360 Pages 7 Color & 63 B/W Illustrations
    by Chapman & Hall

    Exploring the relationship between mathematics and ecology, Spatial Ecology focuses on some important emerging challenges in the field. These challenges consist of understanding the impact of space on community structure, incorporating the scale and structure of landscapes into mathematical models, and developing connections between spatial ecology and evolutionary theory, epidemiology, and economics.

    The book begins with essays on how spatial effects influence the dynamics of populations and the structure of communities. It then discusses how spatial scale and structure and dispersal behavior connect to phenomena in population dynamics, evolution, epidemiology, and economics. Subsequent chapters focus on the interplay of ecology with evolution, epidemiology, and economics. The chapters on ecology and evolutionary theory provide a guided tour through a number of scenarios and modeling approaches that represent active areas of current research and suggest some paths toward conceptual unification. The book then illustrates how problems in epidemiology and ecology can be profitably addressed by similar modeling regimes. It concludes with essays that describe how ideas from economics, ecology, and quality control theory may be combined to address issues in natural resource management.

    With contributions from some of the best in the field, this volume promotes the advancement of ecology as a truly quantitative science, particularly as it touches on the role of space. The book will inspire readers to open up new areas of research in the mathematical theory of spatial ecology and its connections with evolutionary theory, epidemiology, and economics.

    Competition Dynamics in a Seasonally Varying Wetland Don L. DeAngelis, Joel C. Trexler, and Douglas D. Donalson

    Introduction

    Model

    Results

    Discussion

    Appendix

    Spatial Dynamics of Multi-Trophic Communities Priyanga Amarasekare

    Introduction

    Theoretical Framework

    Results

    Discussion and Conclusions

    Appendix: Spatial Models

    Bistability Dynamics in Structured Ecological Models Jifa Jiang and Junping Shi

    Non-Structured Models

    Diffusion Induced Bistability and Hysteresis

    Threshold Manifold

    Concluding Remarks

    Modeling Animal Movement with Diffusion Otso Ovaskainen and Elizabeth E. Crone

    Introduction

    Advection-Diffusion in Heterogeneous Environments

    Application: Wolf Movement in a Mountainous Landscape

    Applications of Diffusion Models

    Conclusions

    Riverine Landscapes: Ecology for an Alternative Geometry William F. Fagan, Evan H. Campbell Grant, Heather J. Lynch, and Peter J. Unmack

    Spatial Ecology

    Dendritic Landscapes

    Colonization and Extinction

    Metapopulation Model

    Extinction in Fishes

    Conclusion

    Biological Modeling with Quiescent Phases Karl P. Hadeler, Thomas Hillen, and Mark A. Lewis

    Introduction

    Diffusive Coupling and Quiescence

    Stationary States and Stability

    Periodic Orbits

    Rates Depending on Density

    Slow Dynamics

    Delay Equations

    Spread in Space

    Applications

    Discussion

    Spatial Scale and Population Dynamics in Advective Media Roger M. Nisbet, Kurt E. Anderson, Edward McCauley, and Ulrike Feudel

    Introduction

    Models

    Population Persistence and the Drift Paradox

    Response to Abiotic Forcing

    Directions for Future Research

    Using Multivariate State-Space Models to Study Spatial Structure and Dynamics Richard A. Hinrichsen and Elizabeth E. Holmes

    Introduction

    Multivariate State-Space Models

    Population Structure

    Parameter Estimation

    Model Selection

    Snake River Chinook

    Discussion

    Incorporating the Spatial Configuration of the Habitat into Ecology and Evolutionary Biology Ilkka Hanski

    Introduction

    Modeling Migration in Fragmented Landscapes

    Metapopulation Dynamics

    Metacommunity Dynamics of Competing Species

    Genetic and Evolutionary Dynamics

    Conclusion

    Metapopulation Perspectives on the Evolution of Species’ Niches Robert D. Holt and Michael Barfield

    Introduction

    Models for Adaptive Colonization into Sink Habitats

    An Island-Mainland Model with Infrequent Adaptive Colonization

    Gene Flow and Population Extinction

    A Metapopulation Model with Maladaptive Gene Flow

    Discussion

    Evolution of Dispersal in Heterogeneous Landscapes Robert Stephen Cantrell, Chris Cosner, and Yuan Lou

    Introduction

    Random Dispersal: Evolution of Slow Dispersal

    Random Dispersal vs Conditional Dispersal

    Evolution of Conditional Dispersal

    Dispersal and the Ideal Free Distribution

    Dispersal in Temporally Varying Environments

    Future Directions

    Evolution of Dispersal Scale and Shape in Heterogeneous Environments: A Correlation Equation Approach Benjamin M. Bolker

    Introduction

    Methods

    Results

    Discussion and Conclusions

    Spatiotemporal Dynamics of Measles: Synchrony and Persistence in a Disease Metapopulation Alun L. Lloyd and Lisa Sattenspiel

    Introduction

    Data Sources

    Local Dynamics: Periodicity and Endemic Fadeout

    Regional Persistence and Spatial Synchrony

    Spatial Synchrony among Large Population Centers

    Reinvasion Waves and Phase Relationships

    Discussion

    Rules of Thumb for the Control of Vector-Borne Diseases in a Spatial Environment Matthew D. Potts and Tristan Kimbrell

    Introduction

    Model Specification

    Results

    Discussion

    Conclusion

    Modeling Spatial Spread of Communicable Diseases Involving Animal Hosts Shigui Ruan and Jianhong Wu

    Introduction

    Rabies

    Dengue

    West Nile Virus

    Hantavirus

    Lyme Disease

    Feline Immunodeficiency Virus (FIV)

    Summary

    Economically Optimal Management of a Metapopulation James N. Sanchirico and James E. Wilen

    Spatial Ecology

    Optimization

    Optimal Spatial Dynamics

    Cost of Ignoring Spatial Processes

    Conclusion

    Models of Harvesting Donald B. Olson

    Introduction

    Basic Model Formulation

    Explicit Examples

    Conclusions

    Spatial Optimal Control of Renewable Resource Stocks Guillermo E. Herrera and Suzanne Lenhart

    Introduction

    ODE Models with Spatial Components

    PDE Models

    Conclusions

    References appear at the end of each chapter.

    Biography

    Robert Stephen Cantrell, Chris Cosner, and Shigui Ruan are all professors in the Department of Mathematics at the University of Miami, Coral Gables, Florida.