Quantitative Ecology, Second Edition: Measurement, Models and Scaling

Cover Page......Page 1
Title: Quantitative Ecology: Measurement, Models, and Scaling......Page 2
ISBN 9780126278651......Page 3
Contents......Page 6
Preface to First Edition......Page 12
Preface to Second Edition......Page 14
Acknowledgments......Page 16
Part I. Introduction......Page 18
1.1 The Need for Quantitative Reasoning......Page 20
1.2 From Words to Graphs to Equations......Page 22
1.3 Statistical Analysis......Page 24
1.4 Scaled Quantities......Page 25
1.5 Quantitative Reasoning Using the Principle of Similarity......Page 27
1.6 Quantitative Ecology......Page 30
1.7 Tools......Page 31
1.8 Overview of Chapter Concepts and Sequence......Page 32
1.9 Exercises......Page 33
2.1 The Problem of Scale In Ecology......Page 34
2.2 Definition of Scale......Page 37
2.3 The Rise of the Concept of Scale in Ecology......Page 40
2.4 Graphical Expression of the Concept of Scale......Page 48
2.5 Scale, Scope, and Power Laws......Page 49
Part II. Scaled Quantities......Page 60
3.2 Definition of a Quantity......Page 62
3.3 Names and Symbols......Page 63
3.4 Procedural Statement......Page 65
3.5 Types of Measurement Scale......Page 66
3.6 Graphing Scaled Quantities......Page 68
4.2 The Utility of Ratio Scale Units......Page 70
4.3 Standard Units......Page 72
4.4 Unconventional Units......Page 73
4.5 Rules for Ratio Scale Units......Page 75
5.1 Synopsis......Page 80
5.2 Logical Rescaling......Page 81
5.3 Algebraic Operations on Quantities......Page 82
5.4 Application: Individuals, Pairs, Residencies......Page 84
5.5 Rescaling via Normalization......Page 87
5.6 Rigid Rescaling......Page 89
5.7 Elastic Rescaling......Page 93
5.8 Elastic Rescaling with Fractal Exponents......Page 96
6.2 Physical and Chemical Dimensions......Page 104
6.3 Biological Dimensions......Page 107
6.4 Measurement and Dimension......Page 110
6.5 Dimensional Analysis in Biology......Page 116
6.5.1 Case Study 1: Dinosaur Running Speed......Page 119
6.5.2 Case Study 2: Otter Monitoring......Page 123
6.5.3 Case Study 3: Patch Size of Phytoplankton......Page 127
6.6 Applying the Logic of Dimensions......Page 129
6.7 Use and Limitations of Dimensions......Page 133
6.8 Further Reading on Dimensions and Measurement Theory......Page 137
7.1 Synopsis......Page 138
7.2 Temporal Attributes......Page 139
7.3 Geographic Attributes in One Dimension......Page 141
7.3.1 Application: Evaluation of Geographically Explicit Studies......Page 143
7.4 Geographic Attributes in Two and Three Dimensions......Page 144
7.5 Notation......Page 147
7.5.1 Application: Spatial and Temporal Attributes......Page 149
7.6 Spatial and Temporal Scaling......Page 153
8.2 Time Rates of Change......Page 156
8.2.1 Application: Crude Rate of Change in Population Size......Page 159
8.3 Time Rate of Change as a Percentage......Page 160
8.4 Fluxes......Page 163
8.4.1 Application: The Lateral Flux of Genes......Page 165
8.5 Spatial Gradients......Page 166
8.6 Divergences......Page 170
8.7 Curls......Page 175
8.8 Contrasts......Page 177
9.1 Synopsis......Page 180
9.2 Notation......Page 181
9.3 Sums and Weighted Sums of Numbers......Page 182
9.4 Sums of Scaled Quantities......Page 184
9.5 The Mean Value of a Quantity......Page 188
9.6 Sums of Quantities on Nonratio Scales......Page 189
10.1 Synopsis......Page 192
10.2 Deviations......Page 193
10.3 The Total Deviation......Page 194
10.4 The Variance......Page 197
10.5 Scale-Dependent Variance......Page 199
10.6 The Temporal Variance......Page 200
10.7 The Spatial Variance......Page 205
10.7.1 Patchiness......Page 208
10.7.2 Production and Erosion of Spatial Variance......Page 211
10.8 Variance and Hue......Page 212
10.9 Codeviances, Covariances, and Other Measures......Page 217
10.9.1 Potential Contact......Page 221
Part III. Scope......Page 226
11.1 Synopsis......Page 228
11.2 The Scope of a Measurement......Page 229
11.3 The Scope of Instruments......Page 230
11.4 The Scope of Quantities......Page 232
11.5 The Scope of Parameters and Equations......Page 235
11.6 The Scope of Natural Phenomena......Page 236
11.7 Scope Diagrams......Page 238
12.1 Synopsis......Page 242
12.2 The Scope of a Set of Measurements......Page 243
12.3 Partitioning the Scope......Page 249
12.4 The Scope of Surveys......Page 250
12.4.1 Simple Random Surveys......Page 251
12.4.3 Comparison of Surveys Designs......Page 254
12.4.4 Monitoring Programs......Page 257
12.4.5 Hierarchically Structured Surveys......Page 261
12.4.6 Magnitude and Basis of Scale-up in Surveys......Page 263
12.5.1 Experimental Estimate of a Parameter......Page 265
12.5.2 Fisherian Experiments......Page 268
12.5.3 Fisherian Experiments in Ecology......Page 271
12.5.4 Embedded Experiments in Ecology......Page 274
12.5.5 Levels of Inference in Ecological Experiments......Page 276
12.6 The Scope of Computational Models......Page 281
12.7 The Scope of Integrated Research Programs......Page 282
Part IV. Models......Page 288
13.1 Synopsis......Page 290
13.2 The Use of Equations......Page 291
13.3 Verbal, Diagrammatic, and Formal Expression of Ideas......Page 292
13.4 Reading Equations......Page 294
13.5 Dimensional Homogeneity......Page 296
13.6 Calculations Based on Ideas......Page 299
13.7.1 Notation......Page 301
13.7.2 Parsimony......Page 305
13.7.3 Sequential Caricatures......Page 306
13.7.4 General Procedure......Page 308
13.7.5 Combining Equations......Page 310
13.8 Empirical and Theoretical Scaling Functions......Page 311
13.9 Dimensional Analysis of Conservation Laws......Page 315
13.10 Quantitative Reasoning......Page 318
14.2 Derivatives......Page 320
14.3 Spatial Gradients from the Density Function......Page 323
14.4 Quantitative Reasoning with the Chain Rule......Page 325
14.5 Variance Functions with the Delta Method......Page 326
14.6 Scaling Operators......Page 328
15.1 Synopsis......Page 336
15.2 Model-Based Statistical Analysis......Page 337
15.3 Data Equations for the General Linear Model......Page 339
15.4 Interpreting Models and Their Parameters......Page 343
15.5 Goodness of Fit and Hypothesis Testing......Page 344
15.6 Generic Recipe for Applying the General Linear Model......Page 349
15.6.1 Linearized Power Laws......Page 351
15.6.2 Comparing Regression Lines (ANCOVA)......Page 357
15.6.3 Compound Scaling with Multiple Regression......Page 364
15.7 Reduced Major Axis Estimates of Scaling Parameters......Page 367
15.8 Estimates of Scaling Parameters Via Measurement Scope......Page 371
15.9 Scaling and Uncertainty via the General Linear Model......Page 374
16.1 Synopsis......Page 378
16.2 The Role of Theory in Body-Size Scaling......Page 379
16.3.1 Measuring Biodiversity......Page 381
16.3.2 Theoretical Development of Biodiversity Scaling......Page 388
16.4 Spatial and Temporal Scaling......Page 389
References......Page 394
Tables......Page 416
Boxes......Page 418
C......Page 422
D......Page 423
E......Page 424
G......Page 425
M......Page 426
O......Page 427
R......Page 428
S......Page 429
V......Page 431
Z......Page 432