Spatial Ecology via Reaction-Diffusion Equations

Preface.

Series Preface.

1 Introduction.

1.1 Introductory Remarks.

1.2 Nonspatial Models for a Single Species.

1.3 Nonspatial Models For Interacting Species.

1.4 Spatial Models: A General Overview.

1.5 Reaction-Diffusion Models.

1.6 Mathematical Background.

2 Linear Growth Models for a Single Species: Averaging Spatial Effects Via Eigenvalues.

2.1 Eigenvalues, Persistence, and Scaling in Simple Models.

2.2 Variational Formulations of Eigenvalues: Accounting for Heterogeneity.

2.3 Effects of Fragmentation and Advection/Taxis in Simple Linear Models.

2.4 Graphical Analysis in One Space Dimension.

2.5 Eigenvalues and Positivity.

2.6 Connections with Other Topics and Models.

Appendix.

3 Density Dependent Single-Species Models.

3.1 The Importance of Equilibria in Single Species Models.

3.2 Equilibria and Stability: Sub- and Supersolutions.

3.3 Equilibria and Scaling: One Space Dimension.

3.4 Continuation and Bifurcation of Equilibria.

3.5 Applications and Properties of Single Species Models.

3.6 More General Single Species Models.

Appendix.

4 Permanence.

4.1 Introduction.

4.2 Definition of Permanence.

4.3 Techniques for Establishing Permanence.

4.4 Invasibility Implies Coexistence.

4.5 Permanence in Reaction-Diffusion Models for Predation.

4.6 Ecological Permanence and Equilibria.

Appendix.

5 Beyond Permanence: More Persistence Theory.

5.1 Introduction.

5.2 Compressivity.

5.3 Practical Persistence.

5.4 Bounding Transient Orbits.

5.5 Persistence in Nonautonomous Systems.

5.6 Conditional Persistence.

5.7 Extinction Results.

Appendix.

6 Spatial Heterogeneity in Reaction-Diffusion Models.

6.1 Introduction.

6.2 Spatial Heterogeneity within the Habitat Patch.

6.3 Edge Mediated Effects.

6.4 Estimates and Consequences.

Appendix.

7 Nonmonotone Systems.

7.1 Introduction.

7.2 Predator Mediated Coexistence.

7.3 Three Species Competition.

7.4 Three Trophic Level Models.

Appendix.

References.

Index.