Subject index

A algae, 498, 631; see also phytoplankton algebra, 63

–of canonical correspondence analysis, 594-597

–of redundancy analysis, 580-587

algorithm

–agglomerative a. 314

–alternating least-squares (K-means) a., 352

–divisive a., 314

–for correspondence analysis (CA), 473-476

–for canonical correspondence analysis (CCA), 600-601

–for principal component analysis (PCA), 418424

–for principal coordinate analysis (PCoA), 443444

–for redundancy analysis (RDA), 592-594

–sequential a. for clustering, 314

–simultaneous a. for clustering, 314

–two-way weighted averaging a. (TWWA) for CA, 475

–two-way weighted averaging a. (TWWA) for CCA, 601

–two-way weighted summation a. (TWWS) for PCA, 418-422

–two-way weighted summation a. (TWWS) for PCoA, 347, 443

aliasing, 640-641 alphabet, 215 analysis

–4th-corner a., 491, 493, 565-574

–analysis of similarities (ANOSIM), 560-563

–analysis of variance: see analysis (one-way ANOVA, two-way ANOVA)

–association a., 343-344

–Box-Jenkins a., 644, 702-704

–Braun-Blanquet phytosociological a., 347

–canonical a. of species data, 633-635

–canonical a., 188, 191, 482, 492, 575-635, 644, 713

analysis (continued)

–canonical correlation a. (CCorA), 188, 191, 489, 492, 578, 579, 612-616

–canonical correspondence a. (CCA), 34, 188, 189, 191, 491, 492, 494, 495, 576, 578, 579, 594-607, 771

–canonical variate a. (CVA), 617

–classical scaling, 388, 425

–cluster a., 303-385, 389, 575

–co-inertia a., 616

–confirmatory factor a., 476, 480, 496

–contingency table a.: see contingency table analysis

–correspondence a. (CA), 188, 190, 230, 292, 348, 349, 388, 389, 390, 413, 451-476, 489, 576, 578; see also contingency table analysis

–detrended correspondence a. (DCA), 349, 466, 467-471

–dimensional a.: see dimensional (analysis)

–direct gradient a., 486, 488, 575

–discrete discriminant a., 188, 491, 492

–discriminant a., 40, 188, 191, 192, 193, 280, 288, 490, 491, 494, 578, 579, 616-633

–dissimilarity a., 346

–distance-based RDA (db-RDA), 188, 189, 557, 605, 606

–exploratory factor a., 476, 477

–factor a., 188, 190, 388, 476-480

–Friedman two-way ANOVA by ranks, 194

–generalised Procrustes a., 563

–gradient a., 463-464

–harmonic a., 665, 673

–hybrid scaling, 444

–indirect gradient a., 486, 488

–inertia a., 388

–information a., 336-341, 384

–Kedem’s spectral a., 645

–Kruskal-Wallis one-way ANOVA by ranks, 193, 291

analysis (continued)

–lagged contingency a., 645

–line pattern a., 712

–maximum entropy spectral a. (MESA), 688691

–metric multidimensional scaling, 388, 413, 424

–multidimensional (or multivariate) a. of variance (MANOVA), 132, 188, 189, 280, 605, 617

–multidimensional unfolding, 390

–multiple discriminant a., 618; see also analysis (discriminant a.)

–multivariate spectral a., 645

–non-centred PCA, 394

–nonmetric multidimensional scaling (MDS), 188, 190, 286, 388, 389, 413, 425, 444-450, 575

–O-mode a., 248, 249, 299, 300

–one-way ANOVA, 13, 15, 20, 40, 192, 193, 229, 291, 525, 617

–orthogonal Procrustes a., 563

–P-mode a., 248

–partial canonical a., 605-612, 713, 769-779, 783, 785

–partial canonical correspondence a. (CCA), 605-612, 536, 771

–partial Mantel a., 713, 779-785, 783, 785

–partial redundancy a., 605-612, 771

–path a., 167, 172, 88, 191, 496, 533, 546-551

–point pattern a., 711

–principal component a. (PCA), 39, 188, 190, 249, 250, 288, 292, 346, 489, 492, 576, 579, 580, 581, 583, 837

–principal component a. in the frequency domain, 687

–principal component a. with instrumental variables (ACPVI), 576

–principal coordinate a. (PCoA), 188, 190, 250, 275, 286, 324, 326, 328, 346, 360, 388, 389, 424-444, 469

–Procrustes a., 390, 491, 563-564

–Q-mode a., 57, 203, 248, 249, 299, 300, 303

–R-mode a., 57, 248, 249, 252, 301, 303

–reciprocal averaging, 451, 463-464; see also analysis (correspondence a.)

–redundancy a. (RDA), 188, 191, 491, 492, 494, 495, 557, 576, 578, 579-594, 766, 771

–regression a.: see regression

–replication a., 380

–S-mode a., 248

–scaling a., 112

–simple discriminant a., 618; see also analysis (discriminant a.)

analysis (continued)

–spatial a. 707-785

–spectral a., 39, 643, 644, 645, 679-691

–surface pattern a., 712

–T-mode a., 248

–three-way correspondence a., 251

–three-way principal component analysis, 251

–time series a., 9

–trend-surface a., 525, 726, 739-746

–TWINSPAN, 347-348, 368, 381, 385

–two-way ANOVA, 194

–weighted averaging partial least squares (WAPLS), 635

anisotropy, 721

–geometric, 731

–zonal, 731 anthropology, 780 arch effect, 465-472

association; see also coefficient

–measure of a., 247, 252

–biological a.: see species (biological associations)

autocorrelation

–in time series, 653-661

–spatial a., 8-16, 778

–tests of significance in the presence of a.: see test (statistical)

autocorrelogram: see correlogram autocovariance, 653-661

axis

–major a., principal a., 391

–major, minor a. of a concentration ellipse, 152

–time, 637; see also data (time) series

B bacteria, 504, 524, 529, 550, 631, 767, 768, 771, 774, 780-781

barnacles, 440, 726 beetles, 370 Behrens-Fisher problem, 20

benthos, 230, 373, 441, 692; see also molluscs Bergmann’s law, 498

binary question, 211, 213 bioassay, 7 biogeography, 572

biplot (see also joint plot)

–correlation b., 398, 403, 404, 587

–distance b., 398, 403, 586

–in PCA, 403-406

–in RDA, 585-587

birds, 222, 668, 769, 775 bit, 215

Bonferroni correction: see multiple testing bootstrap, 26, 410, 726

boundary

–definition, 762

–detection of b, 713, 760-763 Box-Cox method, 43

broken stick model, 244, 410, 836, 837

C calibration, 604 canonical form, 575 canonical variate, 624 causal model, 167, 168

–developmental sequence, 167

–double cause, 167

–double effect, 167

–intervening sequence, 167

–spurious correlation, 167 causal modelling

–on resemblance matrices, 496, 559, 779-785

–using correlations, 169, 496, 497; see also analysis (path a.)

–using partial canonical analysis, 769-779 causality, 169

central limit theorem, 145 centring, 38, 322, 328 cetaceans, 107

chain, 311

–of primary (external) connections, 312, 315,

321, 483 chaos theory, 2

characteristic equation, 83 characteristic polynomial, 84 characteristic root, 81; see eigenvalue characteristic value, 112

characteristic vector, 81; see eigenvector chart, 106, 107

chess moves, 715 chi-square (X2): see statistic chronobiology, 641

classification, 305, 315; see also clustering Classification Societies, 306

cluster, 311

–isolation, 375

–representation, 381-383

–validation, 378-380, 698

clustering, 5, 16, 17, 188, 190, 207, 247, 251, 305, 481, 482, 489, 491, 644; see also partitioning

–absolute resemblance linkage, 318

–association analysis, 343-344

–average clustering methods, 319, 384

–beta-flexible c., 336

–chronological c., 696-701

–Clifford & Goodall: see clustering (probabilistic methods)

–combinatorial c. methods, 333, 334

clustering (continued)

–combined with an ordination, 482-486

–complete linkage c., 316-317, 335, 384

–descriptive, 307

–dissimilarity analysis, 346

–division in ordination space, 346-347, 385

–Edwards & Cavalli-Sforza, 345

–flexible c., 335-337, 384

–furthest neighbour sorting, 316

–general agglomerative c. model, 333-335

–hierarchical agglomerative c. methods, 316341, 384

–hierarchical c., 487

–hierarchical divisive c., 343-349, 385

–hierarchical methods, 315

–information analysis, 336-341, 384

–integer link linkage c., 318

–intermediate linkage c., 318, 384

–monothetic c. methods, 314, 343-345, 385

–nearest neighbour c., 308

–non-hierarchical complete linkage c., 358361, 385

–non-hierarchical c. methods, 315

–non-probabilistic c. methods, 315

–overlapping c. methods, 359

–polythetic c. methods, 314, 345-346, 385

–probabilistic c. methods, 315, 361-368, 385

–proportional link linkage c., 318

–relative resemblance linkage c., 318

–single linkage c., 308-312, 316, 335, 384, 482, 484

–spatial c., 756

–statistics, 374-378

–synoptic c., 307

–unweighted arithmetic average c. (UPGMA), 319-321, 335, 384

–unweighted centroid c. (UPGMC), 319, 322324, 335, 384

–very large data sets, 315

–Ward’s minimum variance c., 329, 335, 384

–weighted arithmetic average c. (WPGMA), 319, 321-322, 335, 384

–weighted centroid c. (WPGMC), 319, 324-328, 335, 384

–with spatial contiguity constraint, 713, 751, 756-760

co-spectrum, 248

coding, 33-47; see also normalization, transformation of variables

coefficient; see also statistic

–association c., 188, 189., 251-253

–asymmetric uncertainty c., 221

–asymmetrical binary c., 256-258

–asymmetrical c., 253, 299

coefficient (continued)

–asymmetrical quantitative c., 264-268

–average distance (D2), 278, 300

–binary c., 254-256

–Bray-Curtis (D14), 265, 287, 436, 439, 449, 467

–Canberra metric (D10), 282, 287, 296, 299

–chi-square c. (X2): see statistic (chi-square s.)

–chi-square distance (D16), 285, 292, 299, 301, 388, 439, 440, 451, 460, 461, 463, 466, 578

–chi-square metric (D15), 268, 276, 283-284, 296, 298, 299, 301

–chi-square similarity (S21), 268, 299, 301

–choice of a c., 295-301

–chord distance (D3), 279, 299

–city-block metric (D7), 282

–coherence c., 220

–cohesion index, 374

–coincidence index (S8), 257, 294

–connectedness: see connectedness

–contingency c., 188, 221

–correlation c.: see correlation

–Czekanowski, 265, 282

–deviant index, 346

–dissimilarity, 274

–distance c., 252, 274-288

–drag c., 106

–efficiency c., 341

–Estabrook & Rogers (S16), 260-264, 276, 300

–Euclidean distance (D1), 250, 277, 281, 285, 298, 300, 306, 388, 395, 426, 428, 439, 446, 578

–Fager & McGowan (S24), 294

–Faith (S26), 258, 276

–Geary’s spatial autocorrelation c., 715

–geodesic metric (D4), 279, 280, 299

–Goodall probabilistic c. (S23), 269-273, 276, 293, 299, 301

–Gower (S15), 258-260, 266, 276, 300

–Gower (S19), 266-267, 269, 276, 296, 299, 442

–Gower distance (for matrix comparison), 376, 377

–great-circle distance, 715

–Hamann c., 256

–Hellinger distance (D17), 286, 298, 299, 301

–index of association (D9), 282, 299

–information c., 188, 189

–Jaccard c. of community (S7), 256, 264, 275, 294, 299

–Krylov (S25), 295

–Kulczynski (S12), 257, 275, 299

–Kulczynski (S18), 257, 266, 276, 287, 299, 449

–Lance & Williams information statistic, 269

coefficient (continued)

–Legendre & Chodorowski (S20), 267, 276, 296, 299

–Mahalanobis generalized distance (D5), 280, 281, 300

–Manhattan metric (D7), 282, 300, 344

–mean character difference (D8), 282, 299, 300

–Minkowski metric (D6), 281, 344, 446

–Moran’s spatial autocorrelation c., 715

–nonmetric c. (D13), 286

–Ochiai (S14), 257, 276

–Odum c. (D14), 265, 287, 436, 439, 467

–of (multiple) determination c. (R2), 491, 499, 503, 533

–of alienation, 548

–of community: see coefficient (Jaccard c.)

–of concordance (Kendall W), 188, 195, 203205, 490, 491

–of dependence, 56, 189, 252, 288-295

–of divergence (D11), 283, 296, 299

–of light attenuation, 102

–of multiple determination (R2), 158, 164, 165

–of nondetermination, 164, 504, 548

–of partial determination, 165, 166

–of racial likeness (D12), 283, 300

–of species dispersal direction, 764

–path c., 533, 547

–Pearson contingency c., 221

–Pearson phi, 256, 295

–percentage difference, 287, 299

–probabilistic c., 268-274

–probabilistic chi-square similarity (S22), 269, 299

–probabilistic similarity measure of association (S27), 274

–properties of distance c., 275

–Q-mode association c., 189

–quantitative c., 258-264

–R-mode association c., 189

–Rajski’s metric, 220

–Rand index, 376, 491, 492

–Raup & Crick, 273

–reciprocal information c., 301

–redundancy c., 615

–regression c.: see regression

–Rogers & Tanimoto (S2), 255, 257, 275

–Russell & Rao (S11), 257, 275

–similarity c., 252, 253-274, 303

–simple matching c. (S1), 255, 258, 275, 300, 413

–singularity index, 346

–Sørensen coefficient (S8), 256, 266, 275, 286

–spatial autocorrelation c., 715, 719

coefficient (continued)

–Steinhaus (S17), 265, 276, 287, 296, 299, 439, 449

–symmetric uncertainty, c. 221., 301

–symmetrical binary c., 254-256

–symmetrical c., 253, 300

–symmetrical quantitative c., 258-264

–taxicab metric (D7), 282

–transforming S into D, or D into S, 252, 430

–Tschuproff contingency c., 221

–types of c., 296

–uncertainty c., 209

–Whittaker’s index of association (D9), 282

–Yule, 256, 298

coenoclines, coenoplanes, 450, 471 coherence, 248

collinearity, 518 comparison

–indirect, 486, 488, 491, 494, 575

–direct, 486, 488, 491, 494, 575 competitive exclusion principle, 463

computer programs and packages, 26, 302, 704, 785

–3WAYPACK, 251

–4THCORNER, 572

–ADE-4, 579

–ALSCAL, 188, 190

–BMDP, 27

–C2D, 784

–CANOCO, 784

–CLUSTAN, 302

–CORALS, 188

–CRIMINALS, 188

–DECODA, 445

–DECORANA, 468

–DISTPCOA, 436

–EQS, 480

–FACTALS, 188,191

–for clustering, 302, 304

–GBAS, 784

–GEMSCAL, 188, 190

–GEODAT, 784

–GEO-EAS, 784

–GEOSTAT, 784

–GS+, 784

–GSLIB, 784

–HOMALS, 188, 190

–IMSL, 26

–INDVAL, 369

–Interactive Time Series Modelling, 705

–ISATIS, 784

–JMP, 302

–Kellogg’s, 784

–LISREL, 480

computer programs and packages (continued)

–MACGRIDZO, 784

–MANOVALS, 188, 189

–MORALS, 188

–NAG, 26

–NTSYS-PC, 784

–Numerical recipes routines, 94

–ODRPACK, 517

–ordination analysis programs, 390

–OVERALS, 188

–PASSTEC, 705

–PATHALS, 188

–PATN, 302

–PC-ORD, 445

–PRIMER, 445

–PRINCALS, 188

–PRINCIPALS, 188, 190

–RDACCA, 579

–SAAP, 784

–SAS, 27

–SASP, 784

–SPSS, 27

–STAT!, 784

–STATISTICA, 302

–SURFER, 784

–SYSTAT, 302

–The R Package, 784

–The Unit Calculator, 99

–TWINSPAN, 347

–UNIMAP, 784

–VARIOWIN, 784

concentration (Simpson), 242 concentration ellipse, 151, 152 concordance, coefficient of: see coefficient conditional distribution, 173, 183 conditional entropy: see entropy conditional probability distribution: see

distribution connectedness, 311, 318, 374 connection network, 752-756

consensus (index, tree), 380, 489 conservation biology, 370 contiguity constraint, 693

–spatial c. c., 713, 751-760

–temporal c. c., 696

contingency table analysis, 207, 451, 491, 492

–ANOVA hypothesis in c. t. a., 208

–correlation hypothesis in c. t. a., 208

–correspondence in c. t. a., 188, 189, 190, 230235

–cross-contingency, 663

–expected frequencies in c. t. a., 217, 224

–hierarchical models in multiway c. t. a., 223224, 226

contingency table analysis (continued)

–multiway c. t. a., 188, 189, 222-230, 490, 491

–null hypothesis in c. t. a., 216

–test of hypothesis Oij = Eij, 232

–two-way c. t. a., 190, 193, 216-222 cophenetic

–correlation, 331, 375-377

–distance, 312

–matrix, 312-313, 487

–similarity, 312

coral reefs, 112, 566, 588-590

correction for multiple testing: see multiple testing

correlation, 13, 15, 17, 230, 293, 490, 499, 579

–among objects (Q-mode), 411

–causal modelling using c.: see causal modelling

–cophenetic c., 331, 375-377

–cross-correlation, 248, 644, 645, 661-665, 683, 733

–false c., 769

–general c. coefficient, 295

–interpretation of c. coefficients, 166-168

–Kendall c. coefficient (τ), 188, 195, 198-203, 290, 301, 376, 377, 490, 491, 554, 646

–Kendall cross-correlation, 663

–lag c., 661; see also correlation (crosscorrelation)

–matrix, 18, 139-144

–multiple c. coefficient (R2), 158-161, 164, 188, 344, 490

–nonparametric c. coefficient, 290, 293

–partial c. coefficient (nonparametric), 173, 188, 202, 490, 491

–partial c. coefficient (parametric), 161-164, 177, 188, 490, 491, 663

–Pearson c. coefficient (r), 10, 12, 21, 22-24, 140, 144, 148, 188, 289, 292, 293, 301, 376, 377, 399, 490, 491, 503, 533, 554

–point c. coefficient, 295, 344

–principal components of a c. matrix, 406-409

–properties of partial c. coefficient, 166

–properties of Pearson r, 145

–Q-mode c., 289, 290

–rank c. coefficient, 194-203

–serial c., 9

–spatial c., 733

–Spearman c. coefficient (r or ρ), 188, 195-198, 202, 290, 301, 376, 412, 490, 491, 554

–species-environment c. in RDA, 584

–spurious c., 37, 167

correlogram, 9

–all-directional c., 722

–cross-correlogram, 663, 736

–directional c., 722, 731

correlogram (continued)

–in time series, 645, 653-665

–Mantel (multivariate) c., 645, 665, 688, 713, 736-738

–spatial c., 645, 713, 714-728

–spline c., 726

covariance, 15, 131, 135, 188, 289, 292, 293, 301, 397, 399

–cross-covariance, 661-665, 683

–multivariate covariogram, 759

–spatial, 733

crabs, 556-557, 668 crayfish, 668 cross-variance, 248

D Darwin (Charles), 499

data (time) series, 6, 637-705

–binary d. s., 645, 688, 691

–components of d. s., 641

–detrended d. s., 648

–discontinuities in d. s.: see discontinuities (detection of)

–equispaced data, 647

–Eulerian approach, 638

–Lagrangian approach, 638

–multidimensional d. s., 687, 691, 704

–noise in d. s., 641, 642

–periodic variability in d. s., 641-643, 653

–qualitative d. s., 645, 658, 663, 665, 670-673, 688

–residual d. s., 648

–semiquantitative d. s., 663, 665, 688, 691

–short d. s., 673, 676, 690

–trend in d. s.: see trend

–with measurement error, 690

data box, 248, 249 decit, 215

degrees of freedom, 13, 14

–in contingency table analysis, 218, 224, 225 Delaunay triangulation, 746, 752-753, 756, 761,

768, 783 dendrites, 312, 315

dendrogram, 304, 309, 310, 312, 331, 381, 382

–comparison of, 488

dependence (see also independence)

– linear, 46

descriptor, 27-33, 52-53, 56, 303; see also variable

–binary d., 31, 388, 412

–centred d. in PCA, 403

–meristic d., 30

–mixed precision levels, 388, 425

–number of d., 138

–of mixed precision, 187, 188

descriptor (continued)

–presence-absence d., 31, 417

–qualitative d., 30, 185, 186-191

–quantitative d., 29, 186-191, 388

–scale of d.: see scale

–semiquantitative d., 30, 186-191, 388

–standardized d. in PCA, 409

–state, 28

–with mixed levels of precision, 229 deshrinking, 604

determinant, 68-71

–properties of the d., 70 determinantal equation, 83 deterministic relationship, 1 detrending, 12, 465, 643, 646, 727

–controversy about d., 471

diagram

–path d., 546

–quantitative-rank d., 188, 189, 190

–rank d., 188

–rank-rank d., 189, 190

–scatter d., 188, 189, 190

–Shepard d., 389, 390, 409, 446, 449, 450

–Shepard-like d., 331, 376-377, 389

–trellis d., 371

dimensions (physical), 98-103

–of animals, 107 dimensional

–analysis, 3, 97-129

–constant, 99, 103

–homogeneity principle, 103

–variable, 99, 103, 112 dimensionless

–complete set of d. products, 118-126

–constant, 101, 114

–graph, 106

–product, 104

–variable, 101, 112

direction cosine, 157 Dirichlet tessellation, 756

discontinuities (detection of), 644

–chronological clustering, 696-701

–Hawkins & Merriam segmentation method, 693

–Ibanez segmentation method, 696

–in multivariate series, 691-701

–McCoy et al. segmentation method, 696

–Webster segmentation method, 644, 693-696 discrimination, 482, 490

dispersal routes, 763-765

distance (dissimilarity), 55; see also coefficient

–properties of d. coefficients, 275

–square-root transformation of d., 257

–ultrametric, 487

distribution

–bivariate normal d., 148

–conditional d., 173

–conditional probability d., 231

–multinormal conditional d., 173-178

–multinormal d., 144-152

–normal d., 196

–random d., 8

–standard normal (z), 236

–uniform d., 8

–univariate normal d., 146

diversity (species), 188, 189, 235-245, 440, 836

–hierarchical components of d., 241

–indices, 238-242

–numbers (Hill), 239

double-zero problem, 253, 289, 291, 413, 451 drag

–force, 104, 118

–coefficient, 106

E ecological interpretation, 486; see also structure ecological resemblance, 247-302; see also

coefficient

edge (of a graph), 309 eigenanalysis, 83, 454, 575 eigenvalue, 80-90, 154, 391, 837

–multiple e., 91

–negative e., 425, 432-438

–properties of e., 90-93 eigenvector, 80-90, 153, 392-394

–normalized e., 78, 86

–properties of e., 90-93 entropy, 209

–Brillouin H, 241

–conditional e., 219

–generalized e. formula, 239

–negative e., 210

–Shannon H, 240

–Simpson concentration, 242

–unconditional e., 231

equality of variances: see homogeneity of variances

equation

–characteristic e., 83

–determinantal e., 83

–Einstein’s e., 498

–Gaussian logistic e., 541

–logistic e., 536

–Taylor e., 537 equilibrium

–circle of descriptors, 402

–contribution of a descriptor, 399, 408

–projection, 402

equitability: see evenness

Euclidean property, 275; see also space (Euclidean s.)

Euclidean representation, 424, 432, 435, 437; see also space (Euclidean s.)

evenness, 243-245

–Hurlbert e., 243

–index of functional e., 244

–Pielou e., 243

evolution (biological), 60 ex aequo: see tied values expansion by minors, 69 experiment

–field e., 7

–manipulative e., 7, 131, 495, 707

–mensurative e., 131, 495, 707

extent (element of sampling design), 708

F filtration, filter (in time series), 647-652 fish association, 359

fish growth, 115, 125

fish, 171, 230, 237, 472, 572, 588-590, 602, 775 Fisher’s irises, 618

fisheries, 230 Fourier

–fast F. transform (FFT), 680

–series, 674-675

–transform, 680

Freeman-Tukey deviate, 233, 234 frequency (in time series), 638

–fundamental f., 638

–harmonic f., 638

–Nyquist f., 639

Friedman chi-square statistic, 204 function

–classification f., 629

–discriminant f., 281, 618, 624, 626, 630-631

–identification f., 494, 618, 624, 626-629

–objective f., 329, 350, 447

–structure f., 712-738

fundamental niche, 3, 356, 463, 600 fungi, 550

G game theory, 2 Gauss-Jordan method, 76

geostatistics, 16, 32, 50, 708, 712, 714, 725, 728, 729, 731, 734, 749, 750

gradient (ecological), 416, 438, 439, 470, 479; see also structure (spatial)

grain size (element of sampling design), 708 Gram-Schmidt orthogonalization, 527 graph

–connected subgraph, 309-311, 381

–Gabriel g., 752, 753-755, 783

–relative neighbourhood g., 752, 754-755

graph (continued)

–theory, 311

–undirected g., 311 growth

–allometric, 505

–isometric, 505, 506

Guttman effect, 466; see also arch effect

H harmonic, 658; see also frequency, period, wavelength, wavenumber

hartley, 215

heterogeneity of variances, heteroscedasticity, 39, 40

heterogeneity (ecological), 16, 710

–measured h., 711

–functional h., 711

Holm correction, 233; see also multiple testing homogeneity of variances, homoscedasticity, 19,

40, 281

horseshoe, 466; see also arch effect human communication, 215 hypothesis (statistical)

–alternative h., 19

–null h., 17

I icicle plot, 304, 381 independence, 10

–linear i., 10, 155

–of observations (hypothesis of), 19, 20, 134 independent

–observations, 9, 10, 20

–descriptors, 10, 28

–samples, 10

–variable of a model, 10

index: see coefficient

indicator value: see species (indicator value) inference, 6

–design-based, randomization-based, 6, 9

–model-based, superpopulation, 6, 9, 12 inflated data table, 463

information, 210

–shared by two descriptors (B), 219, 670

–theory, 3

insects, 682 intercept, 500

– confidence limits of, 512 invertebrates, 775 isotropy, 721

J jackknife, 26, 245

joint plot, 455, 459, 461, 465, 466; see also biplot

K K-means, 313, 314, 315, 332, 349-355, 385 Kaiser-Guttman criterion, 409

meiofauna, 373 metric

–distance, 275, 276-286, 425, 432

–properties of m. distance, 274

–space, 251, 274, 277

Michaelis-Menten equation, 111 missing data, 47-50, 259, 432

–in time series, 647 mites, 371, 771 model, 106

–all-pole m., 689, 702

–application m., xiii

–autoregressive m. (AR), 689, 702

–autoregressive-integrated-moving average m. (ARIMA)

–autoregressive-moving average m. (ARMA), 703

–backward elimination of terms in a m., 227

–biotic control m., 707, 778

–broken stick m.: see broken stick model

–correlative m., xiii, 493, 495

–environmental control m., 707, 778

–forecasting m., xiii, 493, 495, 498, 546, 644645, 702, 704

–forward selection of terms in a m., 227

–Gaussian logistic m., 541

–hierarchical m., 223

–historical dynamics, 707, 778

–inverse-squared-distance diffusion m., 742-743

–linear m., 500, 501

–log-linear m., 188, 189, 223, 496, 497, 538

–logit m., 188, 496, 497

–mathematical m., 126, 497

–moving average m. (MA), 702

–numerical m., xiii

–path m., 477

–permutational m., 569-571

–physical, 126

–polynomial m., 526

–predictive m., xiii, 493, 495, 498, 546, 704

–saturated m., 223

–simulation m. (types of), xiii

–small-scale, 126

–testing, 106

–theoretical m., xiii

–variogram m., 730-731

molluscs, 405, 440, 668, 735, 745 monomial, 526, 527

monotonic relationship, 186 Monte Carlo method, 26 moving averages, 542, 644, 649

–weighted m. a., 649

–repeated m. a., 649-651

multidimensional

–data, 3

–qualitative data, 207-245

–quantitative data, 131-184

–semiquantitative data, 185-205

–variate, 132

multiple testing, 18, 131

–Bonferroni correction, 18, 233, 671-672, 721, 782

–Hochberg correction, 18

–Holm correction, 18, 574, 721

–progressive Bonferroni correction, 671-672, 721, 722-723, 727, 733, 736, 737, 738

multiplicity, 91

multivariate, 132; see also multidimensional

– Newton n., 104, 121

– Reynolds n., 104, 121, 127 numerical ecology, xii numerical taxonomy, xiii, 306 nunatak hypothesis, 535

O object, 28, 52-53, 55, 303

–number of o., 138, 411

–supplementary o. in PCA, 422 observation: see object Ockham’s razor, 520, 526, 536

ordered comparison case series (OCCAS), 297

ordination, 5, 16, 17, 188, 190, 247, 306, 307, 383, 387-480, 481, 482, 487, 491, 577, 692, 713, 766

–constrained o.: see analysis (canonical a.); see also map (constrained ordination m.)

overall minimum, 446; see also local minimum

P Π (Pi) theorem, 105 palaeoecology, 273, 603-604, 775 parameter, 136, 146

parametric, nonparametric, 3

partial similarity, 259, 261-264, 267, 269 partition, 305, 313; see also K-means

– fuzzy p., 305

patches (detection of), 751-760; see also structure (spatial)

period, 638, 644

–fundamental, 638

–harmonic, 638

–characteristic, 643 periodic phenomena, 638 periodic variability, 653 periodogram, 645, 665-679

–contingency p., 645, 670-673

–Dutilleul modified p., 676-678

–Schuster p., 673-676

–two-dimensional Schuster p., 714

–Whittaker and Robinson, 665-669 periphyton, 775

permutation

–exact or complete p. test, 24

–models, 569-571, 607-612

–number of permutations, 25

–of raw data, 607, 609, 611, 612

–of residuals, 608-612

–restricted p., 25, 609, 612

–sampled p. test, 25

–test, 20-26, 273, 489, 508, 511, 552, 554, 558, 559, 561, 564, 567, 697, 763

phytoplankton, 33, 102, 111, 113, 124, 225, 226, 229, 234, 336, 357, 361, 366, 504, 546, 637, 658, 659, 663, 664, 673, 676, 679, 682, 685, 686, 691, 780

phytosociology, 372

pivotal condensation method, 71 pixel, 709

plant ecology, 550 pollution, 245

polygon; see also Dirichlet tessellation

–Voronoï, 746, 756

–influence, 756

–Thiessen, 756

ponds, 308, 317, 320, 323, 325-327, 330, 332, 338, 340

population genetics, 780 Prim network, 312 principal axis, 152-158

principal component, 391, 394-395, 425; see also analysis (principal component a.)

–meaningful components, 409-411

–misuses of p. c., 411-413

–principal-component axis, 391 principle

–of least squares, 501

–of maximum likelihood (ML), 539

–of parsimony, 520, 526 probability

–frequency theory of, 1

–distribution, 1

–of interspecific encounter, 242 process, 5, 637

–physical p., 8

–stochastic p., 637

product

–cross p., 64

–dot p., 64

–inner p., 64

–postmultiplication, 68

–premultiplication, 68

–properties of matrix p., 66

–scalar p., 64

–vector p., 64

prototype, 106, 127 protozoa, 631, 775

Q Q analysis: see analysis quantification, 34, 597

R R analysis: see analysis

R2-like ratio in PCA and PCoA, 395, 437-438 randomization: see permutation

range of a variable, 38, 185, 235, 729; see also transformation (ranging)

rank statistic, 185-186 rarefaction method (Sanders), 240 redundancy (Patten), 244

redundancy in RDA and CCorA, 579; see also analysis (redundancy a.)

regression, 19, 34, 40, 188, 189, 191, 230, 497545, 644

–Bartlett three-group r., 512

–coefficient, 500; see also slope

–criteria for choosing a model II r. method, 514

–dummy variable r., 188, 490, 491, 493, 494, 525

–frequency r., 687

–geometric mean r., 510

–harmonic r., 678-679

regression (continued)

–linear r.

–logistic r., 188, 192, 193, 230, 490, 491, 493, 494, 538-542

–major axis r. (MA), 502, 507-509, 513-516

–model I r., 500, 501

–model II r., 504-517

–monotone r., 537

–multivariate linear r., 188

–multiple linear r., 15, 21, 79, 490, 493, 494, 517-525, 546, 576, 577, 580, 581-582, 611

–multiple r. on resemblance matrices, 494, 495, 559, 783

–multivariate linear r., 518, 582

–nonlinear r., 188, 494, 536-537

–nonparametric r., 188, 537

–objectives of r. analysis (description, inference, forecasting), 497-498

–on principal components, 494, 522

–ordinary least-squares r. (OLS), 502, 512, 513516

–orthogonal distance r., 517, 518

–partial linear r., 188, 528-536

–partial r. coefficient, 21,166, 518, 528, 530, 611

–periodic r., 673

–polynomial r., 79, 188, 526-528, 739

–ranged major axis r. (RMA), 511-512, 513-516

–recommendations about model II r. methods, 515

–reduced major axis r., 510

–residual, 501

–ridge r., 494, 522

–simple linear r., 13, 15, 78, 188, 500, 579

–standard major axis r. (SMA), 510-511, 513517

–standard minor axis r., 517

–variable selection in multiple r. (backward, forward, stepwise), 521-522

resolution of a study, 708 reversal, 313, 341-342 rhythm

–geophysical r., 638

–endogenous r., 638, 668 river network, 46, 768 rotation

–angle, 155-156

–oblique, 478

–orthogonal, 478

S salamanders, 498 sample

–independent s., 191

–matched s., 191

–paired s., 10, 191

sample (continued)

–related s., 191

–small s., 185 sampling

–design, 7, 16, 228, 638, 708; see also extent, grain size, lag

–interval (element of sampling design), 708

–nested s., 735

–with (or without) replacement, 241

scalar, 54 scale

–broad s., 710

–fine s., 710

–interval s. (of a descriptor), 29

–relative s. (of a descriptor), 29

–spatial s. of pattern, 709

–spatial s. of process, 709

–spatial s. of sampling design, 709

–spatial s., 8, 708-711

scale factor (in dimensional analysis), 117, 128 scaling

–in correspondence analysis (CA), 456

–in principal component analysis (PCA), 403

–in redundancy analysis (RDA), 585-587

–in canonical correspondence analysis (CCA), 596-597

segmentation, 644 semi-variance, 728, 733 semimetric distance, 432

–properties of s. d., 274, 286 seriation, 306, 315, 371-374, 383, 385 sewage, 688

sill of a variogram, 729 similarity, 55

–geometric, 127, 129

–kinematic, 129

–physical, 129

similarity of qualitative descriptors, 220 singleton, 699

singular value decomposition, 94-95, 422, 453 skewness, 39, 178

skyline plot, 304, 381, 382 slope, 500

–confidence interval of s., 508, 511

–estimation of s. of linear relationship: recommendations, 515

–maximum likelihood (ML) estimate of s., 506 Slutzky-Yule effect, 651

small number of observations, 186 smoothing

–cubic splines, 543

–freehand s. method, 649

–LOWESS, 188, 544-545, 651, 735

–splines, 188, 542-545, 651

snails, 550

soil microfungi, 417 space

–A-space, 250, 251, 326, 328

–contraction, 483

–Euclidean s., 251, 274, 275, 277, 286, 425

–I-space, 250, 251

–metric s.: see metric

–reduced s., 389

–solution s., 350, 351

spatial

–heterogeneity, 16

–analysis: see analysis (spatial a.) species

–abundance paradox, 278

–association, 304, 315, 355-371, 385, 413, 465

–bioindicator, 370

–biological associations, 291-295

–differential s., 347

–diversity: see diversity (species)

–fidelity of s., 348, 369

–indicator s., 368-371, 385

–indicator value of a s., 348, 369, 385

–null models for s. associations, 357

–number of s., 188, 189, 240, 245, 836

–presence-absence, 207

–probabilistic association, 293

–pseudospecies, 347

–satellite s., 359

–specificity of s., 369

–succession of s., 644, 691, 696

spectrum, 644, 680

–co-spectrum, 683

–coherence s., 645, 685

–cross-amplitude s., 684

–gain s., 685

–phase s., 645, 685

–power s., 680

–quadrature s., 683

–variance s., 643 spiders, 415, 479, 615 standard deviation, 135

standardization, 139, 140, 141 stationarity, 643, 647

–intrinsic assumption, 718

–second-order s., 718, 726 statistic, 17, 136

–2I s., 217

–chi-square (X2) s., 188, 189, 256, 295

–components of Pearson and Wilks X2 s, 233

–G or G2 s., 217

–Hotelling T2, 281

–information s., 670

–Kullback (X2) s., 623

statistic (continued)

–Mann-Whitney U, 563

–Mantel s., 173, 442, 554

–partitioning a X2 s., 227

–Pearson chi-square s., 217, 268, 452

–pivotal test s., 19, 608

–Procrustes s. (m2), 390, 471, 564

–Shannon (diversity, entropy) s., 240, 336

–Shapiro & Wilk s., 181

–squared error s. (e2), 329, 354

–standardized Mantel s., 375, 554

–strain, 448

–stress, 376, 447-448, 449, 450

–Student t, 281

–sum of squared errors s. (E2), 331, 352-354

–test s., 17, 19

–total error sum of squares (TESS), 332

–Wilks Λ (lambda), 281, 623

–Wilks likelihood ratio, 217

–z (Neu et al.) s., 233, 235, 236

statistics (descriptive, inferential), 17 stopping rules in clustering, 355 structure (ecological), 251, 481

–explanation, 482, 490-493

–forecasting, 482, 493-495, 498, 546, 702

–interpretation of s., 5, 481-574

–prediction, 482, 493, 495-497, 498, 546 structure (spatial), 7, 8, 11-12

–autocorrelation model, 11

–gradient (true, false), 707, 724-725; see also gradient (ecological)

–patch, patchiness, 686, 707, 751; see also patches (detection of)

–spatial dependence model, 11

surface (statistical definition), 712

T table

–Buys-Ballot t., 665-666

–classification t., 541, 625, 629

–confusion t., 541, 625

–contingency t., 291, 566

–inflated data t., 566

Table A, 181, 834 Table B, 202, 835 Table C, 244, 836 Table D, 410, 837 taxocene, 238, 291 taxonomy, 303 Taylor’s power law, 44 terrestrial fauna, 263 test (specific)

–Anderson-Darling t. of normality, 181, 183

–Bartlett t. of equality of variances, 20

–Bartlett t. of independence of variables, 144

test (specific, continued)

–chi-square (X2) t., 192, 193; see also statistic (chi-square s.)

–Cochran Q t., 192, 194

–Cramér-von Mises t. of normality, 181

–Fisher exact probability t., 192, 193

–Friedman t., 192

–goodness-of-fit Mantel t., 555, 556-557, 562

–Hotelling T2 t., 188,189

–Kolmogorov-Smirnov t. of normality, 179, 183, 834

–Kolmogorov-Smirnov two-sample t., 192

–Kruskal-Wallis H t., 192, 193, 291

–Mann-Whitney U t., 192

–Mantel t., 488, 491, 492, 550, 552-557, 644, 713

–McNemar t., 192, 194, 764

–median t., 192, 193

–of Kendall τ, 202, 835

–of multinormality (Dagnelie), 184

–of multiple correlation coefficient, 165

–of partial correlation coefficient, 165

–of Pearson r, 143

–of Spearman r, 198

–partial Mantel t., 558-559, 779-782

–Portmanteau Q-test, 721

–Procrustean randomization t., 564

–Shapiro & Wilk t. of normality, 181, 183

–sign t., 192, 193

–t-test (Student), 15, 40, 192, 193, 611, 623

–up and down runs t., 646

–Wilcoxon signed-ranks t., 192, 194

–Wilks lambda (Λ) t., 189

test (statistical), 134

–classical t. of significance, 17-20

–distribution-free, 185

–for the presence of trends in data series, 646

–multidimensional ranking t., 194-205

–multiple testing, 18

–nonparametric t., 145

–of dependence coefficients, 288

–of differences among groups, 192

–of normality and multinormality, 13, 39, 178184

–of series randomness, 646

–of significance in RDA and CCA, 606

–of significance in the presence of autocorrelation, 12-16, 134, 183

–of trend-surface model, 743

–one-tailed t., 19

–parametric t., 144

–permutation t.: see permutation

–power of a t., 202, 559, 564, 611, 638, 717, 721, 725

test (statistical, continued)

–ranking, 185

–statistic: see statistic

–two-tailed t., 19

tied values, ex aequo, 45, 198, 200 time series: see data (time) series transformation of variables, 40; see also

normalization

–linear t., 34-35

–logarithmic t., 35

–nonlinear t., 35-37

–ranging, 37-39, 511

–square root t., 433

–standardization, 37-39 tree (classification), 304, 381

–minimum-length t., 312

–minimum spanning t., 312, 752, 755

–shortest spanning t., 312

trees (vegetation): see vegetation trend, 11, 641-642, 644-646, 648

–analytical method for estimating t., 651

–cyclic t., 647, 650, 652

–extraction, 647-652

–linear t., 647, 658

–removal, 648

–trend-surface analysis: see analysis (trendsurface a.)

triangle’s inequality, 274, 286, 288, 425, 432 trilobites, 450

turning point, 646 typology, 304

U ultrametric property, 313 units

–base, 98

–derived, 98

–international system (SI), 98, 100-101

V validation: see cluster (validation) variable, 27, 133; see also descriptor

–additive v., 32

–criterion v., 10, 546

–dependent v., 10, 482, 497

–dimensional v., 99, 103, 112

–dimensionless v., 38

–dummy v., 46-47

–explanatory v., 10, 158, 229, 482, 497, 546

–extensive v., 31, 750

–independent v., 10, 133, 482, 497

–intensive v., 31, 750

–non-additive v., 32, 739

–predictor v., 10, 546, 663

–qualitative v., 566, 670

–random v., 1, 133, 497

variable (continued)

–regionalized v., 712

–response v., 10, 158, 229, 482, 497, 546

–scale of a v.: see scale

–selection of v. in multiple regression: see regression

–standardized v., 38

–supplementary v. in PCA, 422

–target v., 10, 644

variance, 135, 185, 235

–partition of v. in spectral analysis, 681

–semi-variance, 728

variate difference method, 644, 652 variate: see random variable variation

–partitioning, 409, 531-532, 770-775, 779 variogram, 9, 713, 714, 728-736, 759

–directional v., 731

–multivariate v., 759

vector, 61, 132

–characteristic, 81; see eigenvector

–length, 62

–linearly independent vectors, 72

–norm, 62

–normalization, 62

–orthogonal v., 65, 394

–row v., 64

–scaling, 62

vegetation, 230, 417, 472, 539, 550, 692, 701, 771, 775, 781-782

W wavelenght, 638

–fundamental w., 638

–harmonic w., 638 wavenumber, 638

–fundamental w., 638

–harmonic w., 638 Williams’ correction, 218, 225 window

–in moving averages, 649-650

–observational w., 638, 639

–smoothing w. in spectral analysis, 681 wombling, 761

–categorical, 761

–triangulation, 761

Z zero

–historical origin of the zero, 59

–sampling, 228

–structural, 228

zooplankton, 33, 271, 308, 338, 450, 484, 516, 546, 637, 691, 692, 699, 775