apex......Page 113
5.2.2. Phyllotaxis in Silene, a function of temperature......Page 115
5.3.1. Various models to use......Page 116
5.3.2. Advantages of the allometry-type model......Page 117
5.4.1. Maksymowych-Erickson method using Xanthium......Page 119
5.4.2. A first method using the Pattern Determination Table......Page 120
5.4.3. Evaluating the phyllotactic patterns for Proserpinaca and Xanthium......Page 121
5.5.2. A second method using the Pattern Determination Table......Page 123
5.5.3. Evaluating phyllotactic patterns in Chrysanthemum and Linum......Page 124
5.6.1. Data collection and Fujita's normal curves......Page 126
5.6.2. Interpretation of particular lattices......Page 128
5.6.3. Interpretation of phyllotactic fractions......Page 131
Epilogue......Page 135
Introduction......Page 138
6.1.1. An a-disciplinary concept......Page 142
6.1.2. Entropy in phyllotaxis......Page 143
6.2.1. Principle of minimal entropy production......Page 146
6.2.2. Particular notions of rhythm......Page 148
6.3. The optimal designs......Page 150
6.4.1. Patterns that can and cannot exist......Page 153
6.4.2. Multijugate systems......Page 156
6.5. By-products and applications......Page 157
7.1. Searching for quantified observations......Page 160
7.2. Data on the frequencies of occurrence of patterns......Page 162
7.3.2. On the sequence 2<6,13,19,32, ...>......Page 167
7.3.4. On the sequence <3,8,11,19,30, ...>......Page 168
7.3.5. On the sequence <3,7,10,17,27,...>......Page 169
7.4.2. On the frequency of the pattern <1,2,3,5,8, ...>......Page 170
7.4.3. Relative frequency of occurrence of the sequences <1,3,4,7,11, ...> and 2<1,2,3,5,8,...)......Page 172
7.4.5. Remarks on methodology......Page 173
8.1. Multimerous patterns......Page 175
8.2.1. Multimery versus multijugy......Page 176
8.2.2. Schoute's false whorls......Page 177
8.3.1. Continuous and discontinuous transitions - natural and induced......Page 178
8.3.2. The mechanism of transition......Page 180
8.4.1. Evolutionary levels in pattern generation......Page 181
8.4.2. Methodological consequences on modeling......Page 183
8.5.1. Generating alternating multimery from multijugate normal systems with t = 2 - the first hypothesis......Page 184
8.5.2. Alternating multimery derivation from anomalous systems - the second hypothesis......Page 186
8.5.4. Summary of the model and existence of predicted patterns......Page 187
8.6.1. Analysis of the phyllotaxis of Dipsacus......Page 191
8.6.2. Correlation with other models......Page 194
8.6.3. Perturbed patterns......Page 196
9.1.1. Packing efficiency; the noble numbers......Page 200
9.1.2. Self-similarity......Page 203
9.2.2. Minimality principles......Page 207
9.3. Ordering the noble numbers......Page 208
9.4. The τ-model and the interpretative model......Page 210
9.5.1. Phyllotaxis as a dissipative structure......Page 211
9.5.3. Priority order in phyllotactic systems......Page 213
9.6.1. The maximin principle and its consequences......Page 214
9.6.2. Comparison with the minimality condition of the r-model......Page 216
9.7. Fujita's a priori spiral patterns......Page 217
Epilogue......Page 219
Introduction......Page 222
10.1. Historical meeting again......Page 224
10.2.1. In biology......Page 226
10.2.2. In cylindrical crystals......Page 227
10.3.1. Protein crystallography and systems research......Page 229
10.3.2. Mathematical analysis of protein lattices and predictions......Page 234
10.4.2. Multimery, multijugy, and transitions revisited......Page 237
10.4.3. The daisy: a living crystal......Page 241
10.4.4. Minimal energy costs with regular transitions......Page 242
11.1. General comparative morphology......Page 244
11.2.1. Minerals, animals, and artifacts......Page 246
11.2.2. Colloidal crystals, quasicrystals, and polymers......Page 248
11.2.3. Properties of space-time......Page 251
11.3.1. Branching processes......Page 253
11.3.2. Gnomonic growth......Page 254
11.4. Levels of organization and layers of models......Page 258
11.5.1. Tenets of autoevolutionism......Page 261
11.5.2. Autoevolutionism and neo-Darwinism......Page 262
12.1.1. General dissatisfaction with chemical hypotheses......Page 265
12.1.2. General dissatisfaction with physical hypotheses......Page 267
12.2.1. Light and water......Page 270
12.2.2. Lines of force and energy......Page 272
12.3.1. A pyramid of models......Page 274
12.3.2. Biological and mathematical phyllotaxis......Page 275
12.3.3. Systemic phyllotaxis......Page 276
12.3.4. Phyllotaxis, magnetic fields, and superconductors......Page 277
12.4.1. Spirality and branching everywhere......Page 280
12.4.2. Prebiotic and modern creations......Page 281
12.4.3. A multidisciplinary problem......Page 282
Epilogue......Page 285
Introduction......Page 288
1. Glossary......Page 290
A2.1. Chapter 1......Page 305
A2.2. Chapter 2......Page 307
A2.3. Chapter 3......Page 310
A2.4. Chapter 4......Page 311
3. Questions......Page 314
A4.1. Phyllotaxis and Farey sequences......Page 319
A4.2. Visible parastichy pairs......Page 322
A4.3. Examples and algorithms......Page 324
A5.1. The mechanism......Page 327
A5.2. The results......Page 329
6. Interpretation of Fujita's frequency diagrams in phyllotaxis......Page 332
A7.1. Preliminaries......Page 336
A7.2. Theorems and applications......Page 338
8. The Meinhardt-Gierer theory of pre-pattern formation......Page 341
9. Hyperbolic transformations of the cylindrical lattice......Page 344
Bibliography......Page 348
Author index......Page 387
Subject index......Page 391