1.0	Numerical analysis of ecological data	1
1.1	Autocorrelation and spatial structure	8
	1 – Types of spatial structures, 11; 2 – Tests of statistical signiﬁcance in the presence
	of autocorrelation, 12; 3 – Classical sampling and spatial structure, 16
1.2	Statistical testing by permutation 17
	1 – Classical tests of signiﬁcance, 17; 2 – Permutation tests, 20; 3 – Numerical
	example, 22; 4 – Remarks on permutation tests, 24

1.3Computers 26

1.4 Ecological descriptors 27

1 – Mathematical types of descriptor, 28; 2 – Intensive, extensive, additive, and nonadditive descriptors, 31

1.5 Coding 33

1 – Linear transformation, 34; 2 – Nonlinear transformations, 35; 3 – Combining descriptors, 37; 4 – Ranging and standardization, 37; 5 – Implicit transformation in association coefﬁcients, 39; 6 – Normalization, 39; 7 – Dummy variable (binary) coding, 46

1.6 Missing data 47

1 – Deleting rows or columns, 48; 2 – Accommodating algorithms to missing data, 48; 3 – Estimating missing values, 48

2. Matrix algebra: a summary

2.0	Matrix algebra	51
2.1	The ecological data matrix 52
2.2	Association matrices		55
2.3	Special matrices	56
2.4	Vectors and scaling		61

vi	Contents

2.5	Matrix addition and multiplication 63
2.6	Determinant 68
2.7	The rank of a matrix 72
2.8	Matrix inversion 73
2.9	Eigenvalues and eigenvectors	80
	1 – Computation, 81; 2 – Numerical examples, 83
2.10	Some properties of eigenvalues and eigenvectors 90
2.11	Singular value decomposition	94

3. Dimensional analysis in ecology

3.0 Dimensional analysis 97

3.1Dimensions 98

3.2	Fundamental principles and the Pi theorem	103
3.3	The complete set of dimensionless products	118
3.4	Scale factors and models 126

4. Multidimensional quantitative data

4.0	Multidimensional statistics		131
4.1	Multidimensional variables and dispersion matrix 132
4.2	Correlation matrix	139
4.3	Multinormal distribution		144
4.4	Principal axes 152
4.5	Multiple and partial correlations			158
	1 – Multiple linear	correlation, 158;		2 – Partial		correlation, 161; 3 – Tests of
	statistical signiﬁcance, 164;		4 – Interpretation of			correlation coefﬁcients, 166;
	5 – Causal modelling using correlations, 169
4.6	Multinormal conditional distribution				173
4.7	Tests of normality and multinormality				178

5. Multidimensional semiquantitative data

5.0	Nonparametric statistics 185
5.1	Quantitative, semiquantitative, and qualitative multivariates 186
5.2	One-dimensional nonparametric statistics 191
5.3	Multidimensional ranking tests	194

Contents	vii

6. Multidimensional qualitative data

6.0	General principles	207
6.1	Information and entropy 208
6.2	Two-way contingency tables		216
6.3	Multiway contingency tables		222
6.4	Contingency tables: correspondence 230
6.5	Species diversity	235

1 – Diversity, 239; 2 – Evenness, equitability, 243

7. Ecological resemblance

7.0	The basis for clustering and ordination							247
7.1	Q and R analyses			248
7.2	Association coefﬁcients				251
7.3	Q mode: similarity coefﬁcients						253
	1	– Symmetrical binary coefﬁcients, 254; 2 – Asymmetrical binary coefﬁcients, 256;
	3	– Symmetrical	quantitative			coefﬁcients, 258; 4 – Asymmetrical			quantitative
	coefﬁcients, 264; 5 – Probabilistic coefﬁcients, 268
7.4	Q mode: distance coefﬁcients					274
	1	– Metric distances, 276; 2 – Semimetrics, 286
7.5	R mode: coefﬁcients of dependence							288
	1	– Descriptors	other	than	species		abundances, 289; 2 – Species		abundances:
	biological associations, 291
7.6	Choice of a coefﬁcient				295
7.7	Computer programs and packages						302

8. Cluster analysis

8.0 A search for discontinuities 303

8.1Deﬁnitions 305

8.2	The basic model: single linkage clustering				308
8.3	Cophenetic matrix and ultrametric property				312
	1 – Cophenetic matrix, 312; 2 – Ultrametric property, 313
8.4	The panoply of methods		314
	1 – Sequential	versus simultaneous		algorithms, 314; 2 – Agglomeration versus
	division, 314;	3 – Monothetic	versus	polythetic	methods, 314; 4 – Hierarchical
	versus non-hierarchical methods, 315; 5 – Probabilistic versus non-probabilistic
	methods, 315


viii	Contents

8.5 Hierarchical agglomerative clustering			316
1 – Single linkage agglomerative		clustering, 316; 2 – Complete			linkage
agglomerative	clustering, 316; 3 – Intermediate			linkage clustering, 318;
4 – Unweighted	arithmetic average	clustering (UPGMA), 319; 5 – Weighted
arithmetic average clustering (WPGMA), 321; 6 – Unweighted centroid clustering
(UPGMC), 322;	7 – Weighted centroid		clustering	(WPGMC), 324;	8 – Ward’s

minimum variance method, 329; 9 – General agglomerative clustering model, 333; 10 – Flexible clustering, 335; 11 – Information analysis, 336

8.6Reversals 341

8.7	Hierarchical divisive clustering		343
	1 – Monothetic methods, 343; 2 – Polythetic			methods, 345;	3 – Division in
	ordination space, 346; 4 – TWINSPAN, 347
8.8	Partitioning by K-means 349
8.9	Species clustering: biological associations			355
	1 – Non-hierarchical	complete	linkage clustering, 358;		2 – Probabilistic
	clustering, 361; 3 – Indicator species, 368
8.10	Seriation 371
8.11	Clustering statistics	374
	1 – Connectedness and isolation, 374; 2 – Cophenetic correlation and related
	measures, 375
8.12	Cluster validation	378
8.13	Cluster representation and choice of a method 381

9. Ordination in reduced space

9.0

Projecting data sets in a few dimensions

387

9.1

Principal component analysis (PCA)

391

– Computing the eigenvectors, 392; 2 – Computing and representing the principal

components, 394;

3 – Contributions of

descriptors, 395;

4 – Biplots, 403;

– Principal

components

correlation

matrix, 406; 6 – The meaningful

components, 409;

7 – Misuses

principal

components, 411;

8 – Ecological

applications, 415; 9 – Algorithms, 418

9.2

Principal coordinate analysis (PCoA)

424

– Computation, 425;

2 – Numerical

example, 427; 3 – Rationale of the

method, 429;

4 – Negative

eigenvalues, 432;

5 – Ecological applications, 438;

– Algorithms, 443

9.3

Nonmetric multidimensional scaling (MDS)

444

9.4

Correspondence analysis (CA)

451

– Computation, 452;

2 – Numerical

example, 457; 3 – Interpretation, 461;

– Site

species

data

tables, 462;

5 – Arch effect, 465;

6 – Ecological

applications, 472; 7 – Algorithms, 473

9.5

Factor analysis

476

							Contents			ix

10. Interpretation of ecological structures
10.0	Ecological structures					481
10.1	Clustering and ordination						482
10.2	The mathematics of ecological interpretation								486
10.3	Regression		497
	1	– Simple	linear		regression:			model I, 500;	2 – Simple linear	regression:
	model II, 504; 3 – Multiple linear regression, 517; 4 – Polynomial regression, 526;
	5	– Partial	linear		regression, 528; 6 – Nonlinear regression, 536;					7 – Logistic
	regression, 538; 8 – Splines and LOWESS smoothing, 542
10.4	Path analysis			546
10.5	Matrix comparisons					551
	1	– Mantel test,		552;		2 – More		than two matrices, 557; 3 – ANOSIM test, 560;
	4	– Procrustes analysis, 563
10.6	The 4th-corner problem						565

1 – Comparing two qualitative variables, 566; 2 – Test of statistical signiﬁcance, 567; 3 – Permutational models, 569; 4 – Other types of comparison among variables, 571

11.	Canonical analysis
	11.0	Principles of canonical analysis							575
	11.1	Redundancy analysis (RDA)						579
		1	– The	algebra	of	redundancy		analysis, 580;			2 – Numerical	examples, 587;
		3	– Algorithms, 592;
	11.2	Canonical correspondence analysis (CCA)								594
		1	– The	algebra	of	canonical		correspondence			analysis, 594;	2 – Numerical
		example, 597; 3 – Algorithms, 600
	11.3	Partial RDA and CCA					605
		1	– Applications, 605; 2 – Tests of signiﬁcance, 606
	11.4	Canonical correlation analysis (CCorA)								612
	11.5	Discriminant analysis					616
		1	– The algebra of discriminant analysis, 620; 2 – Numerical example, 626
	11.6	Canonical analysis of species data							633
12. Ecological data series
	12.0	Ecological series				637
	12.1	Characteristics of data series and research objectives 641
	12.2	Trend extraction and numerical ﬁlters 647
	12.3	Periodic variability: correlogram							653

1 – Autocovariance and autocorrelation, 653; 2 – Cross-covariance and crosscorrelation, 661

x	Contents

12.4 Periodic variability: periodogram 665
1	– Periodogram of Whittaker and Robinson, 665; 2 – Contingency periodogram of
Legendre et al., 670; 3 – Periodograms of Schuster and Dutilleul, 673;
4	– Harmonic regression, 678

12.5 Periodic variability: spectral analysis 679

1 – Series of a single variable, 680; 2 – Multidimensional series, 683; 3 – Maximum entropy spectral analysis, 688

12.6	Detection of discontinuities in multivariate series 691
	1	– Ordinations in	reduced space, 692; 2 – Segmenting data series, 693;
	3	– Webster’s method, 693; 4 – Chronological clustering, 696
12.7	Box-Jenkins models		702
12.8	Computer programs		704

13. Spatial analysis

13.0	Spatial patterns			707
13.1	Structure functions				712
	1	– Spatial	correlograms, 714;				2 – Interpretation			of	all-directional
	correlograms, 721;			3 – Variogram, 728; 4 – Spatial					covariance,		semi-variance,
	correlation, cross-correlation, 733; 5 – Multivariate Mantel correlogram, 736
13.2	Maps 738
	1	– Trend-surface analysis, 739;				2 – Interpolated		maps, 746; 3 – Measures of
	ﬁt, 751
13.3	Patches and boundaries 751
	1	– Connection	networks, 752;			2 – Constrained		clustering, 756;			3 – Ecological
	boundaries, 760; 4 – Dispersal, 763
13.4	Unconstrained and constrained ordination maps								765
13.5	Causal modelling: partial canonical analysis							769
	1	– Partitioning method, 771; 2 – Interpretation of the fractions, 776
13.6	Causal modelling: partial Mantel analysis 779
	1	– Partial Mantel		correlations, 779;			2 – Multiple		regression		approach, 783;
	3	– Comparison of methods, 783
13.7	Computer programs				785

Bibliography 787

Tables 833

Subject index 839

1 / 111 2 3 4 5 6 7 8 9 10 11 > Следующая >>>

Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]

#
01.01.20201.42 Mб41kustova_e_n_ekologicheskoe_pravo-1.pdf
#
19.11.20191.42 Mб121kustova_e_n_ekologicheskoe_pravo.pdf
#
19.11.201924.67 Mб31kuz_mina_t_a_red_problema_soznaniya_v_sovremennoy_zapadnoy_f.pdf
#
01.01.20202.05 Mб411lapina_m_a_ekologicheskoe_pravo.pdf
#
19.11.20191.42 Mб51lega_v_p_istoriya_zapadnoy_filosofii_chast_2_novoe_vremya_so.pdf
#
19.11.20193.55 Mб101legendre_p_legendre_l_numerical_ecology.pdf
#
29.10.2019909.16 Кб61leont_eva_e_yu_filosofiya_nauki_vvedenie_v_distsiplinu.pdf
#
19.11.2019570.15 Кб11lisovoy_a_l_filosofiya_epokhi_vozrozhdeniya_i_novogo_vremeni.pdf
#
19.11.20191.52 Mб11lushnikov_a_m_istoriya_i_metodologiya_yuridicheskoy_nauki.pdf
#
01.01.2020595.33 Кб91lyubomirov_d_e_sapenok_o_v_petrov_s_o_istoriya_i_filosofiya.pdf
#
29.10.2019915.04 Кб71makhova_n_p_mosienko_l_i_nekhaev_v_a_skachkov_a_s_istoriya_i.pdf

Contents