The book "Spatial Ecology via Reaction-Diffusion Equations" by Robert Stephen Cantrell and Chris Cosner, published as part of the Wiley Series in Mathematical and Computational Biology, explores the integration of mathematical and computational methods into biological research. The authors focus on reaction-diffusion equations as a tool to understand how spatial effects influence population dynamics and community structure. The book is structured to provide a comprehensive introduction to the subject, covering both ecological modeling and mathematical theory. Key topics include: - **Introduction**: Discusses the importance of spatial effects in ecology and the role of reaction-diffusion equations in modeling population dynamics. - **Nonspatial Models for a Single Species**: Introduces linear and logistic models for population growth, including density-dependent and Allee effect models. - **Nonspatial Models for Interacting Species**: Examines Lotka-Volterra models for competition, mutualism, and predator-prey interactions. - **Spatial Models**: Focuses on reaction-diffusion models, their derivation, and applications in understanding persistence, coexistence, and extinction of populations. - **Mathematical Background**: Provides essential mathematical tools such as dynamical systems, partial differential equations, and functional analysis. - **Applications**: Applies the theory to specific ecological scenarios, including habitat fragmentation, edge effects, and nonmonotone systems. The book aims to bridge the gap between theoretical ecology and mathematical biology, providing a rigorous and accessible treatment of the subject. It is intended for researchers and students in both fields, offering both ecological insights and mathematical rigor.The book "Spatial Ecology via Reaction-Diffusion Equations" by Robert Stephen Cantrell and Chris Cosner, published as part of the Wiley Series in Mathematical and Computational Biology, explores the integration of mathematical and computational methods into biological research. The authors focus on reaction-diffusion equations as a tool to understand how spatial effects influence population dynamics and community structure. The book is structured to provide a comprehensive introduction to the subject, covering both ecological modeling and mathematical theory. Key topics include: - **Introduction**: Discusses the importance of spatial effects in ecology and the role of reaction-diffusion equations in modeling population dynamics. - **Nonspatial Models for a Single Species**: Introduces linear and logistic models for population growth, including density-dependent and Allee effect models. - **Nonspatial Models for Interacting Species**: Examines Lotka-Volterra models for competition, mutualism, and predator-prey interactions. - **Spatial Models**: Focuses on reaction-diffusion models, their derivation, and applications in understanding persistence, coexistence, and extinction of populations. - **Mathematical Background**: Provides essential mathematical tools such as dynamical systems, partial differential equations, and functional analysis. - **Applications**: Applies the theory to specific ecological scenarios, including habitat fragmentation, edge effects, and nonmonotone systems. The book aims to bridge the gap between theoretical ecology and mathematical biology, providing a rigorous and accessible treatment of the subject. It is intended for researchers and students in both fields, offering both ecological insights and mathematical rigor.