Ecology is capturing the popular imagination like never before, with issues such as climate change, species extinctions, and habitat destruction becoming ever more prominent. This title provides an accessible mathematical foundation for the advances in ecology. It introduces students to the key literature in the field.

List of Figures xi List of Tables xvii Preface xix ONE Elementary Population Dynamics 1 Density Independence: The Exponential Equation 2 Density Dependence 9 The Logistic Equation 13 The Yield-Density Relationship 17 Density Dependence and Mortality: Thinning Laws 22 Density Dependence in Discrete Time Models 28 TWO Projection Matrices: Structured Models 30 Elementary Age-Structured Population Projection Matrices 30 Non-Age Structure: Stage Projection Matrices 39 Eigenvectors, Reproductive Value, Sensitivity, and Elasticity 45 Density Dependence in Structured Populations 48 Density Dependence in a Simple Age-Structured Model 48 Density Dependence in Size-Distributed Populations 50 Density Dependence in a Stage-Structured Model 56 Appendix: Basic Matrix Manipulations 57 Matrix Multiplication 57 Matrix Addition and Subtraction 58 The Identity Matrix 59 The Determinant of a Matrix 59 THREE Applications of Simple Population Models 62 Life History Analysis 63 Investment in Survivorship versus Reproduction: The r-K Continuum 64 The Cost of Reproduction 66 Optimal Reproductive Schedules 67 Applications of Population Projection Matrices 73 The Dall's Mountain Sheep: A Static Life Table 73 Palo de Mayo: A Dynamic Life Table 74 Population Viability Analysis 76 Demography of Invasive and Native Plant Populations 78 FOUR A Closer Look at the "Dynamics" in Population Dynamics 81 Intuitive Ideas of Equilibrium and Stability 83 Eigenvalues: A Key Concept in Dynamic Analysis 92 Basic Concepts of Equilibrium and Stability in One-Dimensional Maps 97 The One-Dimensional Map 98 Stability and Equilibrium in the Logistic Map 106 Basins of Attraction in the Logistic Map 108 Structural Stability 110 Bifurcation Diagrams 116 Concluding Remarks 122 FIVE Patterns and Dynamics in Space 126 The Poisson Distribution 129 Point Pattern Analysis and the Question of Scale 134 Mechanisms of Spatial Pattern Formation: Principles of Reaction/Diffusion 137 Mechanisms of Spatial Pattern Formation: Biological Causes 141 Metapopulations 142 Assumptions of Metapopulation Models 146 The Rescue Effect and Propagule Rain 148 Appendix: Data for Exercises 5.2, 5.3, and 5.4 150 SIX Predator-Prey (Consumer-Resource) Interactions 152 Predator-Prey Interactions: First Principles 153 Density Dependence 158 Functional Response 161 Functional Response and Density Dependence Together 166 Paradoxes in Applications of Predator-Prey Theory 168 Predator-Prey Dynamics: A Graphical Approach 170 Predator-Prey Interactions in Discrete Time 176 SEVEN Disease Ecology 187 Direct Disease Transmission 188 Indirect Transmission 194 EIGHT Competition 198 Competition: First Principles 199 Isocline Analysis of the Lotka-Volterra Competition Equations 203 Niches and Competitive Coexistence and Exclusion 209 The Competitive Production Principle: Applications of Competition Theory to Agriculture 211 Resource Competition 212 NINE Facilitation and Mutualism 225 TEN What This Book Was About 239 Glossary 243 References 247 Index 255

Praise for first edition:"Superbly crafted."--Choice Praise for first edition:"Vandermeer and Goldberg do an admirable job of explaining the ecological meaning and assumptions behind all of the mathematical results presented. They include many figures that illustrate their points clearly and these are accompanied with detailed verbal explanations."--Helen M. Regan, Ecology "As population ecology continues to grow and develop as a discipline, this book will serve as a useful text for undergraduate courses in population ecology or quantitative techniques, and will also serve as a handy resource for professionals."--Tyler M. Harms, Journal of Wildlife Management