The Physics of Foraging

by Viswanathan, Gandhimohan M.; Da Luz, Marcos G. E.; Raposo, Ernesto, P.; Stanley, H. Eugene

• ISBN13: 9781107006799
• ISBN10: 1107006791
• Format: Hardcover
• Copyright: 2011-07-11
• Publisher: Cambridge Univ Pr

Summary

Do the movements of animals, including humans, follow patterns that can be described quantitatively by simple laws of motion? If so, then why? These questions have attracted the attention of scientists in many disciplines, and stimulated debates ranging from ecological matters to queries such as 'how can there be free will if one follows a law of motion?' This is the first book on this rapidly evolving subject, introducing random searches and foraging in a way that can be understood by readers without a previous background on the subject. It reviews theory as well as experiment, addresses open problems and perspectives, and discusses applications ranging from the colonization of Madagascar by Austronesians to the diffusion of genetically modified crops. The book will interest physicists working in the field of anomalous diffusion and movement ecology as well as ecologists already familiar with the concepts and methods of statistical physics.

Author Biography

Gandhimohan M. Viswanathan is Professor of Physics at the Universidade Federal do Rio Grande do Norte, in Natal. Marcos G. E. da Luz is Associate Professor in the Departamento de Fisica, Universidade Federal do Paran, in Curitiba. Ernesto P. Raposo is Associate Professor in the Laboratrio cie Fisica Terica e Computacional, Departamento de Fsica, Universidade Federal de Pernambuco, in Recife. H. Eugene Stanley is University Professor, Professor of Physics, Chemistry, and Biomedical Engineering at Boston University, Professor of Physiology at Boston University School of Medicine, and Director of the Boston University Center for Polymer Studies.

Table of Contents

Preface	p. xi
Introduction: Movement
Empirical motivation for studying movement	p. 3
How do organisms really move, and why?	p. 3
Biological encounters as a reaction-diffusion process	p. 4
Impact and scientific importance	p. 7
Follow the data	p. 9
Beyond model comparison	p. 12
Statistical physics of biological motion	p. 14
Optimal foraging theory	p. 14
Microscopic versus macroscopic levels of description	p. 15
Disorder and incomplete information	p. 16
Scaling and universality	p. 17
The extraordinary success of limiting models	p. 20
Random walks and Lévy flights	p. 23
Central limit theorems	p. 23
Normal diffusion and Brownian motion	p. 24
Anomalous diffusion	p. 27
Lévy flights and Lévy walks	p. 34
The wandering albatross	p. 42
Do good theories always come from good data?	p. 42
Lévy flights of the wandering albatross	p. 42
Power laws and Pareto's principle	p. 46
Scientific progress as a random walk	p. 48
Experimental findings
Early studies	p. 53
Fickian transport	p. 53
Directional persistence	p. 54
A new idea: Lévy flights and walks	p. 55
Evidence of anomalous diffusion	p. 58
Arthropods and mollusks	p. 58
Marine and aquatic animals	p. 60
Mammals	p. 61
Micro-organisms	p. 62
Birds	p. 63
Human dispersal	p. 64
Hunter-gatherers and archaeological evidence	p. 64
Lévy nights of dollar bills	p. 65
GPS tracking of humans	p. 65
Fishermen as foragers	p. 66
Austronesians in Madagascar	p. 67
How strong is the evidence?	p. 71
Measurement and data analysis	p. 71
Special issues related to power laws	p. 72
Anomalous diffusion: Not if, but when and why	p. 72
Theory of foraging
Optimizing encounter rates	p. 77
A general theory of searchers and targets	p. 77
A limiting but general model of optimal foraging	p. 79
Random walk propagators and encounter rates	p. 80
Lévy flight foraging	p. 85
The Lévy flight foraging hypothesis	p. 85
Analytical and numerical results	p. 87
Discrete versus continuous media	p. 91
Energy and entropy	p. 96
Other search models	p. 100
Correlated random walks with a single scale	p. 100
Intermittent searches with two scales	p. 103
A unified approach	p. 106
Finale: A broader context
Superdiffusive random searches	p. 111
Submarine warfare and operations research	p. 111
Enzymatic searches on DNA	p. 112
Robot foraging	p. 113
Eye microsaccades	p. 113
Learning, memory, and databases	p. 114
Genetically modified crops and disease vectors	p. 115
Adaptational versus emergent superdiffusion	p. 116
Are Lévy walks really adaptive?	p. 117
Self-organization and emergence	p. 118
Deterministic induction of Lévy behavior	p. 119
Why the answer is crucial	p. 121
Perspectives and open problems	p. 123
The flavor of foraging research	p. 123
Biological mechanisms underlying superdiffusion	p. 124
Determinism, randomness, and free will	p. 127
Globally optimum random searches	p. 129
Final remarks	p. 130
Appendices
Data analysis	p. 131
A criterion for inferring superdiffusion	p. 131
Log-log plots and surrounding controversies	p. 133
Maximum likelihood estimation	p. 134
Lévy walkers inside absorbing boundaries	p. 136
References	p. 140
Index	p. 161
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