Complex Population Dynamics: Nonlinear M: Nonlinear Modeling in Ecology, Epidemiology and Genetics

Contents......Page 10
Preface......Page 6
References......Page 8
1.1. Introduction......Page 12
1.2. Food web model formulation......Page 15
1.3. Detecting and quantifying chaotic dynamics in model food webs......Page 18
1.4. Dynamical patterns in food webs......Page 21
1.5. Chaos in real food webs and conclusion......Page 26
References......Page 27
2. Generalized models T. Gross et al.......Page 32
2.1. Introduction......Page 33
2.2. The basic idea of generalized models......Page 35
2.3. Example: A general predator-prey system......Page 36
2.4. Additional difficulties in complex models......Page 39
2.5. A generalized spatial model......Page 43
2.6. Local stability in small and intermediate models......Page 44
2.7. Some results on global dynamics......Page 50
2.8. Numerical investigation of complex networks......Page 52
2.9. Discussion......Page 55
References......Page 57
3.1. Introduction......Page 60
3.2. Model for dryland water-vegetation systems......Page 63
3.3.1. Mapping the landscape states along aridity gradients......Page 67
3.3.2. Coexistence of landscape states and state transitions......Page 70
3.3.3. Landscape states and aridity classes......Page 72
3.4. Plants as ecosystem engineers......Page 73
3.4.1. Facilitation vs. resilience......Page 74
3.4.2. Facilitation vs. competition......Page 75
3.5. Species richness: Pattern formation aspects......Page 76
3.5.2. Landscape diversity......Page 77
3.5.3. Environmental changes......Page 78
3.6. Conclusion......Page 80
Acknowledgments......Page 82
References......Page 83
4.1.1. What is a metapopulation?......Page 88
4.1.2. Levins metapopulation model......Page 89
4.2.1. Local dynamics......Page 91
4.2.2. Finite number of patches with the Ricker model......Page 92
4.2.3. Infinite number of patches......Page 94
4.2.3.1. Model presentation......Page 95
4.2.3.2. Resident equilibrium......Page 96
4.3.1. Invasion fitness......Page 99
4.3.2. Pairwise Invasibility Plots (PIP)......Page 100
4.4. Evolution of dispersal......Page 101
4.4.1.1. Fitness......Page 102
4.4.1.2. Fixed-point attractor......Page 103
4.4.1.3. Cyclic orbits......Page 104
4.4.2. Infinite number of patches......Page 105
4.4.2.1. Invasion fitness for the mutant......Page 106
4.4.2.2. Results......Page 107
4.4.3.1. Local population growth with an Allee effect......Page 109
4.4.3.2. Allee effect in the metapopulation model......Page 110
4.4.3.3. Bifurcation to evolutionary suicide......Page 111
4.4.3.4. Theory of evolutionary suicide......Page 112
4.5. Summary......Page 114
References......Page 116
5. The scaling law of human travel - A message from George D. Brockmann and L. Hufnagel......Page 120
References......Page 136
6.1. Introduction......Page 140
6.2. Models for Zipf ’s law in language......Page 143
6.3. City sizes and the distribution of languages......Page 150
6.4. Family names......Page 155
6.4.1. The effects of mortality......Page 160
6.4.2. The distribution of given names......Page 165
6.5. Conclusion......Page 166
Acknowledgments......Page 167
References......Page 168
7.1. Introduction......Page 170
7.2.1. The SIS epidemic......Page 173
7.2.2. Solution of the SIS system shows criticality......Page 174
7.2.3. The spatial SIS epidemic......Page 176
7.2.4. Dynamics for the spatial mean......Page 178
7.2.5. Moment equations......Page 180
7.2.6. Mean field behavior......Page 181
7.3.1. Accidental pathogens......Page 182
7.3.3. The meningococcal disease model: SIRYX......Page 185
7.3.4. Divergent fluctuations for vanishing pathogenicity: power law......Page 187
7.3.5. Evolution towards criticality......Page 189
7.4. Empiric data show fast epidemic response and long last- ing fluctuations......Page 190
7.4.1. Modeling fast epidemic response finds long lasting fluctuations......Page 192
Acknowledgments......Page 196
References......Page 197
8.1. Introduction......Page 200
8.2.1. Network models as a research tool......Page 202
8.2.2. Epidemiologic settings......Page 203
8.3.1. Motivation......Page 205
8.3.2. Metrics......Page 206
8.3.3. Canonical network types......Page 211
8.4.1. Epidemic processes......Page 213
8.4.2.1. Dynamics in the longer term......Page 216
8.5.1. Impact of heterogeneity......Page 217
8.5.2. Impact of other network properties......Page 219
8.6. Control of infection......Page 220
Acknowledgements......Page 222
References......Page 223
9.1. Introduction......Page 226
9.2. The concept of biological network......Page 228
9.3. Structural properties of networks......Page 231
9.4. Modeling gene regulatory dynamics......Page 233
9.4.1. Dynamical models of gene......Page 234
9.4.2. Well-stirred and spatial models......Page 236
9.5.2. Multistability......Page 237
9.5.4. Engineering networks......Page 239
9.6.1. Availability of data......Page 241
9.6.2. Need of integration......Page 242
References......Page 244
Author Index......Page 248
Subject Index......Page 250