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Bibliografická citace

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BK
Chichester : John Wiley & Sons, c2003
xiii,411 s. : il. ; 25 cm

objednat
ISBN 0-471-49301-5 (váz.)
Wiley series in mathematical and computational biology
Obsahuje předmluvy, rejstřík
Bibliografie: s. [395]-408
Ekologie prostorová - modelování matematické - studie
000103544
Contents // Preface... ix // Series Preface ...xiii // 1 Introduction ... 1 // 1.1 Introductory Remarks... 1 // 1.2 Nonspatial Models for a Single Species... 3 // 1.3 Nonspatial Models For Interacting Species... 8 // 1.3.1 Mass-Action and Lotka-Volterra Models... 8 // 1.3.2 Beyond Mass-Action: The Functional Response... 9 // 1.4 Spatial Models: A General Overview... 12 // 1.5 Reaction-Diffusion Models ... 19 // 1.5.1 Deriving Diffusion Models ... 19 // 1.5.2 Diffusion Models Via Interacting Particle Systems: The Importance // of Being Smooth... 24 // 1.5.3 What Can Reaction-Diffusion Models Tell Us?... 28 // 1.5.4 Edges, Boundary Conditions, and Environmental Heterogeneity ... 30 // 1.6 Mathematical Background... 33 // 1.6.1 Dynamical Systems ... 33 // 1.6.2 Basic Concepts in Partial Differential Equations: An Example ... 45 // 1.6.3 Modern Approaches to Partial Differential Equations: Analogies // with Linear Algebra and Matrix Theory ... 50 // 1.6.4 Elliptic Operators: Weak Solutions, State Spaces, and Mapping // Properties... 53 // 1.6.5 Reaction-Diffusion Models as Dynamical Systems... 72 // 1.6.6 Classical Regularity Theory for Parabolic Equations... 76 // 1.6.7 Maximum Principles and Monotonicity... 78 // 2 Linear Growth Models for a Single Species: Averaging Spatial Effects Via // Eigenvalues... 89 // 2.1 Eigenvalues, Persistence, and Scaling in Simple Models... 89 // 2.1.1 An Application: Species-Area Relations ... 91 // 2.2 Variational Formulations of Eigenvalues: Accounting
for Heterogeneity . . 92 // 2.3 Effects of Fragmentation and Advection/Taxis in Simple Linear Models . . 102 // 2.3.1 Fragmentation ...102 // 2.3.2 Advection/Taxis ...104 // 2.4 Graphical Analysis in One Space Dimension...107 // 2.4.1 The Best Location for a Favorable Habitat Patch...107 // 2.4.2 Effects of Buffer Zones and Boundary Behavior...112 // 2.5 Eigenvalues and Positivity...117 // 2.5.1 Advective Models...119 // 2.5.2 Time Periodicity...123 // 2.5.3 Additional Results on Eigenvalues and Positivity ...125 // 2.6 Connections with Other Topics and Models...126 // 2.6.1 Eigenvalues, Solvability, and Multiplicity ...126 // 2.6.2 Other Model Types: Discrete Space and Time...127 // Appendix...130 // 3 Density Dependent Single-Species Models...141 // 3.1 The Importance of Equilibria in Single Species Models...141 // 3.2 Equilibria and Stability: Sub- and Supersolutions...144 // 3.2.1 Persistence and Extinction...144 // 3.2.2 Minimal Patch Sizes...146 // 3.2.3 Uniqueness of Equilibria...148 // 3.3 Equilibria and Scaling: One Space Dimension...151 // 3.3.1 Minimum Patch Size Revisited...151 // 3.4 Continuation and Bifurcation of Equilibria...159 // 3.4.1 Continuation...159 // 3.4.2 Bifurcation Results...164 // 3.4.3 Discussion and Conclusions...173 // 3.5 Applications and Properties of Single Species Models...175 // 3.5.1 How Predator Incursions Affect Critical Patch Size...175 // 3.5.2 Diffusion and Allee Effects...178 // 3.5.3 Properties of Equilibria ...182 // 3.6 More General
Single Species Models...185 // Appendix...193 // 4 Permanence...199 // 4.1 Introduction...199 // 4.1.1 Ecological Overview...199 // 4.1.2 ODE Models as Examples...202 // 4.1.3 A Little Historical Perspective...211 // 4.2 Definition of Permanence...213 // 4.2.1 Ecological Permanence...214 // 4.2.2 Abstract Permanence...216 // 4.3 Techniques for Establishing Permanence...217 // 4.3.1 Average Lyapunov Function Approach...218 // 4.3.2 Acyclicity Approach...219 // 4.4 Invasibility Implies Coexistence...220 // 4.4.1 Acyclicity and an ODE Competition Model...221 // 4.4.2 A Reaction-Diffusion Analogue...224 // 4.4.3 Connection to Eigenvalues...228 // 4.5 Permanence in Reaction-Diffusion Models for Predation...231 // 4.6 Ecological Permanence and Equilibria...239 // 4.6.1 Abstract Permanence Implies Ecological Permanence...239 // 4.6.2 Permanence Implies the Existence of a Componentwise Positive // Equilibrium...240 // Appendix...241 // 5 Beyond Permanence: More Persistence Theory ...245 // 5.1 Introduction...245 // 5.2 Compressi vity...246 // 5.3 Practical Persistence...252 // 5.4 Bounding Transient Orbits...261 // 5.5 Persistence in Nonautonomous Systems...265 // 5.6 Conditional Persistence...278 // 5.7 Extinction Results...284 // Appendix...290 // 6 Spatial Heterogeneity in Reaction-Diffusion Models...295 // 6.1 Introduction...295 // 6.2 Spatial Heterogeneity within the Habitat Patch...305 // 6.2.1 How Spatial Segregation May Facilitate Coexistence...308 // 6.2.2 Some Disparities Between
Local and Global Competition...312 // 6.2.3 Coexistence Mediated by the Shape of the Habitat Patch...316 // 6.3 Edge Mediated Effects...318 // 6.3.1 A Note About Eigenvalues ...319 // 6.3.2 Competitive Reversals Inside Ecological Reserves Via External // Habitat Degradation: Effects of Boundary Conditions...321 // 6.3.3 Cross-Edge Subsidies and the Balance of Competition in Nature // Preserves...329 // 6.3.4 Competition Mediated by Pathogen Transmission...335 // 6.4 Estimates and Consequences...340 // Appendix...344 // 7 Nonmonotone Systems...351 // 7.1 Introduction...351 // 7.2 Predator Mediated Coexistence ...356 // 7.3 Three Species Competition...364 // 7.3.1 How Two Dominant Competitors May Mediate the Persistence of // an Inferior Competitor...364 // 7.3.2 The May-Leonard Example Revisited...373 // 7.4 Three Trophic Level Models...378 // Appendix...386 // References...395 // Index // 409

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