Contributors .................................................. xix
1. Introduction ................................................. 1
1.1. Part 1: Applied statistical theory ...................... 1
1.2. Part 2: The case studies ................................ 3
1.3. Data, software and flowcharts ........................... 6
2. Data management and software ................................. 7
2.1. Introduction ............................................ 7
2.2. Data management ......................................... 8
2.3. Data preparation ........................................ 9
2.4. Statistical software ................................... 13
3. Advice for teachers ......................................... 17
3.1 Introduction ............................................ 17
4. Exploration ................................................. 23
4.1. The first steps ........................................ 24
4.2. Outliers, transformations and standardisations ......... 38
4.3. A final thought on data exploration .................... 47
5. Linear regression ........................................... 49
5.1. Bivariate linear regression ............................ 49
5.2. Multiple linear regression ............................. 67
5.3. Partial linear regression .............................. 73
6. Generalised linear modelling ................................ 79
6.1. Poisson regression ..................................... 79
6.2. Logistic regression .................................... 88
7. Additive and generalised additive modelling ................. 97
7.1. Introduction ........................................... 97
7.2. The additive model .................................... 101
7.3. Example of an additive model .......................... 102
7.4. Estimate the smoother and amount of smoothing ......... 104
7.5. Additive models with multiple explanatory variables ... 108
7.6. Choosing the amount of smoothing ...................... 112
7.7. Model selection and validation ........................ 115
7.8. Generalised additive modelling ........................ 120
7.9. Where to go from here ................................. 124
8. Introduction to mixed modelling ............................ 125
8.1. Introduction .......................................... 125
8.2. The random intercept and slope model .................. 128
8.3. Model selection and validation ........................ 130
8.4. A bit of theory ....................................... 135
8.5. Another mixed modelling example ....................... 137
8.6. Additive mixed modelling .............................. 140
9. Univariate tree models ..................................... 143
9.1. Introduction .......................................... 143
9.2. Pruning the tree ...................................... 149
9.3. Classification trees .................................. 152
9.4. A detailed example: Ditch data ........................ 152
10.Measures of association .................................... 163
10.1.Introduction .......................................... 163
10.2.Association between sites: Q analysis ................. 164
10.3.Association among species: R analysis ................. 171
10.4.Q and R analysis: Concluding remarks .................. 176
10.5.Hypothesis testing with measures of association ....... 179
11.Ordination - First encounter ............................... 189
11.1 Bray-Curtis ordination ................................ 189
12.Principal component analysis and redundancy analysis ....... 193
12.1.The underlying principle of PCA ....................... 193
12.2.PCA: Two easy explanations ............................ 194
12.3.PCA: Two technical explanations ....................... 196
12.4.Example of PCA ........................................ 197
12.5.The biplot ............................................ 200
12.6.General remarks ....................................... 205
12.7.Chord and Hellinger transformations ................... 206
12.8.Explanatory variables ................................. 208
12.9.Redundancy analysis ................................... 210
12.10.Partial RDA and variance partitioning ................ 219
12.11.PCA regression to deal with collinearity ............. 221
13.Correspondence analysis and canonical correspondence
analysis ................................................... 225
13.1.Gaussian regression and extensions .................... 225
13.2.Three rationales for correspondence analysis .......... 231
13.3.From RGR to CCA ....................................... 238
13.4.Understanding the CCA triplot ......................... 240
13.5.When to use PCA, CA, RDA or CCA ....................... 242
13.6.Problems with CA and CCA .............................. 243
14.Introduction to discriminant analysis ...................... 245
14.1.Introduction .......................................... 245
14.2.Assumptions ........................................... 248
14.3.Example ............................................... 250
14.4.The mathematics ....................................... 254
14.5.The numerical output for the sparrow data ............. 255
15.Principal coordinate analysis and non-metric
multidimensional scaling ................................... 259
15.1.Principal coordinate analysis ......................... 259
15.2.Non-metric multidimensional scaling ................... 261
16.Time series analysis — Introduction ........................ 265
16.1.Using what we have already seen before ................ 265
16.2.Auto-regressive integrated moving average models
with exogenous variables .............................. 281
17.Common trends and sudden changes ........................... 289
17.1.Repeated LOESS smoothing .............................. 289
17.2.Identifying the seasonal component .................... 293
17.3.Common trends: MAFA ................................... 299
17.4.Common trends: Dynamic factor analysis ................ 303
17.5.Sudden changes: Chronological clustering .............. 315
18.Analysis and modelling of lattice data ..................... 321
18.1.Lattice data .......................................... 321
18.2.Numerical representation of the lattice structure ..... 323
18.3.Spatial correlation ................................... 327
18.4.Modelling lattice data ................................ 331
18.5.More exotic models .................................... 334
18.6.Summary ............................................... 338
19.Spatially continuous data analysis and modelling ........... 341
19.1.Spatially continuous data ............................. 341
19.2.Geostatistical functions and assumptions .............. 342
19.3.Exploratory variography analysis ...................... 346
19.4.Geostatistical modelling: Kriging ..................... 358
19.5.A full spatial analysis of the bird radar data ........ 363
20.Univariate methods to analyse abundance of decapod
larvae ..................................................... 373
20.1.Introduction .......................................... 373
20.2.The data .............................................. 374
20.3.Data exploration ...................................... 377
20.4.Linear regression results ............................. 379
20.5.Additive modelling results ............................ 381
20.6.How many samples to take? ............................. 383
20.7.Discussion ............................................ 385
21.Analysing presence and absence data for flatfish
distribution in the Tagus estuary, Portugal ................ 389
21.1.Introduction .......................................... 389
21.2.Data and materials .................................... 390
21.3.Data exploration ...................................... 392
21.4.Classification trees .................................. 395
21.5.Generalised additive modelling ........................ 397
21.6.Generalised linear modelling .......................... 398
21.7.Discussion ............................................ 401
22.Crop pollination by honeybees in Argentina using
additive mixed modelling ................................... 403
22.1.Introduction .......................................... 403
22.2.Experimental setup .................................... 404
22.3.Abstracting the information ........................... 404
22.4.First steps of the analyses: Data exploration ......... 407
22.5.Additive mixed modelling .............................. 408
22.6.Discussion and conclusions ............................ 414
23.Investigating the effects of rice farming on aquatic
birds with mixed modelling ................................. 417
23.1.Introduction .......................................... 417
23.2.The data .............................................. 419
23.3.Getting familiar with the data: Exploration ........... 420
23.4.Building a mixed model ................................ 424
23.5.The optimal model in terms of random components ....... 427
23.6.Validating the optimal linear mixed model ............. 430
23.7.More numerical output for the optimal model ........... 431
23.8.Discussion ............................................ 433
24.Classification trees and radar detection of birds for
North Sea wind farms ....................................... 435
24.1.Introduction .......................................... 435
24.2.From radars to data ................................... 436
24.3.Classification trees .................................. 438
24.4.A tree for the birds .................................. 440
24.5.A tree for birds, clutter and more clutter ............ 445
24.6.Discussion and conclusions ............................ 447
25.Fish stock identification through neural network
analysis of parasite fauna ................................. 449
25.1.Introduction .......................................... 449
25.2.Horse mackerel in the northeast Atlantic .............. 450
25.3.Neural networks ....................................... 452
25.4.Collection of data .................................... 455
25.5.Data exploration ...................................... 456
25.6.Neural network results ................................ 457
25.7.Discussion ............................................ 460
26.Monitoring for change: Using generalised least squares,
non-metric multidimensional scaling, and the Mantel test
on western Montana grasslands .............................. 463
26.1.Introduction .......................................... 463
26.2.The data .............................................. 464
26.3.Data exploration ...................................... 467
26.4.Linear regression results ............................. 472
26.5.Generalised least squares results ..................... 476
26.6.Multivariate analysis results ......................... 479
26.7.Discussion ............................................ 483
27.Univariate and multivariate analysis applied on a Dutch
sandy beach community ...................................... 485
27.1.Introduction .......................................... 485
27.2.The variables ......................................... 486
27.3.Analysing the data using univariate methods ........... 487
27.4.Analysing the data using multivariate methods ......... 494
27.5.Discussion and conclusions ............................ 499
28.Multivariate analyses of South-American zoobenthic
species - spoilt for choice ................................ 503
28.1.Introduction and the underlying questions ............. 503
28.2.Study site and sample collection ...................... 504
28.3.Data exploration ...................................... 506
28.4.The Mantel test approach .............................. 509
28.5.The transformation plus RDA approach .................. 512
28.6.Discussion and conclusions ............................ 512
29.Principal component analysis applied to harbour porpoise
fatty acid data ............................................ 515
29.1.Introduction .......................................... 515
29.2.The data .............................................. 515
29.3.Principal component analysis .......................... 517
29.4.Data exploration ...................................... 518
29.5.Principal component analysis results .................. 518
29.6.Simpler alternatives to PCA ........................... 524
29.7.Discussion ............................................ 526
30.Multivariate analyses of morphometric turtle data - size
and shape .................................................. 529
30.1.Introduction .......................................... 529
30.2.The turtle data ....................................... 530
30.3.Data exploration ...................................... 531
30.4.Overview of classic approaches related to PCA ......... 534
30.5.Applying PCA to the original turtle data .............. 536
30.6.Classic morphometric data analysis approaches ......... 537
30.7.A geometric morphometric approach ..................... 542
31.Redundancy analysis and additive modelling applied on
savanna tree data .......................................... 547
31.1.Introduction .......................................... 547
31.2.Study area ............................................ 548
31.3.Methods ............................................... 548
31.4.Results ............................................... 551
31.5.Discussion ............................................ 559
32.Canonical correspondence analysis of lowland pasture
vegetation in the humid tropics of Mexico .................. 561
32.1.Introduction .......................................... 561
32.2.The study area ........................................ 562
32.3.The data .............................................. 563
32.4.Data exploration ...................................... 565
32.5.Canonical correspondence analysis results ............. 568
32.6.African star grass .................................... 571
32.7.Discussion and conclusion ............................. 573
33.Estimating common trends in Portuguese fisheries
landings ................................................... 575
33.1.Introduction .......................................... 575
33.2.The time series data .................................. 576
33.3.MAFA and DFA .......................................... 579
33.4.MAFA results .......................................... 580
33.5.DFA results ........................................... 582
33.6.Discussion ............................................ 587
34.Common trends in demersal communities on the
Newfoundland-Labrador Shelf ................................ 589
34.1.Introduction .......................................... 589
34.2.Data .................................................. 590
34.3.Time series analysis .................................. 591
34.4.Discussion ............................................ 598
35.Sea level change and salt marshes in the Wadden Sea:
A time series analysis ..................................... 601
35.1.Interaction between hydrodynamical and biological
factors ............................................... 601
35.2.The data .............................................. 603
35.3.Data exploration ...................................... 605
35.4.Additive mixed modelling .............................. 607
35.5.Additive mixed modelling results ...................... 610
35.6.Discussion ............................................ 613
36.Time series analysis of Hawaiian waterbirds ................ 615
36.1.Introduction .......................................... 615
36.2.Endangered Hawaiian waterbirds ........................ 616
36.3.Data exploration ...................................... 617
36.4.Three ways to estimate trends ......................... 619
36.5.Additive mixed modelling .............................. 626
36.6.Sudden breakpoints .................................... 630
36.7.Discussion ............................................ 631
37.Spatial modelling of forest community features in the
Volzhsko-Kamsky reserve .................................... 633
37.1.Introduction .......................................... 633
37.2.Study area ............................................ 635
37.3.Data exploration ...................................... 636
37.4.Models of boreality without spatial auto-
correlation ........................................... 638
37.5.Models of boreality with spatial auto-correlation ..... 640
37.6.Conclusion ............................................ 646
References .................................................... 649
Index ......................................................... 667
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