Population Ecology: First Principles, Second Edition by Deborah E. Goldberg and John H. Vandermeer

2458207d0b5c1c6-261x361.jpg Author Deborah E. Goldberg and John H. Vandermeer
Isbn 978-0691160313
File size 22MB
Year 2013
Pages 288
Language English
File format PDF
Category biology


Population Ecology B Population Ecology First Principles Second Edition John H. Vandermeer Deborah E. Goldberg Princeton University Press Princeton and Oxford B Copyright © 2013 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW press.princeton.edu All Rights Reserved ISBN 978-0-691-16030-6 ISBN (pbk.) 978-0-691-16031-3 Library of Congress Control Number: 2013940462 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon LT Std with Gotham Narrow display by Princeton Editorial Associates Inc., Scottsdale, Arizona. Printed on acid-free paper ∞ Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 Dedicated to the memory of our colleague and dear friend Beverly Rathcke Contents 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 vii 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 viii Contents 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 Contents ix Figures 1.1 Graphs of equation 5 5 1.2 Plot of aphid data (from table 1.1) 7 1.3 Aphid data from figure 1.2 plotted arithmetically 8 1.4 Growth of a culture of Paramecium bursaria in a test tube 13 1.5 Logarithmic plot of the data from figure 1.4 14 1.6 Long-term data for the same populations of Paramecium bursaria 15 1.7 Fit of logistic equation to the Paramecium bursaria data from figure 1.6 17 1.8 Exemplary yield versus density data for maize, rape, and beets 18 1.9 Equation of Shinozaki and Kira superimposed on the rape data from figure 1.8 19 1.10 Diagrammatic representation of the process of thinning 23 1.11 Typical relationship between log density of surviving plants and log dry weight 24 1.12 Expected pattern of growth and mortality as the thinning process and growth in biomass interact 25 1.13 Relationship between the density of genets and the mean weight per genet 26 1.14 Yoda and colleagues’ interpretation of the origin of the three-halves thinning law 27 2.1 Population trajectories for different starting points in an agedistributed population 35 xi xii 2.2 Long-term projections of the hypothetical tree population discussed in the text 43 2.3 Diagrammatic summary of the general structure of a stage projection matrix 45 2.4 Time series resulting from density dependence in a simple agestructured model 50 2.5 Size frequency distributions of two taxa of mangrove seedlings 51 2.6 Intraspecific competition and growth in populations of a limpet 53 2.7 An experiment on vines in which root and shoot competition were separated 54 3.1 Difference in per caouta egg production between the O lines and B lines from Rose and Charlesworth’s experiment 67 3.2 Alternative solutions for the Schaffer model of energy allocation 69 3.3 Elasticity of survival, growth, and fecundity for invasive and native species as a function of life span 79 4.1 Illustration of the dynamical behavior associated with a point attractor 84 4.2 Illustration of the dynamical behavior of a point repeller 84 4.3 Physical models of a classical attractor and repeller 85 4.4 Beaker and magnet model of dynamics 86 4.5 Traditional representations of an oscillatory attractor and an oscillatory repeller 87 4.6 Physical model illustrating a periodic attractor 88 4.7 Cross section (Poincaré section) through the surface of figure 4.6 88 4.8 Poincaré section with a strange attractor rather than a periodic attractor 89 4.9 State space for a one-dimensional (one-variable) model 92 4.10 The vectors of the example from figure 4.9 rotated 92 4.11 State space for a one-dimensional model based on the logistic equation 93 4.12 Dynamics of the logistic equation in one dimension 93 4.13 Physical model of the dynamics of a point attractor in two dimensions 95 4.14 Conditions of eigenvalues for the three most common qualitatively distinct arrangements in two dimensions 96 4.15 Conditions of eigenvalues for the two most common qualitatively distinct arrangements in two dimensions 96 4.16 Step-by-step illustration of the process of stair-stepping for a onedimensional map 99 Figures 4.17 Step-by-step projection using a function rather than numerical values 100 4.18 Exponential equation presented as a one-dimensional graph 101 4.19 Graph of equation 3, illustrating a point attractor 101 4.20 Graph of equation 4, illustrating an unstable equilibrium 102 4.21 Graphs of equation 5, illustrating an oscillatory attractor and repeller 103 4.22 Eigenvalues for the various forms of stability in a one-dimensional map 105 4.23 Graphs of equation 5, illustrating a two-point periodic attractor, a strange attractor, and an oscillatory repeller 105 4.24 The difference between stability and instability in the regional sense 107 4.25 Graph of equation 6, illustrating the two basins of attraction for the two point attractors 109 4.26 Illustration of a structurally unstable parameter configuration for equation 16 111 4.27 Graphs of equation 8 (the logistic map), illustrating the structurally unstable configuration obtained when λ = 2.0 112 4.28 Graphs of equation 8 (the logistic map), illustrating the structurally unstable configuration obtained when λ = 3.0 113 4.29 Illustration of a saddle–node bifurcation 113 4.30 Example of a possible application of a saddle–node bifurcation 115 4.31 Illustration of a basin boundary collision 116 4.32 Illustration of the basic bifurcation process 117 4.33 Bifurcation diagram for the logistic map 118 4.34 Close-up of part of the bifurcation diagram of figure 4.33 119 4.35 Bifurcation diagram of the Tribolium model 120 4.36 Experimental results of a Tribolium experiment 121 4.37 Theoretical situations in which repellers and attractors coexist 123 5.1 Distribution of two species of trees on a 1-hectare plot 128 5.2 Birds on a telephone line 128 5.3 All possible ways that two birds can fit on three places on a telephone line 129 5.4 The telephone line divided into segments, each of which could contain a large number of birds 130 5.5 The graph in figure 5.1 with grid lines dividing the plot into 100 quadrats 131 5.6 Comparison of expected with observed density of two species of trees 132 Figures xiii xiv 5.7 The upper right quarters of the plots shown in figures 5.1 and 5.5 134 5.8 Stylized version of Ripley’s K analysis, showing Ripley’s K as a function of spatial scale 135 5.9 Spatial distribution of two tree species at the scale of 4 hectares 136 5.10 Spatial distribution of two tree species at the scale of 9 hectares 136 5.11 Artificial example of the diffusion of individual plants in a onedimensional space 139 5.12 Spatial distribution of individual plants using equation 6 141 5.13 Examples of Turing patterns emerging from equations 7a and 7b 142 5.14 Diagrammatic representation of the Turing effect 143 5.15 Simplified classification of spatially structured dynamics 144 5.16 Results of seed addition experiments 147 5.17 Differences in extinction rates (the rescue effect) and immigration rates (the propagule rain) 149 6.1 Qualitative construction of isoclines separating regions of space where prey increases or decreases and predator either increases or decreases 155 6.2 Construction of trajectories from the combination of the prey and predator isoclines in figure 6.1 156 6.3 Examples of oscillating predator–prey dynamics 157 6.4 The changes in the isoclines and population trajectory from adding density dependence to the prey 160 6.5 Type II functional response of ladybird beetles at different densities of aphids 162 6.6 Forms of the functional response 163 6.7 The changes in the isoclines and population trajectory from adding a type II functional response 165 6.8 Changing dynamics due to adding both density dependence and a nonlinear functional response to the predator–prey equations 167 6.9 Trajectories of the predator–prey system 168 6.10 The paradox of enrichment 169 6.11 Isocline arrangements illustrating the paradox of biological control 170 6.12 The two dynamic functions that make up the prey dynamic system 171 6.13 Constructing the prey isocline from the attractors and repellers of the graph of rate versus density 173 6.14 Constructing the prey isocline using graphic arguments 174 6.15 The prey isocline and its dynamics under conditions of a prey refuge 175 Figures 6.16 The three forms of the functional response 176 6.17 Constructing the prey isocline from the attractors and repellers of the rate-versus-density graph 177 6.18. Results from the discrete form of the predator–prey equations 179 6.19 The probability of avoiding attack by the predator as a function of the net attack rate 181 6.20 Solution of equations 16a and 16b 182 6.21 Solution of equations 17 and 16b 183 6.22 Solution of equations 17 and 16b with different parameters 184 6.23 Dynamic trajectories of the equation set 17 and 16b 185 6.24 Phase plane representation of equation set 17 and 16b illustrating an invariant loop, a deformed invariant loop, a fragmented attractor, and a possibly chaotic attractor 185 7.1 Time course of an infection 189 7.2 The basic idea of the SIR model 191 7.3 Typical trajectories from the classical SIR model 192 7.4 Expanded view of figure 7.3B illustrating the meaning of the recovery/ transmission ratio 193 7.5 Isoclines and vector fields for equation set 6 196 7.6 The two qualitatively distinct arrangements of the isoclines of equation system 6 196 8.1 Diagrammatic representation of the meaning of carrying capacity and competition coefficient 202 8.2 Isoclines of the competition equations 204 8.3 Putting both isoclines on the same graph and summing the vectors to get the vector field of the two-dimensional system 205 8.4 The four classic cases of interspecific competition 206 8.5 Physical model illustrating the behavior of a saddle point repeller 207 8.6 Explanation of the competitive exclusion principle 208 8.7 The graphic interpretation of the land equivalent ratio criterion 213 8.8 Relationship between birth and mortality rates and resource availability, and growth patterns of consumer and resource populations over time 217 8.9 Resource-dependent growth and mortality rates for two species using the same resource and the time course expected 218 8.10 Consumption and supply vectors and resource equilibrium for two essential resources 219 8.11 Zero net growth isoclines (ZNGIs) for substitutive and essential resources 220 Figures xv xvi 8.12 The four distinct cases of resource competition 221 8.13 Equilibrial consumption and supply vectors in monocultures for two competitors with different supply points 223 9.1 The basic dynamics of equations 1a and 1b, showing the two fundamental outcomes of facilitative mutualism 227 9.2 The various forms of isocline placement in the basic mutualism model 228 9.3 Complications with obligate mutualisms 231 9.4 Summary of the qualitative results with symmetrical mutualisms 232 9.5 Transforming the isocline of equation 1a 233 9.6 Dynamic consequences of adding nonlinearity in the facilitative effects of each of the mutualists for high mutualism coefficients 234 9.7 The eight qualitatively distinct cases of mutualistic interactions 236 9.8 Production of latex as a function of the proportion of roots infected with mycorrhizal fungi 237 10.1 Diagrammatic representation of the subject matter of the text 239 Figures Tables 1.1 Number of aphids observed per plant in a field of corn and beans in Guatemala 7 3.1 Attributes of r- and K-selected species and the environmental characteristics that select for them 65 3.2 Static life table for Dall’s mountain sheep 74 3.3 Results of a population viability analysis for Florida manatees under different hypothetical scenarios 77 xvii PREFACE W hen ecology emerged from the general subject of biology, it did so in the tradition of the world’s great naturalists—Maria Sibylla Merian, Thomas H. Huxley, Alfred Russel Wallace, Charles Darwin, and others. When Ernst Haeckel finally coined the term “ecology,” the field was little more than what natural history had always been, the detailed study of the way organisms interact with one another and their environment, a series of fascinating stories about nature. Use of quantitative techniques was minimal. Larry Slobodkin, one of the pioneers in the development of theory, once quipped to a class that an ecologist is “someone who wears khaki pants, doesn’t know much about mathematics, and misidentifies local beetles.” Indeed, maturation of the field emerged from a more serious mathematical approach. The foundational equations of Lotka and Volterra were invented in 1926, and their application to a laboratory system by Gause was complete by 1935. Yet what turned out to be foundational was largely ignored until the late 1960s, when Robert MacArthur, Richard Levins, and Robert May began their illustrious careers, with many others to follow. Mathematically based theory became an acceptable, even essential ingredient, with increasingly sophisticated theoretical approaches. As a consequence, the average ecology student today faces some daunting literature. The legacy of the late 1960s and early 1970s has been a fascinating, yet sometimes perplexing, collection of theoretical approaches that have transformed the field dramatically. A course in ecology today is as likely to contain complicated differential equations as descriptions of life histories, a dramatic change from the situation 40 years ago, when mathematics was little mentioned. And observational studies as much as experiments now rely on predictions from abstract theory. Ecology has become a remarkably exciting xix

Author Deborah E. Goldberg and John H. Vandermeer Isbn 978-0691160313 File size 22MB Year 2013 Pages 288 Language English File format PDF Category Biology Book Description: FacebookTwitterGoogle+TumblrDiggMySpaceShare Ecology is capturing the popular imagination like never before, with issues such as climate change, species extinctions, and habitat destruction becoming ever more prominent. At the same time, the science of ecology has advanced dramatically, growing in mathematical and theoretical sophistication. Here, two leading experts present the fundamental quantitative principles of ecology in an accessible yet rigorous way, introducing students to the most basic of all ecological subjects, the structure and dynamics of populations. John Vandermeer and Deborah Goldberg show that populations are more than simply collections of individuals. Complex variables such as distribution and territory for expanding groups come into play when mathematical models are applied. Vandermeer and Goldberg build these models from the ground up, from first principles, using a broad range of empirical examples, from animals and viruses to plants and humans. They address a host of exciting topics along the way, including age-structured populations, spatially distributed populations, and metapopulations. This second edition of Population Ecology is fully updated and expanded, with additional exercises in virtually every chapter, making it the most up-to-date and comprehensive textbook of its kind. Provides an accessible mathematical foundation for the latest advances in ecology Features numerous exercises and examples throughout Introduces students to the key literature in the field The essential textbook for advanced undergraduates and graduate students An online illustration package is available to professors     Download (22MB) Approaches To Plant Evolutionary Ecology Paleoecology: Past, Present and Future Temperate Crop Science and Breeding: Ecological and Genetic Studies Ecological Speciation Progress in Botany: Genetics Physiology Systematics Ecology Load more posts

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