This book provides a practical introduction to analyzing ecological data using real data sets. The first part gives a largely non-mathematical introduction to data exploration, univariate methods (including GAM and mixed modeling techniques), multivariate analysis, time series analysis, and spatial statistics. The second part provides 17 case studies. The case studies include topics ranging from terrestrial ecology to marine biology and can be used as a template for a reader’s own data analysis. Data from all case studies are available from www.highstat.com. Guidance on software is provided in the book.
Author(s): Alain F. Zuur, Elena N. Ieno, Graham M. Smith
Series: Statistics for Biology and Health
Edition: 1
Publisher: Springer
Year: 2007
Language: English
Pages: 686
0387459677......Page 1
Contents......Page 10
Contributors......Page 17
1.1 Part 1: Applied statistical theory......Page 25
1.2 Part 2: The case studies......Page 27
1.3 Data, software and flowcharts......Page 30
2.1 Introduction......Page 31
2.2 Data management......Page 32
2.3 Data preparation......Page 33
2.4 Statistical software......Page 37
3.1 Introduction......Page 42
4. Exploration......Page 47
4.1 The first steps......Page 48
4.2 Outliers, transformations and standardisations......Page 62
4.3 A final thought on data exploration......Page 71
5.1 Bivariate linear regression......Page 73
5.2 Multiple linear regression......Page 91
5.3 Partial linear regression......Page 97
6.1 Poisson regression......Page 102
6.2 Logistic regression......Page 111
7.1 Introduction......Page 120
7.2 The additive model......Page 124
7.3 Example of an additive model......Page 125
7.4 Estimate the smoother and amount of smoothing......Page 127
7.5 Additive models with multiple explanatory variables......Page 131
7.6 Choosing the amount of smoothing......Page 135
7.7 Model selection and validation......Page 138
7.8 Generalised additive modelling......Page 143
7.9 Where to go from here......Page 147
8.1 Introduction......Page 148
8.2 The random intercept and slope model......Page 151
8.3 Model selection and validation......Page 153
8.4 A bit of theory......Page 158
8.5 Another mixed modelling example......Page 160
8.6 Additive mixed modelling......Page 163
9.1 Introduction......Page 166
9.2 Pruning the tree......Page 172
9.4 A detailed example: Ditch data......Page 175
10.1 Introduction......Page 185
10.2 Association between sites: Q analysis......Page 186
10.3 Association among species: R analysis......Page 193
10.4 Q and R analysis: Concluding remarks......Page 198
10.5 Hypothesis testing with measures of association......Page 201
11.1 Bray–Curtis ordination......Page 210
12.1 The underlying principle of PCA......Page 214
12.2 PCA: Two easy explanations......Page 215
12.3 PCA: Two technical explanations......Page 217
12.4 Example of PCA......Page 218
12.5 The biplot......Page 221
12.6 General remarks......Page 226
12.7 Chord and Hellinger transformations......Page 227
12.8 Explanatory variables......Page 229
12.9 Redundancy analysis......Page 231
12.10 Partial RDA and variance partitioning......Page 240
12.11 PCA regression to deal with collinearity......Page 242
13.1 Gaussian regression and extensions......Page 246
13.2 Three rationales for correspondence analysis......Page 252
13.3 From RGR to CCA......Page 259
13.4 Understanding the CCA triplot......Page 261
13.5 When to use PCA, CA, RDA or CCA......Page 263
13.6 Problems with CA and CCA......Page 264
14.1 Introduction......Page 266
14.2 Assumptions......Page 269
14.3 Example......Page 271
14.4 The mathematics......Page 275
14.5 The numerical output for the sparrow data......Page 276
15.1 Principal coordinate analysis......Page 280
15.2 Non-metric multidimensional scaling......Page 282
16.1 Using what we have already seen before......Page 286
16.2 Auto-regressive integrated moving average models with exogenous variables......Page 302
17.1 Repeated LOESS smoothing......Page 310
17.2 Identifying the seasonal component......Page 314
17.3 Common trends: MAFA......Page 320
17.4 Common trends: Dynamic factor analysis......Page 324
17.5 Sudden changes: Chronological clustering......Page 336
18.1 Lattice data......Page 342
18.2 Numerical representation of the lattice structure......Page 344
18.3 Spatial correlation......Page 348
18.4 Modelling lattice data......Page 352
18.5 More exotic models......Page 355
18.6 Summary......Page 359
19.1 Spatially continuous data......Page 361
19.2 Geostatistical functions and assumptions......Page 362
19.3 Exploratory variography analysis......Page 366
19.4 Geostatistical modelling: Kriging......Page 378
19.5 A full spatial analysis of the bird radar data......Page 383
20.1 Introduction......Page 393
20.2 The data......Page 394
20.3 Data exploration......Page 397
20.4 Linear regression results......Page 399
20.5 Additive modelling results......Page 401
20.6 How many samples to take?......Page 403
20.7 Discussion......Page 405
21.1 Introduction......Page 409
21.2 Data and materials......Page 410
21.3 Data exploration......Page 412
21.4 Classification trees......Page 415
21.5 Generalised additive modelling......Page 417
21.6 Generalised linear modelling......Page 418
21.7 Discussion......Page 421
22.1 Introduction......Page 423
22.3 Abstracting the information......Page 424
22.4 First steps of the analyses: Data exploration......Page 427
22.5 Additive mixed modelling......Page 428
22.6 Discussion and conclusions......Page 434
23.1 Introduction......Page 436
23.2 The data......Page 438
23.3 Getting familiar with the data: Exploration......Page 439
23.4 Building a mixed model......Page 443
23.5 The optimal model in terms of random components......Page 446
23.6 Validating the optimal linear mixed model......Page 449
23.7 More numerical output for the optimal model......Page 450
23.8 Discussion......Page 452
24.1 Introduction......Page 454
24.2 From radars to data......Page 455
24.3 Classification trees......Page 457
24.4 A tree for the birds......Page 459
24.5 A tree for birds, clutter and more clutter......Page 464
24.6 Discussion and conclusions......Page 466
25.1 Introduction......Page 468
25.2 Horse mackerel in the northeast Atlantic......Page 469
25.3 Neural networks......Page 471
25.4 Collection of data......Page 474
25.5 Data exploration......Page 475
25.6 Neural network results......Page 476
25.7 Discussion......Page 479
26.1 Introduction......Page 482
26.2 The data......Page 483
26.3 Data exploration......Page 486
26.4 Linear regression results......Page 491
26.5 Generalised least squares results......Page 495
26.6 Multivariate analysis results......Page 498
26.7 Discussion......Page 502
27.1 Introduction......Page 504
27.2 The variables......Page 505
27.3 Analysing the data using univariate methods......Page 506
27.4 Analysing the data using multivariate methods......Page 513
27.5 Discussion and conclusions......Page 518
28.1 Introduction and the underlying questions......Page 521
28.2 Study site and sample collection......Page 522
28.3 Data exploration......Page 524
28.4 The Mantel test approach......Page 527
28.6 Discussion and conclusions......Page 530
29.2 The data......Page 532
29.3 Principal component analysis......Page 534
29.5 Principal component analysis results......Page 535
29.6 Simpler alternatives to PCA......Page 541
29.7 Discussion......Page 543
30.1 Introduction......Page 545
30.2 The turtle data......Page 546
30.3 Data exploration......Page 547
30.4 Overview of classic approaches related to PCA......Page 550
30.5 Applying PCA to the original turtle data......Page 552
30.6 Classic morphometric data analysis approaches......Page 553
30.7 A geometric morphometric approach......Page 558
31.1 Introduction......Page 563
31.3 Methods......Page 564
31.4 Results......Page 567
31.5 Discussion......Page 575
32.1 Introduction......Page 577
32.2 The study area......Page 578
32.3 The data......Page 579
32.4 Data exploration......Page 581
32.5 Canonical correspondence analysis results......Page 584
32.6 African star grass......Page 587
32.7 Discussion and conclusion......Page 589
33.1 Introduction......Page 591
33.2 The time series data......Page 592
33.3 MAFA and DFA......Page 595
33.4 MAFA results......Page 596
33.5 DFA results......Page 598
33.6 Discussion......Page 603
34.1 Introduction......Page 605
34.2 Data......Page 606
34.3 Time series analysis......Page 607
34.4 Discussion......Page 614
35.1 Interaction between hydrodynamical and biological factors......Page 616
35.2 The data......Page 618
35.3 Data exploration......Page 620
35.4 Additive mixed modelling......Page 622
35.5 Additive mixed modelling results......Page 625
35.6 Discussion......Page 628
36.1 Introduction......Page 630
36.2 Endangered Hawaiian waterbirds......Page 631
36.3 Data exploration......Page 632
36.4 Three ways to estimate trends......Page 634
36.5 Additive mixed modelling......Page 641
36.6 Sudden breakpoints......Page 645
36.7 Discussion......Page 646
37.1 Introduction......Page 647
37.2 Study area......Page 649
37.3 Data exploration......Page 650
37.4 Models of boreality without spatial auto-correlation......Page 652
37.5 Models of boreality with spatial auto-correlation......Page 654
37.6 Conclusion......Page 660
References......Page 663
C......Page 681
G......Page 682
M......Page 683
Q......Page 684
T......Page 685
Z......Page 686
