Author | Deborah E. Goldberg and John H. Vandermeer | |

Isbn | 978-0691160313 | |

File size | 22MB | |

Year | 2013 | |

Pages | 288 | |

Language | English | |

File format | ||

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