Taylor's Power Law: Order and Pattern in Nature is a broad synthesis of this ubiquitous property of natural and man-made phenomena. This stimulating and approachable work surveys the biological and non-biological empirical data, describes the statistical uses of Taylor’s power law (TPL) and its relationship to statistical distributions, exposes the mathematical connections to other power laws, covers the competing explanatory models; and develops an argument for TPL's genesis.
Taylor’s power law relates the variability of a process or population to its average value. It was first described in relation to insect populations and then more broadly to other animal and plant populations. Subsequently it has been recognized in microbiology, genetics, economics, astronomy, physics, and computer science, and it is thought to be one of the few general laws in ecology where it is routinely used to describe the spatial and temporal distributions of populations.
Biologists who know the law as Taylor's power law and physical scientists who know it as fluctuation scaling will be interested in the bigger picture on this fascinating subject. As the relationship between variance and mean is found in so wide a range of disciplines, it seems possible it is a deep property of number, not just a phenomenon in ecology as was thought originally. Although theories abound that purport to explain or predict TPL, none is entirely satisfactory either because it fails to be very predictive, or it does not account for all the available empirical data. To uncover such a property requires a synthesis across disciplines, an acute need that is approached by this exciting work.
Author(s): R.A.J. Taylor
Edition: 1
Publisher: Academic Press
Year: 2019
Language: English
Pages: 629
Cover......Page 1
Taylor’s Power Law:
Order and Pattern in Nature......Page 3
Copyright......Page 4
Preface......Page 5
1
Introduction......Page 7
References......Page 15
Sampling......Page 17
Negative binomial distribution......Page 20
Neymans A distribution......Page 21
Lognormal distribution......Page 22
Inverse Gaussian distribution......Page 23
Tweedie family of distributions......Page 24
Origins of aggregation......Page 25
Censuses......Page 27
References......Page 452
3
Measuring aggregation......Page 30
Nearest neighbor......Page 31
Variance-mean ratio......Page 32
Fitting the negative binomial......Page 33
Interpretation of k......Page 34
Negative binomial with common k......Page 35
Lloyds mean crowding......Page 36
Variance-mean relationship......Page 38
TPL as an index of aggregation......Page 40
Adès distribution......Page 42
Perry and Hewitts number of moves index......Page 45
SADIE......Page 46
References......Page 376
4
Fitting TPL......Page 51
The standard regression model......Page 52
Functional regression......Page 53
Geometric mean regression......Page 54
Deming regression......Page 55
Bartletts 3-group regression......Page 56
Methods for fitting TPL......Page 57
Fitting split lines......Page 59
Bias in estimating TPL......Page 60
Comparison of models......Page 62
Ordinary dependent regression......Page 63
Reduced major Axis (geometric mean) regression......Page 64
References......Page 66
Gymnamoebae......Page 68
Bacteria in a Siberian reservoir......Page 69
Foraminifera in Delaware......Page 71
Invasive flagellate in Sweden......Page 72
Ciliates in the East China Sea......Page 74
Marine viruses in California and Sweden......Page 76
Tobacco mosaic virus on beans......Page 77
Verticillium dahliae in potato fields......Page 78
Passalora fulva on tomatoes......Page 80
Mummy berry disease of blueberries......Page 81
Powdery mildew on apples......Page 82
Pear scab......Page 84
On peppers and soybeans......Page 85
In the air......Page 86
Strawberry anthracnose and rain splashes......Page 88
Ciliates on flatworms......Page 89
Pasteuria penetrans on Meloidogyne arenaria......Page 90
Bacteria cultures......Page 92
The human microbiome......Page 93
Appendix: TPL estimates for microorganisms......Page 96
References......Page 597
6
Plants......Page 102
Farmland in England......Page 103
Field margins in Wisconsin......Page 108
In soybean fields......Page 109
Tree seedbank in Taiwan......Page 111
Seedbank diversity in Catalonia......Page 112
Invasive devils thorn in Australia......Page 113
Invasive ragweed in France......Page 114
Grasslands......Page 116
Grassland in Shaanxi Province......Page 117
Tallgrass prairies in Texas......Page 118
Rangeland in Mongolia......Page 120
Edible palm in Brazil......Page 122
Insectivorous plants in Morocco and Iberia......Page 123
Eelgrass in Chesapeake Bay......Page 124
Pollination success in a Yucatan shrub......Page 125
Maize......Page 127
Sugar cane......Page 128
Wheat......Page 129
Potatoes......Page 130
Appendix: TPL estimates for plants......Page 131
References......Page 139
Nematodes......Page 142
Sampling......Page 143
Urban turfgrass in Ohio......Page 147
Oak forest in Bulgaria......Page 150
Subarctic heath......Page 152
Metabolic footprint......Page 153
Perrine marl soil in Florida......Page 155
Cowpeas and cotton in California......Page 157
Potatoes......Page 159
Broad beans......Page 163
Tobacco......Page 164
Mixed vegetables......Page 165
Citrus......Page 166
Clover......Page 168
Banana......Page 169
Pine trees......Page 170
Sampling methods......Page 172
Steinernema feltiae and S. glaseri......Page 173
Steinernema carpocapsae and Heterorhabditis bacteriophora......Page 174
Effect of habitat......Page 177
Baiting effects......Page 178
Cockroaches......Page 179
Vertebrate hosts......Page 180
Sheep......Page 182
Rabbits......Page 184
Mice......Page 186
Carp......Page 187
Aquatic nematodes......Page 188
Rivers in Germany......Page 189
Highland streams in Germany......Page 190
Farm ponds in Belgium......Page 191
Restored wetland in Georgia......Page 193
Comparing samplers......Page 194
Sediment texture......Page 195
Pollution gradient......Page 196
Depth gradient......Page 197
Nematodes on kelp......Page 198
An extreme case......Page 199
Other worms......Page 201
Platyhelminths......Page 202
Primary hosts-grey mullet......Page 203
Primary hosts-Domestic fowl......Page 204
Leeches in a Cumbrian stream......Page 205
Earthworms in Scotland......Page 206
Earthworms in Colombia......Page 207
Biomass as proxy for abundance......Page 208
Ways of arranging data......Page 210
Appendix: TPL estimates for nematodes and other worms......Page 212
References......Page 324
Lepidoptera......Page 234
European corn borer......Page 235
Winter moth......Page 236
Gypsy moth......Page 238
Wireworms......Page 241
In England and Wales......Page 242
Colorado potato beetle......Page 243
Larvae......Page 246
Adults......Page 249
In the Azores......Page 251
Chthamalus species in Japan......Page 253
Stratification in barnacle distribution......Page 256
Settling behavior of barnacle cyprid larvae......Page 257
A general survey......Page 259
Consistency across space, time, and stage......Page 260
Sampling efficiency and consistency between samplers......Page 265
Effect of sampling method......Page 267
Predation......Page 270
Competition......Page 272
Effect of changes in scale......Page 273
Crustaceans......Page 275
Appendix: TPL estimates for arthropods......Page 276
Appendix 8.M......Page 279
Key to Appendix 8.M......Page 294
References......Page 295
Lake Eufaula, Oklahoma......Page 303
Upper Paraña River basin, Brazil......Page 304
River Elbe Estuary, Germany......Page 306
Molluscs......Page 307
Tellina tenuis in the Firth of Clyde, Scotland......Page 308
Intertidal molluscs on the Isle of Man......Page 309
Terrestrial gastropods in Alberta......Page 311
Slugs in Northumberland......Page 313
Starfish in North Wales......Page 315
Crinoids in São Paulo State, Brazil......Page 316
Bryozoans in the Greenland Sea......Page 317
Hydroids in the Argentine Sea......Page 318
Jellyfish in Oregon-Washington coastal waters......Page 320
Appendix: TPL estimates for other invertebrates......Page 322
Distance sampling......Page 325
Haddock and whiting off Massachusetts......Page 326
Herring and Mackerel in the Norwegian Sea......Page 327
Salmon in the Northeast Pacific Ocean......Page 329
Demersal fish in a tropical bay in Brazil......Page 330
Pelagic fish larvae in Portugal......Page 332
Pelagic fish larvae in New Jersey......Page 333
Fish larvae entering Pamlico and Albemarle Sounds, North Carolina......Page 334
Sea trout fry in England's Lake District......Page 335
Adult sea trout catches in England and Wales......Page 338
Californian commercial fisheries......Page 340
Reptiles in the Florida Everglades......Page 342
Herptiles in Arizonas Rincón Mountains......Page 343
Frogs in an Alpine habitat in California......Page 345
Eagle prey in Northern Greece......Page 346
Willow ptarmigan in Norway......Page 347
Jays in Western USA......Page 349
Grassland sparrows in continental USA......Page 351
Birds in urban and nonurban environments......Page 352
British trust for ornithology annual survey......Page 354
Audubon Societys Christmas Bird Count......Page 357
Cetaceans near the Azores......Page 361
Cetaceans around the British Isles......Page 362
Harbor porpoise in the North Sea......Page 364
Herding ungulates in Kenyas Rift Valley......Page 367
Kangaroo rat mounds in New Mexico......Page 369
Appendix: TPL estimates for vertebrates abstracted or calculated from the literature......Page 370
Rate of evolution......Page 380
Exoenzymes in soil......Page 382
Metabolism in a river system......Page 384
Phosphorus in lakes......Page 385
Metastatic cancers......Page 386
Physiological responses to stimuli......Page 387
United States decennial census......Page 389
Population of Norway......Page 392
Mortality in England and Wales......Page 394
Human immunodeficiency virus......Page 396
Typhoid in Cambodia......Page 398
Measles and whooping cough......Page 399
Disease monitoring......Page 400
Stress in air traffic controllers......Page 402
Crime in Britain......Page 403
European wars......Page 406
Convenience store sales in Japan......Page 407
Size of corporations......Page 409
Size of cities......Page 411
Appendix: TPL estimates for other biological examples......Page 413
Cyanogen in a comet halo......Page 420
The distribution of heavenly bodies......Page 421
Yale Bright Star Catalog......Page 422
Principal Galaxy Catalog......Page 423
Earthquakes off the east coast of Japan......Page 425
Tornadoes in the continental USA......Page 426
Precipitation actual and simulated......Page 428
Traffic through networks......Page 430
Foreign exchange markets......Page 432
Prime numbers......Page 434
Appendix: TPL estimates for nonbiological phenomena......Page 437
References......Page 439
Inadequate NQ or NB......Page 441
Meiobenthos in the Balearic Islands......Page 442
Thrips in a cucumber crop......Page 443
Powdery mildew on apples......Page 444
A modeling example......Page 445
Effect of pesticides......Page 446
Parasite prevalence......Page 447
Commodity crops......Page 448
Temperature......Page 451
14
Applications of TPL......Page 454
Transformations......Page 455
Stabilizing variance......Page 456
Sampling......Page 458
Binomial sampling......Page 459
Sequential sampling......Page 461
Optimum sample size......Page 462
Number of samples......Page 463
Sampling efficiency......Page 465
Postscript......Page 468
Detecting environmental perturbations......Page 469
The cost of conservation......Page 471
Stream water quality......Page 472
Testing vaccines......Page 474
Model calibration and validation......Page 475
Quality control......Page 476
References......Page 477
Self-similarity......Page 481
Effect of small samples......Page 483
Direct effect......Page 484
Anatomy......Page 487
Sampling efficiency......Page 488
Density-dependence......Page 489
Trap saturation......Page 492
References......Page 557
Pareto distribution......Page 495
Spectra......Page 496
Scale-free networks......Page 497
Diffusion-limited aggregation......Page 498
Repetition as a source of self-similarity......Page 499
Self-organized criticality......Page 500
Meteorology......Page 501
Hydrology......Page 502
Allometric growth......Page 503
Dimensional relationships for flying animals......Page 504
Species-area......Page 507
Respiration......Page 510
Self-thinning and space-filling......Page 511
Soil fertility and crop yields......Page 514
Binomial power law......Page 515
Density-size and variance-size laws......Page 516
Taxonomy......Page 518
Richardsons law of conflict......Page 519
Physical models......Page 525
Diffusion-limited aggregation......Page 527
A network model......Page 528
Statistical physics......Page 529
A biophysical model......Page 531
Reformulating TPL......Page 533
Higher moments......Page 534
Simulated sampling......Page 535
Sampling and feasible sets......Page 536
A lattice model......Page 537
Biological models......Page 538
Models in time......Page 539
Strong density dependence......Page 540
Effect of competition......Page 543
Temporal TPL and stability......Page 544
The Lewontin-Cohen model......Page 545
A singularity in TPL......Page 546
Singularities in other models......Page 548
Dispersal distance......Page 550
Ideal free distribution......Page 552
Agent-based models......Page 553
Cellular automaton......Page 554
Arrangement in space......Page 555
18
Summary and synthesis......Page 560
The biological evidence......Page 562
TPL and the pattern of sampling......Page 563
Physical versus biological......Page 564
Sources of range of means......Page 565
The role of the sampler......Page 566
Sampling effort and efficiency......Page 567
The time of sampling......Page 568
Box counting......Page 569
Orthogonal directions......Page 570
Intersection of TPL and Poisson line......Page 571
The effect of scale......Page 572
Super aggregation......Page 574
Predation......Page 575
Competition......Page 576
Mixed-species and community TPLs......Page 577
Human demographics and sociology......Page 578
Other uses of TPL......Page 579
When TPL doesnt work......Page 581
Models......Page 582
Are the power laws related?......Page 586
Is TPL universal?......Page 587
References......Page 590
19
Epilogue......Page 595
B......Page 598
C......Page 600
E......Page 601
G......Page 602
H......Page 603
K......Page 604
L......Page 605
M......Page 606
O......Page 607
R......Page 608
S......Page 609
T......Page 610
W......Page 611
Z......Page 612
A......Page 614
B......Page 615
C......Page 616
F......Page 617
H......Page 618
L......Page 619
M......Page 620
P......Page 621
R......Page 623
S......Page 624
T......Page 625
V......Page 627
Z......Page 628
Back Cover......Page 629
