List of Illustrations ......................................... xix
List of Tables ................................................ xxv
Acknowledgements ............................................ xxvii
Chapter 1 ECOLOGICAL MECHANICS
An Introduction ................................................. 1
Mechanics and Ecology Combined: Coral Reefs ..................... 1
Response Functions .............................................. 5
Transport- Phenomena ............................................ 6
What's in a Nome? ............................................... 7
What's Left Our ................................................. 8
A Road Map ...................................................... 9
Online Supplements .............................................. 9
A Note on Notation .............................................. 9
Part I Basic Concepts
Chapter 2 BASIC PHYSICS AND MATH
Location ....................................................... 13
Dimensions and Units of Measure ................................ 13
Converting Units ............................................... 15
Trigonometry ................................................... 15
Translation .................................................... 16
Translational Velocity ......................................... 17
Translational Acceleration ..................................... 18
Rotation ....................................................... 19
Force and Translational Acceleration ........................... 20
Moment and Rotational Acceleration ............................. 21
Momentum ....................................................... 23
Pressure ....................................................... 24
Buoyancy ....................................................... 25
Energy ......................................................... 26
Conservation of Energy ......................................... 30
Friction ....................................................... 31
Power .......................................................... 31
Summary ........................................................ 32
Online Supplements
2.1 Centripetal Acceleration
2.2 The Rotational Moment of Inertia for a Cylinder
2.3 Calculating Distance Using Calculus
2.4 Resting Mass
Chapter 3 RESPONSE FUNCTIONS
Concepts and Terminology ....................................... 33
Monotonie Functions ............................................ 34
Peaks and Valleys: Unimodal Response Functions ................. 39
Complications .................................................. 43
Jensen's Inequality: The Fallacy of the Average ................ 45
Linear versus Nonlinear ........................................ 46
The Effects of Nonlinearity .................................... 47
Concepts and Conclusions ....................................... 50
Online Supplements
3.1 Scope for Growth in Anemones
3.2 Modeling Reaction Norms
3.3 The Mean of a Linear Function Equals the Function of the
Mean
Part II The Mechanics of Transport
Chapter 4 DIFFUSION
Random Motion and its Consequences ............................. 55
Rules of a Random Walk ......................................... 55
Average Position ............................................... 56
Dispersion: The Variance of Position ........................... 57
The Diffusion Coefficient ...................................... 59
What Drives Random Walks? ...................................... 61
Fick's Equation ................................................ 67
The Maximum Size of Phyroplankton 69 Concepts and Conclusions .. 71
Online Supplements
4.1 The Exponential Distribution of Intervals
4.2 Steady Concentration Gradient in a Radially Symmetrical
System
Chapter 5 AN INTRODUCTION TO FLUID MECHANICS
Shear .......................................................... 72
What Is a Fluid? ............................................... 72
Liquids and Gases .............................................. 73
Dynamic Viscosity .............................................. 75
Viscous Friction ............................................... 77
Reynolds Number ................................................ 77
Conservation of Mass and Volume ................................ 80
Streamlines .................................................... 81
Conservation of Energy: Bernoulli's Principle .................. 82
Concepts, Conclusions, and Caveats ............................. 84
Online Supplements
5.1 Why Are Air and Water Viscous?
5.2 Deriving Bernoulli's Equation
Chapter 6 BOUNDARY LAYERS I
Equilibrium Layers ............................................. 86
Basic Concepts ................................................. 87
Laminar Boundary Layers: An Introduction ....................... 87
Moment and Rotation ............................................ 91
Turbulent Boundary Layers: An Introduction ..................... 92
The Onset of Turbulence ........................................ 93
Turbulent Shear Stress ......................................... 95
Reynolds Shear Stress .......................................... 96
The Turbulent Velocity Profile ................................. 98
Measuring u* .................................................. 101
Sweeps and Bursts ............................................. 102
Concepts, Conclusions, and Caveats ............................ 103
Online Supplements
6.1 Solving for the Laminar Velocity Profile
6.2 Reynolds Stress
6.3 Deriving the Low of the Wall for Smooth Plates
Chapter 7 BOUNDARY LAYERS II
Dynamic Layers ................................................ 105
Boundary-Layer Thickness Defined .............................. 105
Thickness of Dynamic Laminar Boundary Layers .................. 106
Shear Stress in Dynamic Laminar Boundary Layers ............... 109
Mass Transport ................................................ 110
The Dynamic Laminar Velocity Profile .......................... 114
Dynamic Turbulent Boundary Layers ............................. 115
Mass Flux in Turbulent Boundary Layers ........................ 116
Oscillating Flow .............................................. 117
Concepts, Conclusions, and Caveats ............................ 120
Online Supplements
7.1 Converting OH- Concentration to pH
7.2 The Blasius Profile
7.3 z of umax
Chapter 8 FLUID-DYNAMIC FORCES I
Introduction and Low-Reynolds-Number Flows ................... 121
Drag at Low Reynolds Number ................................... 122
Low-Re Ecomechanics: Sensory Ecology and Predator-Prey
Interactions .................................................. 126
Concepts, Conclusions, and Caveats ............................ 129
Online Supplements
8.1 Sinking Rates of Diatoms
8.2 Fluid Strain Around a Sphere
Chapter 9 FLUID-DYNAMIC FORCES II
High Reynolds Numbers ......................................... 131
Forces ........................................................ 131
Force Coefficients ............................................ 142
Rules of Thumb ................................................ 150
Ecomechanical Examples ........................................ 152
Concepts, Conclusions, and Caveats ............................ 156
Online Supplements
9.1 Pressure Gradient in an Accelerating Fluid
9.2 Acceleration Reaction of a Moving Object in a Moving
Fluid
9.3 Viscous Drag at High Re
9.4 Defining the Coefficient of Viscous Drag, CDV
9.5 Waves in the Surf Zone
Chapter 10 LOCOMOTION
The Physics of Locomotion ..................................... 158
Sources of Power: The Motors .................................. 162
Drifting: Passive Locomotion .................................. 167
Crawling: Adhesive Locomotion ................................. 168
Burrowing ..................................................... 171
Walking and Running ........................................... 172
Wheels ........................................................ 174
Swimming ...................................................... 175
Gliding Flight ................................................ 177
Flapping Flight ............................................... 180
Speed and Power of Transport: A Summary ....................... 182
Cost of Transport ............................................. 183
Climbing and Jumping .......................................... 186
Locomotion in Context ......................................... 188
Winter Migration .............................................. 189
Concepts, Conclusions, and Caveats ............................ 193
Online Supplements
10.1 Muscle Kinetics
10.2 The Power of Adhesive Locomotion
10.3 Speed of Muscle Contraction in a Snail
10.4 Bending Cilia
10.5 Internal Power of Legged Locomotion
10.6 Mechanics of Flagellar Thrust
10.7 Components of Drag in Flight
10.8 Acceleration in a Jump
10.9 When Is It Viable to Migrate?
Chapter 11 THERMAL MECHANICS I
Introduction, Solar Heating, Convection, Metabolism, and
Evaporation ................................................... 195
Why Temperature Matters ....................................... 196
Heat-Budget Models: A Prospectus .............................. 197
Hear .......................................................... 198
Temperature ................................................... 199
Specific Hear ................................................. 200
Thermal Diffusion ............................................. 200
Latent Hear ................................................... 201
The Heat Budget ............................................... 201
Solar Heating ................................................. 202
Convective Heat Transport ..................................... 206
A Convection-Dominated System: Littorine Snails ............... 209
Metabolism .................................................... 212
Evaporation and Condensation .................................. 214
Systems Dominated by Convection and Evaporation: Desert
Herbs and Seaweeds ............................................ 215
Concepts and Interim Conclusions .............................. 219
Online Supplements
11.1 Measuring Temperature
11.2 Solar Hear Influx
11.3 Measuring the Heat-Transfer Coefficient
11.4 A Nontraditional Mass-Transfer Coefficient
11.5 Relating Mass Transfer to Heat Transfer
11.6 Calculating Wet-Bulb Temperature
Chapter 12 THERMAL MECHANICS II
Stored Energy, Conduction, Long-Wave Radiation, and
Synthesis ..................................................... 221
Stored Energy ................................................. 221
Conductive Hear Transport ..................................... 224
Long-Wave Radiative Heat Transfer ............................. 229
The Hear Budget Revisited ..................................... 235
The Environmental Niche ....................................... 237
Concepts, Conclusions, and Caveats ............................ 240
Online Supplements
12.1 Response Time
12.2 Calculating the Thermal Gradient
12.3 Linearizing Long-Wave Hear Exchange
12.4 Emissivity of rhe Sky
12.5 Solving the Time-Dependent Heat-Budget Equation
Part III Solid Mechanics
Chapter 13 BIOLOGICAL MATERIALS I
Materials Mechanics ........................................... 245
Bonding Forces ................................................ 245
Why Solids Are Elosric ........................................ 249
Theoretical Srrengfh of Solids ................................ 250
Polymers and Sofr Elasticity .................................. 251
Rubber Elasticity ............................................. 253
Viscoelasticity ............................................... 254
Load .......................................................... 255
Stress ........................................................ 255
Srrain ........................................................ 258
Elastic Modulus ............................................... 261
Srrain Energy ................................................. 264
Failure ....................................................... 266
Conceprs, Conclusions, and Caveats ............................ 267
Online Supplements
13.1 An Alternative Perspecrive on Shear Loading
13.2 The Utility of True Strain
13.3 The Standard Linear Solid
13.4 Calculating Strain Energy
Chapter 14 BIOLOGICAL MATERIALS II
The Spectrum of Biological Materials .......................... 268
Stiffness ..................................................... 268
Sfrengrh ...................................................... 271
Toughness ..................................................... 271
Composite Materials ........................................... 272
Designing a Giant Kelp ........................................ 276
Mussels, Patch Dynamics, and Disturbance ...................... 278
Conceprs, Conclusions, and Caveats ............................ 280
Online Supplements
14.1 Mechanical Design of Anemones
14.2 Force from Pressure in a Cylinder
14.3 Unidirectional Fiber Reinforcement
14.4 Multidirecrionol Fiber Reinforcement
Chopter 15 FRACTURE MECHANICS AND FATIGUE
Stress Concentrations ......................................... 282
Energy and Fracture ........................................... 284
Breaking Stress ............................................... 287
Fracture Toughness ............................................ 288
Crack Stoppers ................................................ 290
Fatigue ....................................................... 291
Fracture and Fatigue in Evolution ............................. 294
Concepts, Conclusions, and Caveats ............................ 295
Chapter 16 ADHESION AND ADHESION RESISTANCE
Attachment and Adhesion ....................................... 297
Close Physical Contact ........................................ 298
Pressure-Difference Adhesion .................................. 302
Surface Tension and Surface Energy ............................ 304
Interaction at the Interface .................................. 306
Capillary Adhesion ............................................ 308
Viscous Adhesion .............................................. 309
Glue .......................................................... 311
Adhesives Compared ............................................ 312
Adhesion Is Easy .............................................. 313
Adhesion in Reverse ........................................... 315
Conceprs, Conclusions, and Caveats ............................ 318
Chapter 17 STATICS
Bending and Twisting .......................................... 319
Bending ....................................................... 319
Specifying .................................................... 323
Cantilever Bending ............................................ 326
Stress in Corals .............................................. 328
Shear ......................................................... 331
Anemones as Beams ............................................. 334
Maximum Height ................................................ 335
Optimal Shape ................................................. 338
Torsion ....................................................... 341
Concepts, Conclusions, and Caveats ............................ 343
Online Supplements
17.1 I of a Circle
17.2 Approximate I of a Hollow Circular Cross Section
17.3 I for Hollow Beams of Constant Volume
17.4 Thickness per Radius for a Hollow Beam
17.5 I of Complex Shapes
17.6 Deflection of a Cantilever
17.7 Stiffness of Divided Beams
17.8 Maximum Height
17.9 Optimal Shape of a Cantilever
17.10 Second Polar Momenr of Area
Chapter 18 DYNAMICS
The Mechanics of Oscillation .................................. 345
Harmonic Oscillation .......................................... 345
Damped Harmonic Motion ........................................ 350
Forced Harmonic Motion ........................................ 353
Abruptly Applied Loads ........................................ 356
Nonlinear Springs and Chaos ................................... 359
Conceprs, Conclusions, and Caveats ............................ 359
Online Supplements
18.1 Damped Harmonic Morion
18.2 Forced Harmonic Motion
Part IV Ecological Mechanics
Chapter 19 ECOLOGICAL VARIATION AND ITS CONSEQUENCES .......... 363
Scale Transition Theory: A Brief Inrroducrion ................. 364
Background .................................................... 366
Scale Transition Theory in Action: Intermediate Disturbance ... 369
Covariance .................................................... 371
Examples from Nature .......................................... 376
Concepts, Conclusions, and Caveats ............................ 377
Online Supplements
19.1 Deriving the Scale Transition Equation
19.2 ST of Some Common Response Functions
19.3 Poisson Interval Statistics
19.4 The Effect of Covariance on the Mean
19.5 The Effect of Variation in More Complicated Functions
Chapter 20 SPECTRAL ANALYSIS
Quantifying Variation in Time and Space ....................... 379
Sequence, Signal, and Power 380 Fourier Series ................ 383
Choosing Frequencies: The Role of Harmonics ................... 386
Fourier Coefficient ........................................... 387
The Periodogram ............................................... 388
Specifying Fourier Coefficient ................................ 391
The Power Specrrum ............................................ 397
Spectral Analysis in Biology .................................. 401
Conceprs, Conclusions, and Caveats ............................ 404
Online Supplements
20.1 The Sum of Sine and Cosine Waves
20.2 Specifying Fourier Coefficients
20.3 p at the Nyquist Frequency
20.4 Practical Considerations in Spectral Analysis
Chapter 21 QUANTIFYING THE EFFECTS OF SCALE
1/f Noise ..................................................... 406
The Color of Specrral Dato .................................... 408
Patterns of 1/f Noise ......................................... 408
Asymptotes for β < 1 .......................................... 412
Estimating β and kvar ......................................... 412
Scale Transition: An Example .................................. 413
Other Specrra ................................................. 415
Concepts, Conclusions, and Caveats ............................ 416
Online Supplements
21.1 Calculating the Time or Distance Required to Reach
a Given Fraction of Maximum Variance
21.2 Cavears Regarding the Estimation of kvar and β
21.3 Numerically Integrating a Specrrum
Chapter 22 BIOLOGY OF EXTREMES ................................ 419
Statistics of Extremes ........................................ 420
Extreme Cavears ............................................... 428
An Interim Synopsis ........................................... 432
The Environmental Bootstrap ................................... 432
Evolution and Extremes ........................................ 439
Bootstrap Cavears ............................................. 441
Concepts and Conclusions ...................................... 442
Online Supplements
22.1 The Normal Curve
22.2 Probability and Return Time
22.3 Connections to the Poisson Interval Distribution
Chapter 23 PATTERN AND SELF-ORGANIZATION ...................... 443
Facilitation-Inhibition ....................................... 444
Criticality ................................................... 451
Concepts, Conclusion, and Caveats ............................. 454
Chapter 24 THOUGHTS AT THE END
Take-Home Messages ............................................ 455
Plankton Ecology .............................................. 458
A Look to the Future .......................................... 462
ONLINE RESOURCES
Additional supporting materials can be found at
http://press.princeton.edu/titles/10641.html
References .................................................... 463
Symbol Index .................................................. 479
Author Index .................................................. 485
Subject Index ................................................. 489
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