The Physics of Foraging: An Introduction to Random Searches and Biological Encounters

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
Part I: Introduction: Movement......Page 17
1.1 How do organisms really move, and why?......Page 19
1.2 Biological encounters as a reaction-diffusion process......Page 20
1.3 Impact and scientific importance......Page 23
1.4 Follow the data......Page 25
1.5 Beyond model comparison......Page 28
2.1 Optimal foraging theory......Page 30
2.2 Microscopic versus macroscopic levels of description......Page 31
2.3 Disorder and incomplete information......Page 32
2.4 Scaling and universality......Page 33
2.5 The extraordinary success of limiting models......Page 36
3.1 Central limit theorems......Page 39
3.2 Normal diffusion and Brownian motion......Page 40
Anomalous diffusion with H=1/2......Page 43
Generalized Hurst exponents......Page 45
Mathematical formalisms for anomalous diffusion......Page 46
3.4 Levy flights and Levy walks......Page 50
4.2 Levy flights of the wandering albatross......Page 58
4.3 Power laws and Pareto\'s principle......Page 62
4.4 Scientific progress as a random walk......Page 64
Part II: Experimental findings......Page 67
5.1 Fickian transport......Page 69
5.2 Directional persistence......Page 70
5.3 A new idea: Levy flights and walks......Page 71
Honey bees, fruit flies, and desert ants......Page 74
Snails......Page 75
Bony fish, sharks, sea turtles, and penguins......Page 76
Spider monkeys......Page 77
Dinoflagellates......Page 78
6.5 Birds......Page 79
7.1 Hunter-gatherers and archaeological evidence......Page 80
7.3 GPS tracking of humans......Page 81
7.4 Fishermen as foragers......Page 82
7.5 Austronesians in Madagascar......Page 83
8.1 Measurement and data analysis......Page 87
8.3 Anomalous diffusion: Not if, but when and why......Page 88
Part III: Theory of foraging......Page 91
9.1 A general theory of searchers and targets......Page 93
9.2 A limiting but general model of optimal foraging......Page 95
9.3 Random walk propagators and encounter rates......Page 96
10.1 The Levy flight foraging hypothesis......Page 101
Destructive and nondestructive foraging......Page 103
Generalization to regenerative targets......Page 106
Random search on lattices and networks......Page 107
Efficient navigation in a small world......Page 111
Energy......Page 112
Entropy, information, and patchiness......Page 113
11.1 Correlated random walks with a single scale......Page 116
Levy-modulated CRWs and correlated Levy walks......Page 118
11.2 Intermittent searches with two scales......Page 119
Scale-free intermittent searches......Page 121
11.3 A unified approach......Page 122
Part IV: Finale: A broader context......Page 125
12.1 Submarine warfare and operations research......Page 127
12.2 Enzymatic searches on DNA......Page 128
12.4 Eye microsaccades......Page 129
12.5 Learning, memory, and databases......Page 130
12.6 Genetically modified crops and disease vectors......Page 131
13 Adaptational versus emergent superdiffusion......Page 132
13.1 Are Levy walks really adaptive?......Page 133
13.2 Self-organization and emergence......Page 134
13.3 Deterministic induction of Levy behavior......Page 135
13.4 Why the answer is crucial......Page 137
Levy searches on small-world networks......Page 139
Environmentally induced superdiffusion......Page 140
Feedback with long-range memory......Page 141
Neurophysiological mechanisms......Page 142
14.3 Determinism, randomness, and free will......Page 143
14.4 Globally optimum random searches......Page 145
Epilogue: The main challenges for the future......Page 146
A.1 A criterion for inferring superdiffusion......Page 147
A.2 Log-log plots and surrounding controversies......Page 149
A.3 Maximum likelihood estimation......Page 150
Appendix B: Levy walkers inside absorbing boundaries......Page 152
References......Page 156
Index......Page 177