Spatial Ecology via Reaction-Diffusion Equations

Robert Stephen Cantrell is the author of Spatial Ecology via Reaction-Diffusion Equations, published by Wiley. Chris Cosner is the author of Spatial Ecology via Reaction-Diffusion Equations, published by Wiley.

"…particularly attractive and useful for graduate students and other researchers who are interested in studying applications of reaction-diffusion theory to spatial ecology." (Mathematical Reviews, Issue 2007a) "…I would recommend this book to anyone who wants a well supported journey into the modern theory of partial differential equations and dynamic systems…" (The Mathematical Gazette, March 2005)

• 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.