Note: Intro -- Dispersal, Individual Movement and Spatial Ecology -- A Mathematical Perspective -- Foreword -- References -- Preface -- Contents -- Part I Individual Animal Movement -- Stochastic Optimal Foraging Theory -- 1 Introduction -- 2 Some Preliminary Assumptions of the Model -- 3 Calculation of < -- L> -- and < -- |l|> -- -- 4 Discrete Space Calculation -- 5 Lévy Random Searchers -- 6 Search Diffusivity -- 6.1 Characterizing First-Passage-Time Diffusivity -- 6.2 Characterizing Search Dynamics Diffusivity -- 7 Search in Heterogeneous Landscapes: Distributions of Starting Points -- 8 Discussion -- References -- Lévy or Not? Analysing Positional Data from Animal Movement Paths -- 1 Introduction -- 1.1 Lévy Walks -- 1.2 Correlated Random Walks and Composite Strategies -- 1.3 Determining Movement Processes from Observational Data -- 2 Sampling and Processing of Movement Path Data -- 2.1 Discrete Time Sampling -- 2.2 Identification of Turning Points -- 3 Analysing Data from a Composite Correlated Random Walk -- 3.1 The Composite Correlated Random Walk Model -- 3.2 Fitting a Composite Exponential Distribution -- 3.3 Testing Step Length Data -- 3.4 Testing Uniformity of Turning Angles -- 4 Discussion -- References -- Beyond Optimal Searching: Recent Developments in the Modelling of Animal Movement Patterns as Lévy Walks -- 1 Introduction -- 2 Underlying Mechanisms: The Key to Prediction and Understanding -- 2.1 Serial Correlation -- 2.2 Random Reorientation at Cues Left by Correlated Random Walkers -- 2.3 Lévy Walks as by Products of Advantageous Foraging Behaviours -- 2.4 Innate Physiology -- 3 Translating Observations Taken at Small Spatiotemporal Scales into Expected Patterns at Greater Scales -- 4 Enlarging the Framework of Lévy Walk Search Theory -- 4.1 Balancing the Demands of Foraging and Safety from Predation -- 4.2 Red Queen Dynamics. , 4.3 Intermittent Searches -- 4.4 Optimizing the Encounter Rate in Biological Interactions -- 5 Some Closing Remarks and Some Open Questions -- 5.1 Opening the Lévy Gates -- 5.2 Lévy Walks in Collective Motions: How the Blind Could Lead the Blind -- 5.3 Mathematical Challenges -- References -- Part II From Individuals to Populations -- The Mathematical Analysis of Biological Aggregation and Dispersal: Progress, Problems and Perspectives -- 1 Introduction -- 2 An Overview of Population-Level Descriptions -- 2.1 A Summary of the Levels of Description -- 2.2 The Fokker-Planck and Smoluchowski Equations -- 2.3 Interacting Particles, Liouville's Equation and Reduced Descriptions -- 3 Simple and Reinforced Random Walks in Space -- 3.1 The Pearson Random Walk -- 3.2 The General Evolution Equation for Space-Jump or Kangaroo Processes -- 3.3 The Evolution of Spatial Moments for General Kernels -- 3.4 The Effects of Long Waits or Large Jumps -- 3.5 Biased Jumps Dependent on Gradients or Internal Dynamics -- 3.6 Aggregation in Reinforced Random Walks -- 4 Velocity Jump Processes and Taxis Equations -- 4.1 The General Velocity-Jump Process -- 4.2 The Telegraph Process -- 4.3 Reduction of the VJ Process to a Diffusion Process -- 4.4 The Role of Internal Dynamics -- 4.5 Macroscopic Descriptions of Eukaryotic Cell Movement -- 5 Discussion -- References -- Hybrid Modelling of Individual Movement and Collective Behaviour -- 1 Introduction -- 2 Continuum vs. Agent-Based Models -- 2.1 Agent-Based Modelling -- 3 Hybrid Modelling: Theoretical Framework -- 3.1 A Position-Based Hybrid Model -- 3.2 Initial and Boundary Conditions -- 4 Hybrid Modelling: Numerical Implementation -- 4.1 Spatial Matching in Numerical Simulations -- 4.2 Other Aspects of Numerical Simulations -- 5 Case Study: Hybrid Modelling of Chemotaxis -- 5.1 The Keller-Segel Model. , 5.2 Hybrid Models of Chemotaxis -- 5.3 Analysis of the Dropout -- 6 Discussion -- References -- From Individual Movement Rules to Population Level Patterns: The Case of Central-Place Foragers -- 1 Introduction -- 2 Model Derivation -- 2.1 Population Dynamics -- 2.2 Individual Movement -- 2.2.1 Resource-Dependent Settling -- 2.2.2 Time-Dependent Settling -- 2.2.3 Prospect-Dependent Settling -- 2.2.4 Nondimensionalization -- 3 Effects of Movement Rules on Persistence -- 4 Effects of Movement Rules on Stability -- 4.1 Resource-Dependent Settling -- 4.2 Time-Dependent Settling -- 4.3 Prospect-Dependent Settling -- 5 Discussion -- References -- Transport and Anisotropic Diffusion Models for Movement in Oriented Habitats -- 1 Introduction -- 1.1 Biological Motivation -- 1.2 Mathematical Modelling -- 2 Transport Equations -- 2.1 Movement in an Oriented Environment -- 2.2 Environmental Distributions -- 3 The Parabolic Scaling -- 3.1 Motivation of the Parabolic Limit -- 3.2 Parabolic Limit in an Oriented Landscape -- 4 The Hyperbolic Scaling -- 5 The Moment Approach -- 5.1 Moment Closure -- 5.2 Fast Flux Relaxation -- 6 Comparison Between Scalings -- 6.1 Relationships Between Limit Equations -- 6.2 Assumptions Behind Limit Equations -- 7 Examples and Applications -- 7.1 Bidirectional and Nondirectional Environments -- 7.1.1 Isotropic Diffusion: The Pearson Walk -- 7.1.2 Anisotropic Diffusion Example -- 7.1.3 Steady States -- 7.1.4 Application to Seismic Line Following -- 7.2 Unidirectional Environments -- 7.2.1 Anisotropic Diffusion-Drift Example -- 7.2.2 Relation to Haptotaxis and Chemotaxis -- 7.3 Singular Distributions -- 7.3.1 Strictly Bidirectional: Degenerate Diffusion -- 7.3.2 Strictly Unidirectional: Relation to ODEs -- 7.4 Life in a Stream -- 8 Discussion -- 9 Moments of von Mises Distributions -- 9.1 Unimodal von Mises Distribution. , 9.2 Bimodal von Mises Distribution -- 10 Numerical Methods -- 10.1 Simulations of Transport Model -- 10.2 Simulations of Macroscopic Models -- References -- Incorporating Complex Foraging of Zooplankton in Models: Role of Micro- and Mesoscale Processes in Macroscale Patterns -- 1 Introduction -- 2 The Lagrangian vs. the Eulerian Approach in the Modelling of Zooplankton Dynamics -- 3 Modelling and Scaling the Zooplankton Functional Response -- 3.1 Defining the Zooplankton Functional Response in Real Ecosystems -- 3.2 Emergence of a Sigmoid (Holling Type III) Overall Zooplankton Functional Response -- 4 The Role of Intra-population Variability of Zooplankton in Population Persistence -- 4.1 Describing the Intra-population Variability of Zooplankton Grazers -- 4.2 Analysis of the Model of the Intra-population Variability of Zooplankton -- 5 Discussion and Conclusions -- Appendix 1 -- Appendix 2 -- References -- Part III Populations, Communities and Ecosystems -- Life on the Move: Modeling the Effects of Climate-Driven Range Shifts with Integrodifference Equations -- 1 Introduction -- 2 Is Further Better? -- 3 The Critical Range-Shift Speed -- 4 Numerical Approaches -- 5 Analytic Approximations -- 6 A Simple Example -- 7 A Simplifying Approximation -- 8 Realistic Kernels -- 8.1 Gaussian Distribution -- 8.2 Laplace Distribution -- 8.3 Cauchy Distribution -- 8.4 Modified Bessel Distribution -- 9 Discussion -- References -- Control of Competitive Bioinvasion -- 1 Introduction -- 2 A Competition-Diffusion Model with Annual Cycles and Random Extreme Events -- 2.1 Existence and Stability Ranges of Spatially Uniform Stationary Solutions -- 2.2 Annual Cycles of Growth, Harvesting and Diffusion -- 2.3 Random Extreme Events and Assisted Long-Distance Transport -- 2.4 Numerical Simulations I -- 3 A Competition-Diffusion Model with Infected Invader. , 3.1 Local Dynamics with Infection -- 3.2 Spatiotemporal Dynamics with Infection -- 3.3 Numerical Simulations II -- 4 Concluding Remarks -- References -- Destruction and Diversity: Effects of Habitat Loss on Ecological Communities -- 1 Introduction -- 2 The Ecological Model -- 2.1 The Single-Species Model -- 2.2 Two Independent Populations -- 2.3 Competition: Two Competing Species -- 2.4 Competition: More Than Two Competing Species -- 2.5 Predation -- 2.6 Food Chains -- 2.7 Mutualism -- 2.8 A Simple Food Web -- 2.9 Heterogeneity -- 3 Discussion -- References -- Emergence and Propagation of Patterns in Nonlocal Reaction-Diffusion Equations Arising in the Theory of Speciation -- 1 Speciation Theory and Nonlocal Reaction-Diffusion Equations -- 2 Spectrum of the Operator Linearized about a Stationary Solution -- 2.1 Equation (3) -- 2.2 Equation (4) -- 2.3 Essential Spectrum of the Operator Linearized about a Wave -- 3 Nonlinear Stability -- 3.1 An Abstract Theorem on Stability of Stationary Solutions -- 3.2 Stability of the Homogeneous Solution -- 3.3 Stability of Waves -- 3.4 Numerical Examples -- 4 Discussion -- References -- Numerical Study of Pest Population Size at Various Diffusion Rates -- 1 Introduction -- 1.1 Spatial Heterogeneity and the Effect of Diffusion -- 1.2 Goals and the Road Map -- 2 Numerical Integration on Coarse Grids: The Problem Outline -- 2.1 The Method -- 3 Simulation Data -- 3.1 Estimating Pest Population Size on Coarse Grids: Numerical Test Cases -- 4 The Impact of the Diffusion Rates on the Accuracy of Numerical Integration -- 4.1 Uniform Grid -- 4.2 The Analysis of the Grid Step Size for Ecological Distributions -- 4.3 Arbitrary Location of the Peak on a Uniform Coarse Grid -- 5 Nonuniform Grid -- 6 Discussion and Conclusions -- References -- LECTURE NOTES IN MATHEMATICS.

Note: Cover -- Title -- Copyright -- Preface -- Contents -- List of Figures -- Chapter 1: Introduction -- Chapter 2: Models of biological invasion -- Chapter 3: Basic methods and relevant examples -- Chapter 4: Single-species models -- Chapter 5: Density-dependent diffusion -- Chapter 6: Models of interacting populations -- Chapter 7: Some alternative and complementary approaches -- Chapter 8: Ecological examples and applications -- Chapter 9: Appendix: Basic background mathematics -- References -- Index.

Note: Cover -- Half Title -- Title Page -- Copyright Page -- Original Title Page -- Dedication Page -- Supplementary Resources Disclaimer -- Preface -- Table of Contents -- I Introduction -- 1 Ecological patterns in time and space -- 1.1 Local structures -- 1.2 Spatial and spatiotemporal structures -- 2 An overview of modeling approaches -- II Models of temporal dynamics -- 3 Classical one population models -- 3.1 Isolated populations models -- 3.1.1 Scaling -- 3.2 Migration models -- 3.2.1 Harvesting -- 3.3 Glance at discrete models -- 3.4 Peek into chaos -- 4 Interacting populations -- 4.1 Two-species prey-predator population model -- 4.2 Classical Lotka-Volterra model -- 4.2.1 More on prey-predator models -- 4.2.2 Scaling -- 4.3 Other types of population communities -- 4.3.1 Competing populations -- 4.3.2 Symbiotic populations -- 4.3.3 Leslie-Gower model -- 4.3.4 Classical Holling-Tanner model -- 4.3.5 Other growth models -- 4.3.6 Models with prey switching -- 4.4 Global stability -- 4.4.1 General quadratic prey-predator system -- 4.4.2 Mathematical tools for analyzing limit cycles -- 4.4.3 Routh-Hurwitz conditions -- 4.4.4 Criterion for Hopf bifurcation -- 4.4.5 Instructive example -- 4.4.6 Poincaré map -- 4.5 Food web -- 4.6 More about chaos -- 4.7 Age-dependent populations -- 4.7.1 Prey-predator, age-dependent populations -- 4.7.2 More about age-dependent populations -- 4.7.3 Simulations and brief discussion -- 5 Case study: biological pest control in vineyards -- 5.1 First model -- 5.1.1 Modeling the human activity -- 5.2 More sophisticated model -- 5.2.1 Models comparison -- 5.3 Modeling the ballooning effect -- 5.3.1 Spraying effects and human intervention -- 5.3.2 Ecological discussion -- 6 Epidemic models -- 6.1 Basic epidemic models -- 6.1.1 Simplest models -- 6.1.2 Standard incidence -- 6.2 Other classical epidemic models. , 6.3 Age- and stage-dependent epidemic system -- 6.4 Case study: Aujeszky disease -- 6.5 Analysis of a disease with two states -- 7 Ecoepidemic systems -- 7.1 Prey-diseased-predator interactions -- 7.1.1 Some biological considerations -- 7.2 Predator-diseased-prey interactions -- 7.3 Diseased competing species models -- 7.3.1 Simulation discussion -- 7.4 Ecoepidemics models of symbiotic communities -- 7.4.1 Disease effects on the symbiotic system -- 7.4.2 Disease control by use of a symbiotic species -- III Spatiotemporal dynamics and pattern formation: deterministic approach -- 8 Spatial aspect: diffusion as a paradigm -- 9 Instabilities and dissipative structures -- 9.1 Turing patterns -- 9.1.1 Turing patterns in a multispecies system -- 9.2 Differential flow instability -- 9.3 Ecological example: semiarid vegetation patterns -- 9.3.1 Pattern formation due to nonlocal interactions -- 9.4 Concluding remarks -- 10 Patterns in the wake of invasion -- 10.1 Invasion in a prey-predator system -- 10.2 Dynamical stabilization of an unstable equilibrium -- 10.2.1 A bifurcation approach -- 10.2.2 Comparison of wave speeds -- 10.3 Patterns in a competing species community -- 10.4 Concluding remarks -- 11 Biological turbulence -- 11.1 Self-organized patchiness and the wave of chaos -- 11.1.1 Stability diagram and the hierarchy of regimes -- 11.1.2 Patchiness in a two-dimensional case -- 11.2 Spatial structure and spatial correlations -- 11.2.1 Intrinsic lengths and scaling -- 11.3 Ecological implications -- 11.3.1 Plankton patchiness on a biological scale -- 11.3.2 Self-organized patchiness, desynchronization, and the paradox of enrichment -- 11.4 Concluding remarks -- 12 Patchy invasion -- 12.1 Allee effect, biological control, and one-dimensional patterns of species invasion -- 12.1.1 Patterns of species spread. , 12.2 Invasion and control in the two-dimensional case -- 12.2.1 Properties of the patchy invasion -- 12.3 Biological control through infectious diseases -- 12.3.1 Patchy spread in SIR model -- 12.4 Concluding remarks -- IV Spatiotemporal patterns and noise -- 13 Generic model of stochastic population dynamics -- 14 Noise-induced pattern transitions -- 14.1 Transitions in a patchy environment -- 14.1.1 No noise -- 14.1.2 Noise-induced pattern transition -- 14.2 Transitions in a uniform environment -- 14.2.1 Standing waves driven by noise -- 15 Epidemic spread in a stochastic environment -- 15.1 Model -- 15.2 Strange periodic attractors in the lytic regime -- 15.3 Local dynamics in the lysogenic regime -- 15.4 Deterministic and stochastic spatial dynamics -- 15.5 Local dynamics with deterministic switch from lysogeny to lysis -- 15.6 Spatiotemporal dynamics with switches from lysogeny to lysis -- 15.6.1 Deterministic switching from lysogeny to lysis -- 15.6.2 Stochastic switching -- 16 Noise-induced pattern formation -- References -- Index.