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How can the future number of deer, agricultural pests, or cod be calculated based on the present number of individuals and their age distribution? How long will it take for a viral outbreak in a particular city to reach another city five hundred miles away? In addressing such basic questions, ecologists today are as likely to turn to complicated differential equations as to life histories - a dramatic change from thirty years ago. Population ecology is the mathematical backbone of ecology. Here, two leading experts provide the underlying quantitative concepts that all modern-day ecologists need. John Vandermeer and Deborah Goldberg show that populations are more than simply collections of individuals. Complex variables such as the size distribution of individuals and allotted territory for expanding groups come into play when mathematical models are applied. The authors build these models from the ground up, from first principles, using a much broader range of empirical examples - from plants to animals, from viruses to humans - than do standard texts. And they address several complicating issues such as age-structured populations, spatially distributed populations, and metapopulations. Beginning with a review of elementary principles, the book goes on to consider theoretical issues involving life histories, complications in the application of the core principles, statistical descriptions of spatial aggregation of individuals and populations as well as population dynamic models incorporating spatial information, and introductions to two-species interactions. Complemented by superb illustrations that further clarify the links between the mathematical models and biology, "Population Ecology" is the most straightforward and authoritative overview of the field to date. It will have broad appeal among undergraduates, graduate students, and practicing ecologists.
List of Figures xi
List of Tables xvii
Preface xix
CHAPTER 1: Elementary Population Dynamics 1 Density Independence: The Exponential Equation 3 Density Dependence: Intraspecific Competition 10 The Logistic Equation 14 The Yield-Density Relationship 21 Density Dependence and Mortality: Thinning Laws 26
CHAPTER 2: Life History Analysis 35 Investment in Survivorship versus Reproduction: The r, K Continuum 37 Cost of Reproduction 41 Optimal Reproductive Schedules 44
CHAPTER 3: Projection Matrices: Structured Models 51 Elementary Population Projection Matrices 52 Non-age Structure: Stage Projection Matrices 62 Eigenvectors, Reproductive Value, Sensitivity, and Elasticity 69 Applications of Population Projection Matrices 73 The Dalls Mountain Sheep: A Static Life Table 74 Palo de Mayo: A Dynamic Life Table 75 The American Beech: Testing Hypotheses with Dynamic Life Tables 77 Density Dependence in Structured Populations 80 Density Dependence in a Simple Age-Structured Model 81 Density Dependence in Size-Distributed Populations 84 Density Dependence in a Stage-Structured Model 92 Appendix A. Basic Matrix Manipulations 94
CHAPTER 4: A Closer Look at the "Dynamics" in Population Dynamics 101 Intuitive Ideas of Equilibrium and Stability 103 Eigenvalues: A Key Concept in Dynamic Analysis 114 Basic Concepts of Equilibrium and Stability in One-Dimensional Maps 120 The One-Dimensional Map 121 Stability and Equilibrium in the Logistic Map 130 Basins of Attraction in the Logistic Map 133 Structural Stability 135 Bifurcation Diagrams 142 Concluding Remarks 149
CHAPTER 5: Patterns in Space and Metapopulations 155 The Poisson Distribution 158 The Question of Scale 163 Metapopulations 167 Assumptions of Metapopulation Models 171 The Rescue Effect and Propagule Rain 173
CHAPTER 6: Predator-Prey (Consumer-Resource) Interactions 177 Predator-Prey Interactions: First Principles 179 Density Dependence 185 Functional Response 186 Functional Response and Density Dependence Together 193 Paradoxes in Applications of Predator-Prey Theory 195 Predator-Prey Dynamics: A Graphical Approach 198 Predator-Prey Interactions in Discrete Time 205
CHAPTER 7: Epidemiology 209 Direct Disease Transmission 210 Indirect Disease Transmission 217
CHAPTER 8: Competition and a Little Bit of Mutualism 221 Competition: First Principles 222 The Competitive Production Principle: Applications of Competition Theory to Agriculture 234 Mutualism 235 Competition: The Details 240
CHAPTER 9: What This Book Was About 255
Glossary 261
References 265
Index 273
John H. Vandermeer is Margaret Davis Collegiate Professor of Ecology and Evolutionary Biology at the University of Michigan. He is the author of several books, including Breakfast of Biodiversity and Reconstructing Biology.
Deborah E. Goldberg is Professor of Ecology and Evolutionary Biology at the University of Michigan. She has published widely in journals such as Ecology, American Naturalist, and the Journal of Ecology and is currently interim director of the University of Michigan Herbarium.
"Amidst the recent plethora of undergraduate books on population ecology emerges this superbly crafted volume [...] What distinguishes this from most of its predecessors is an uncommon breadth of subject matter [...] a fine balance between patronizing the knowledgeable reader and overwhelming the interested novice, and a highly commendable means by which the information is communicated. Following an impressive range of topics in the opening chapter is one of the best-written introductions to the life history theory that this reviewer has encountered in 20 years of research on the topic."
– Choice
"What distinguishes this book from others in the field is the diverse array of topics covered that are rarely or only cursorily treated in other books [...] What I enjoyed most about this book were the frequent discussions on the ecological interpretation of the mathematical results and the corresponding caveats [...] 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
