Spatial Ecology via Reaction-Diffusion Equations [Hardcover]

Many ecological phenomena may be modelled using apparently random processes involving space (and possibly time). Such phenomena are classified as spatial in their nature and include all aspects of pollution. This book addresses the problem of modelling spatial effects in ecology and population dynamics using reaction-diffusion models.
* Rapidly expanding area of research for biologists and applied mathematicians
* Provides a unified and coherent account of methods developed to study spatial ecology via reaction-diffusion models
* Provides the reader with the tools needed to construct and interpret models
* Offers specific applications of both the models and the methods
* Authors have played a dominant role in the field for years
Essential reading for graduate students and researchers working with spatial modelling from mathematics, statistics, ecology, geography and biology.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 Densl“.