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