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Stochastic Foundations in Movement Ecology: Anomalous Diffusion, Front Propagation and Random Searches 2014 ed. [Kõva köide]

  • Formaat: Hardback, 310 pages, kõrgus x laius: 235x155 mm, kaal: 664 g, 16 Illustrations, color; 68 Illustrations, black and white; XVII, 310 p. 84 illus., 16 illus. in color., 1 Hardback
  • Sari: Springer Series in Synergetics
  • Ilmumisaeg: 07-Oct-2013
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642390099
  • ISBN-13: 9783642390098
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  • Formaat: Hardback, 310 pages, kõrgus x laius: 235x155 mm, kaal: 664 g, 16 Illustrations, color; 68 Illustrations, black and white; XVII, 310 p. 84 illus., 16 illus. in color., 1 Hardback
  • Sari: Springer Series in Synergetics
  • Ilmumisaeg: 07-Oct-2013
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642390099
  • ISBN-13: 9783642390098
This book presents the fundamental theory for non-standard diffusion problems in movement ecology. Lévy processes and anomalous diffusion have shown to be both powerful and useful tools for qualitatively and quantitatively describing a wide variety of spatial population ecological phenomena and dynamics, such as invasion fronts and search strategies.

Adopting a self-contained, textbook-style approach, the authors provide the elements of statistical physics and stochastic processes on which the modeling of movement ecology is based and systematically introduce the physical characterization of ecological processes at the microscopic, mesoscopic and macroscopic levels. The explicit definition of these levels and their interrelations is particularly suitable to coping with the broad spectrum of space and time scales involved in bio-ecological problems.  

Including numerous exercises (with solutions), this text is aimed at graduate students and newcomers in this field at the interface of theoretical ecology, mathematical biology and physics.

Arvustused

From the book reviews:

This book attempts to provide an overview of the essential mathematical, physical and modelling aspects which describe the motion of living entities at various scales. This book is interdisciplinary, intuitive and versatile, bridging a gap between mathematics and ecology in a pedagogically sound and scientifically relevant manner, from which a broad audience may benefit. (Paul Georgescu, zbMATH, Vol. 1295, 2014)

Part I Theoretical Foundations
1 Elements of Probability Theory
3(20)
1.1 Random Variables and Probability
3(3)
1.2 Moments and the Characteristic Function
6(2)
1.3 Well-Known Probability Distributions
8(6)
1.3.1 Normal Distribution
8(1)
1.3.2 Exponential Distribution
9(1)
1.3.3 Uniform Distribution
10(1)
1.3.4 Cauchy Distribution
11(1)
1.3.5 Levy Distribution
11(1)
1.3.6 Dirac Delta Distribution
12(1)
1.3.7 Poisson Distribution
12(1)
1.3.8 Binomial Distribution
13(1)
1.4 Multivariate Distributions
14(3)
1.4.1 Conditional Probabilities
15(1)
1.4.2 Correlation and Covariance
16(1)
1.5 The Central Limit Theorem
17(1)
1.6 Convolution Theorems
18(5)
References
21(2)
2 Introduction to Stochastic Processes
23(40)
2.1 Fluctuations and Non-determinism
23(1)
2.2 Noise
24(4)
2.3 Stochastic Process
28(2)
2.4 Markov Process
30(5)
2.4.1 Gaussian Process
31(1)
2.4.2 Wiener Process
32(2)
2.4.3 Poisson Process
34(1)
2.5 Microscopic Description of Stochastic Processes
35(5)
2.5.1 Stochastic Differential Equations
35(5)
2.6 Mesoscopic Description of Stochastic Processes
40(3)
2.6.1 Chapman-Kolmogorov Equation
40(3)
2.7 Macroscopic Description of Stochastic Processes
43(13)
2.7.1 The Master Equation
43(5)
2.7.2 The Fokker-Planck Equation
48(8)
2.8 Summary: Micro, Meso and Macroscopic Descriptions of a Stochastic Process
56(7)
References
59(4)
Part II Stochastic Modelling for Dispersal and Movement
3 Microscopic, Mesoscopic and Macroscopic Descriptions of Dispersal
63(50)
3.1 The Diffusion Equation
65(13)
3.1.1 Macroscopic Derivation
66(4)
3.1.2 Mesoscopic Derivation
70(2)
3.1.3 Microscopic Derivation: Langevin's Approach
72(3)
3.1.4 Fundamental Solution and Statistics
75(2)
3.1.5 Pathologies of the Diffusion Equation
77(1)
3.2 Persistent Motion
78(9)
3.2.1 The Telegrapher's Equation
78(6)
3.2.2 Langevin Approach to Persistent Motion
84(3)
3.3 Intermittent Motion
87(7)
3.3.1 Combination of Diffusion with Pauses
88(4)
3.3.2 Combination of Diffusion with Ballistic Displacements *
92(2)
3.4 Externally-Directed Movement
94(8)
3.4.1 Chemotaxis
94(2)
3.4.2 Animal Grouping *
96(6)
3.5 Dispersal in Two and Three Dimensions
102(11)
3.5.1 Diffusion Equations in Two and Three Dimensions
103(2)
3.5.2 Correlated Dispersal and Turn Angle Distributions
105(4)
References
109(4)
4 Anomalous Diffusion and Continuous-Time Random Walks
113(36)
4.1 What Does Anomalous Mean?
113(2)
4.2 General Mechanisms of Anomalous Diffusion
115(6)
4.2.1 Long-Range Correlations
116(2)
4.2.2 Non-identical Displacements
118(1)
4.2.3 Displacements with Non-finite Mean or Variance
119(2)
4.3 Diffusion on Fractals
121(3)
4.4 Levy Flights and Levy Walks
124(3)
4.5 Continuous-Time Random Walks
127(14)
4.5.1 Random Jump Lengths: Position of a Random Walk
127(2)
4.5.2 Random Waiting Times
129(2)
4.5.3 Formulation of Continuous-Time Random Walks
131(4)
4.5.4 CTRWs and Anomalous Diffusion *
135(2)
4.5.5 Macroscopic Limit *
137(2)
4.5.6 Large Waiting Times and Subdiffusion *
139(1)
4.5.7 Large Distance Jumps and Superdiffusion *
140(1)
4.6 Random Velocity Models
141(8)
4.6.1 Velocity Models and Anomalous Diffusion *
144(2)
References
146(3)
5 Reaction-Dispersal Models and Front Propagation
149(28)
5.1 Reaction-Diffusion
150(2)
5.2 Reaction-Telegrapher's Equation
152(1)
5.3 Reaction-Correlated Random Walks
153(2)
5.4 Reaction-Dispersal Models
155(5)
5.4.1 Discrete-Time Models
155(1)
5.4.2 Continuous-Time Models *
156(2)
5.4.3 Including Life Statistics
158(2)
5.5 Front Propagation
160(17)
5.5.1 Determination of the Front Speed
162(1)
5.5.2 Reaction-Diffusion Fronts
163(4)
5.5.3 Reaction-Dispersal Fronts *
167(8)
References
175(2)
6 Random Search Strategies
177(32)
6.1 Mean First-Passage Time
180(10)
6.1.1 Diffusion
180(3)
6.1.2 Persistent Motion
183(3)
6.1.3 Intermittent Searches
186(4)
6.2 Selective Target Detection
190(4)
6.3 The Extensive-Intensive Search Tradeoff
194(15)
References
203(6)
Part III Selected Applications
7 Cell Motility
209(36)
7.1 Key Physical Factors of Cell Motion
210(3)
7.1.1 Motion Mechanisms
210(1)
7.1.2 Substrate and Cell Density
211(1)
7.1.3 Size
212(1)
7.1.4 Shape
213(1)
7.2 Analysis of Individual Cell Trajectories
213(9)
7.2.1 Velocity Distributions
214(2)
7.2.2 Velocity Correlations
216(1)
7.2.3 Mean Square Displacement
216(2)
7.2.4 Kurtosis
218(1)
7.2.5 Turn Angle Distributions
219(1)
7.2.6 Angle Correlations
220(1)
7.2.7 Run and Tumble
221(1)
7.3 Microscopic Descriptions of Cell Motility
222(7)
7.3.1 The OU Process and Its Extensions
222(4)
7.3.2 Passing to the Cell's Frame of Reference *
226(3)
7.4 Mesoscopic Descriptions of Cell Motility
229(8)
7.4.1 Run and Tumble with Turn Angle Distributions *
230(2)
7.4.2 The Velocity Jump Model *
232(2)
7.4.3 Two-Dimensional Random Velocity Models *
234(3)
7.5 Summary: Cell Motion and Superdiffusion
237(8)
References
241(4)
8 Biological Invasions
245(22)
8.1 Estimating Dispersal Kernels and Diffusion Coefficients from Data
246(6)
8.1.1 Non-parametric Estimator from 1D Dispersal Data
248(1)
8.1.2 Non-parametric Estimator from 1D Density Data
249(1)
8.1.3 Non-parametric Estimator from 2D Dispersal Data
250(1)
8.1.4 Non-parametric Estimator from 2D Density Data
250(1)
8.1.5 Estimation of the Diffusion Coefficient
251(1)
8.2 Estimating the Waiting-Time PDF and the Intrinsic Growth Rate from Data
252(1)
8.2.1 Non-parametric Estimator from Life-Tables
252(1)
8.3 Case Examples
253(8)
8.3.1 House-Finch Invasion
253(2)
8.3.2 Muskrat Invasion
255(2)
8.3.3 Sea Otter Invasion
257(2)
8.3.4 Grey Squirrel Invasion
259(2)
8.4 Age-Structured Models and Plant Invasions
261(6)
References
265(2)
9 Biological Searches and Random Animal Motility
267(22)
9.1 Experiments in the Field
269(9)
9.1.1 Levy Patterns in Marine Predators: Knowing When but Not Why
269(1)
9.1.2 Displaced Honey Bees: Where Is Home?
270(1)
9.1.3 Seabirds and Fishery Discards
271(4)
9.1.4 Human Random Searches in a Soccer Field
275(3)
9.2 Experiments in the Lab
278(11)
9.2.1 Ants Search Strategies in Interrumpted Tandem Runs
278(1)
9.2.2 Desert Locusts: Run, Pause, and Tumble
279(4)
9.2.3 Pattern Formation in Mussels
283(1)
9.2.4 Cell Searching Without External Signals
284(1)
References
285(4)
A Mathematical and Numerical Tools
289(16)
A.1 Taylor Series
289(2)
A.2 Dirac Delta Function
291(1)
A.3 Fourier Transform
292(1)
A.4 Laplace Transform
293(2)
A.5 Numerical Implementation of Langevin Equations
295(1)
A.6 Method of Characteristics
296(2)
A.7 Determination of the Moments for a 2D Model with Random Turn Angles
298(3)
A.8 Rice's Method
301(4)
References
303(2)
Index 305