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E-grāmata: Numerical Ecology

4.18/5 (30 ratings by Goodreads)
(Département de Sciences Biologiques, Université de Montréal, H3C 3J7, Québec, Canada),
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Numerical EcologyPalielināt
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The book describes and discusses the numerical methods which are successfully being used for analysing ecological data, using a clear and comprehensive approach. These methods are derived from the fields of mathematical physics, parametric and nonparametric statistics, information theory, numerical taxonomy, archaeology, psychometry, sociometry, econometry and others.
  • An updated, 3rd English edition of the most widely cited book on quantitative analysis of multivariate ecological data
  • Relates ecological questions to methods of statistical analysis, with a clear description of complex numerical methods
  • All methods are illustrated by examples from the ecological literature so that ecologists clearly see how to use the methods and approaches in their own research
  • All calculations are available in R language functions

Recenzijas

"Pierre Legendreand Louis Legendre present this text of data analysis methods for ecologists, with an emphasis on use of the statistical computer language R. The book begins by articulating salient points about ecological data in particular, such as the many functional correlations that must be adjusted for without ascribing as-yet-unexplained variation to random noise, then covers the mathematical foundations of matrix algebra and dimensional analysis."--Reference & Research Book News, December 2013"What I really love about this book is that for most methods the formulae are given. Thus, we learn the statistical rea-soning, the mathematics and the ecological interpretationNumerical Ecology is a definite must-have for any quanti-tative ecologist."--Basic and Applied Ecology, December 2013

Papildus informācija

Clear and comprehensive approach to the numerical methods that are successfully used for analysing ecological data
Preface xii
1 Complex ecological data sets
1.0 Numerical analysis of ecological data
1(7)
1.1 Spatial structure, spatial dependence, spatial correlation
8(14)
1 Origin of spatial structures
11(6)
2 Tests of significance in the presence of spatial correlation
17(4)
3 Classical sampling and spatial structure
21(1)
1.2 Statistical testing by permutation
22(10)
1 Classical tests of significance
22(3)
2 Permutation tests
25(3)
3 Numerical example
28(1)
4 Remarks on permutation tests
29(3)
1.3 Computer programs and packages
32(1)
1.4 Ecological descriptors
33(6)
1 Mathematical types of descriptors
34(3)
2 Intensive, extensive, additive, and non-additive descriptors
37(2)
1.5 Coding
39(15)
1 Linear transformation
40(1)
2 Nonlinear transformations
41(2)
3 Combining descriptors
43(1)
4 Ranging and standardization
43(2)
5 Implicit transformation in association coefficients
45(1)
6 Normalization
45(7)
7 Dummy variable coding
52(2)
1.6 Missing data
54(3)
1 Delete rows or columns
55(1)
2 Accommodate algorithms to missing data
55(1)
3 Estimate missing values
55(2)
1.7 Software
57(2)
2 Matrix algebra: a summary
2.0 Matrix algebra
59(1)
2.1 The ecological data matrix
60(3)
2.2 Association matrices
63(1)
2.3 Special matrices
64(5)
2.4 Vectors and scaling
69(2)
2.5 Matrix addition and multiplication
71(5)
2.6 Determinant
76(4)
2.7 Rank of a matrix
80(2)
2.8 Matrix inversion
82(7)
2.9 Eigenvalues and eigenvectors
89(10)
1 Computation
90(2)
2 Numerical examples
92(7)
2.10 Some properties of eigenvalues and eigenvectors
99(4)
2.11 Singular value decomposition
103(4)
2.12 Software
107(2)
3 Dimensional analysis in ecology
3.0 Dimensional analysis
109(1)
3.1 Dimensions
110(5)
3.2 Fundamental principles and the Pi theorem
115(15)
3.3 The complete set of dimensionless products
130(8)
3.4 Scale factors and models
138(5)
4 Multidimensional quantitative data
4.0 Multidimensional statistics
143(1)
4.1 Multidimensional variables and dispersion matrix
144(7)
4.2 Correlation matrix
151(6)
4.3 Multinormal distribution
157(8)
4.4 Principal axes
165(6)
4.5 Multiple and partial correlations
171(16)
1 Multiple linear correlation
173(2)
2 Partial correlation
175(5)
3 Tests of statistical significance
180(2)
4 Causal modelling using correlations
182(5)
4.6 Tests of normality and multinormality
187(7)
4.7 Software
194(1)
5 Multidimensional semiquantitative data
5.0 Nonparametric statistics
195(2)
5.1 Quantitative, semiquantitative, and qualitative multivariates
197(4)
5.2 One-dimensional nonparametric statistics
201(4)
5.3 Rank correlations
205(8)
1 Spearman r
205(4)
2 Kendall τ
209(4)
5.4 Coefficient of concordance
213(5)
1 Computing Kendall W
214(2)
2 Testing the significance of W
216(1)
3 Contributions of individual variables to Kendall's concordance
217(1)
5.5 Software
218(1)
6 Multidimensional qualitative data
6.0 General principles
219(1)
6.1 Information and entropy
220(8)
6.2 Two-way contingency tables
228(7)
6.3 Multiway contingency tables
235(8)
6.4 Contingency tables: correspondence
243(4)
6.5 Species diversity
247(17)
1 Diversity
250(5)
2 Evenness, equitability
255(3)
3 Species diversity through space
258(6)
6.6 Software
264(1)
7 Ecological resemblance
7.0 The basis for clustering and ordination
265(1)
7.1 Q and R analyses
266(3)
7.2 Association coefficients
269(4)
1 Similarity, distance, and dependence coefficients
270(1)
2 The double-zero problem
271(2)
7.3 Q mode: similarity coefficients
273(22)
1 Symmetrical binary coefficients
273(2)
2 Asymmetrical binary coefficients
275(3)
3 Symmetrical quantitative coefficients
278(6)
4 Asymmetrical quantitative coefficients
284(4)
5 Probabilistic coefficients
288(7)
7.4 Q mode: distance coefficients
295(18)
1 Metric distances
299(11)
2 Semimetrics
310(3)
7.5 R mode: coefficients of dependence
313(7)
1 Descriptors other than species abundances
313(3)
2 Species abundances: biological associations
316(4)
7.6 Choice of a coefficient
320(7)
7.7 Transformations for community composition data
327(7)
1 Transformation formulas
328(4)
2 Numerical example
332(2)
3 Beals smoothing
334(1)
7.8 Software
334(3)
8 Cluster analysis
8.0 A search for discontinuities
337(1)
8.1 Definitions
338(3)
8.2 The basic model: single linkage clustering
341(5)
8.3 Cophenetic matrix and ultrametric property
346(1)
1 Cophenetic matrix
346(1)
2 Ultrametric property
347(1)
8.4 The panoply of methods
347(3)
1 Sequential versus simultaneous algorithms
347(1)
2 Agglomeration versus division
348(1)
3 Monothetic versus polythetic methods
348(1)
4 Hierarchical versus non-hierarchical methods
348(1)
5 Constrained clustering methods
349(1)
6 Probabilistic versus non-probabilistic methods
349(1)
8.5 Hierarchical agglomerative clustering
350(26)
1 Single linkage agglomerative clustering
350(1)
2 Complete linkage agglomerative clustering
350(1)
3 Intermediate linkage clustering
351(1)
4 Unweighted arithmetic average clustering (UPGMA)
352(3)
5 Weighted arithmetic average clustering (WPGMA)
355(2)
6 Unweighted centroid clustering (UPGMC)
357(3)
7 Weighted centroid clustering (WPGMC)
360(1)
8 Ward's minimum variance method
360(7)
9 General agglomerative clustering model
367(3)
10 Flexible clustering
370(2)
11 Information analysis
372(4)
8.6 Reversals
376(1)
8.7 Hierarchical divisive clustering
377(6)
1 Monothetic methods
377(2)
2 Polythetic methods
379(1)
3 Division in ordination space
380(1)
4 Twinspan
381(2)
8.8 Partitioning by K-means
383(6)
8.9 Species clustering: biological associations
389(14)
1 Non-hierarchical complete linkage clustering
392(3)
2 Concordance analysis
395(2)
3 Indicator species
397(6)
8.10 Seriation
403(3)
8.11 Multivariate regression trees (MRT)
406(5)
8.12 Clustering statistics
411(4)
1 Connectedness and isolation
411(1)
2 Cophenetic correlation and related measures
412(3)
8.13 Cluster validation
415(3)
8.14 Cluster representation and choice of a method
418(5)
8.15 Software
423(2)
9 Ordination in reduced space
9.0 Projecting data sets in a few dimensions
425(4)
9.1 Principal component analysis (PCA)
429(35)
1 Computing the eigenvectors of a dispersion matrix
431(1)
2 Computing and representing the principal components
432(2)
3 Contributions of the descriptors
434(9)
4 PCA biplots
443(2)
5 Principal components of a correlation matrix
445(3)
6 The meaningful components
448(2)
7 Misuses of principal component analysis
450(2)
8 Ecological applications
452(4)
9 Algorithms
456(6)
10 Metric ordination of community composition data
462(2)
9.2 Correspondence analysis (CA)
464(28)
1 Computation
466(5)
2 Numerical example
471(5)
3 Interpretation
476(1)
4 Site x species data tables
477(5)
5 Arch effect and detrended correspondence analysis
482(5)
6 Ecological applications
487(3)
7 Algorithms
490(2)
9.3 Principal coordinate analysis (PCoA)
492(20)
1 Computation
493(1)
2 Numerical example
494(3)
3 Rationale of the method
497(3)
4 Negative eigenvalues
500(6)
5 Ecological applications
506(5)
6 Algorithm
511(1)
9.4 Nonmetric multidimensional scaling (nMDS)
512(7)
9.5 Software
519(2)
10 Interpretation of ecological structures
10.0 Ecological structures
521(1)
10.1 Clustering and ordination
522(4)
10.2 The mathematics of ecological interpretation
526(10)
1 Explaining ecological structures
530(2)
2 Forecasting ecological structures
532(2)
3 Ecological prediction
534(2)
10.3 Regression
536(56)
1 Simple linear regression: model I
539(4)
2 Simple linear regression: model II
543(12)
3 Multiple linear regression
555(13)
4 Polynomial regression
568(2)
5 Partial linear regression and variation partitioning
570(13)
6 Nonlinear regression
583(1)
7 Logistic regression
584(5)
8 Splines and Lowess smoothing
589(3)
10.4 Path analysis
592(5)
10.5 Matrix comparisons
597(16)
1 Two association matrices: Mantel test
598(6)
2 More than two association matrices
604(4)
3 Anosim test
608(3)
4 Procrustes test
611(2)
10.6 The fourth-corner problem
613(9)
1 Comparing two qualitative variables
614(2)
2 Test of statistical significance
616(2)
3 Permutational models
618(3)
4 Other types of comparisons among variables
621(1)
10.7 Software
622(3)
11 Canonical analysis
11.0 Principles of canonical analysis
625(4)
11.1 Redundancy analysis (RDA)
629(32)
1 Simple RDA
630(2)
2 Statistics in simple RDA
632(3)
3 The algebra of simple RDA
635(7)
4 Numerical examples, simple RDA
642(4)
5 RDA and CCA of community composition data
646(3)
6 Partial RDA
649(2)
7 Statistics in partial RDA
651(1)
8 Tests of significance in partial RDA
651(2)
9 Numerical example, partial RDA
653(1)
10 Some applications of partial RDA
654(4)
11 Variation partitioning by RDA
658(3)
11.2 Canonical correspondence analysis (CCA)
661(12)
1 The algebra of canonical correspondence analysis
662(5)
2 Numerical example
667(6)
11.3 Linear discriminant analysis (LDA)
673(17)
1 The algebra of discriminant analysis
676(6)
2 Statistics in linear discriminant analysis
682(1)
3 Numerical example
683(7)
11.4 Canonical correlation analysis (CCorA)
690(6)
1 The algebra of canonical correlation analysis
691(3)
2 Statistics in canonical correlation analysis
694(1)
3 Applications of CCorA
694(2)
11.5 Co-inertia (CoIA) and Procrustes (Proc) analyses
696(10)
1 The algebra of co-inertia analysis (CoIA)
697(6)
2 Symmetric Procrustes analysis (Proc)
703(2)
3 Canonical correlation, Procrustes, or co-inertia analysis?
705(1)
11.6 Canonical analysis of community composition data
706(3)
11.7 Software
709(2)
12 Ecological data series
12.0 Ecological series
711(3)
12.1 Characteristics of data series and research objectives
714(8)
12.2 Trend extraction and numerical filters
722(5)
12.3 Periodic variability: correlogram
727(12)
1 Autocovariance and autocorrelation
728(7)
2 Cross-covariance and cross-correlation
735(4)
12.4 Periodic variability: periodogram
739(15)
1 Periodogram of Whittaker and Robinson
739(5)
2 Contingency periodogram of Legendre et al.
744(3)
3 Periodogram of Schuster
747(4)
4 Periodogram of Dutilleul
751(2)
5 Harmonic regression
753(1)
12.5 Periodic variability: spectral and wavelet analyses
754(14)
1 Series of a single variable
754(5)
2 Multidimensional series
759(4)
3 Maximum entropy spectral analysis
763(3)
4 Wavelet analysis
766(2)
12.6 Detection of discontinuities in multivariate series
768(12)
1 Ordinations in reduced space
768(1)
2 Segmenting data series
769(1)
3 Webster's method
770(3)
4 Time-constrained clustering by MRT
773(1)
5 Chronological clustering
773(7)
12.7 Box-Jenkins models
780(2)
12.8 Software
782(3)
13 Spatial analysis
13.0 Spatial patterns
785(7)
13.1 Structure functions
792(29)
1 Spatial correlograms
793(7)
2 Interpretation of all-directional correlograms
800(7)
3 Variogram
807(6)
4 Multivariate variogram
813(3)
5 Spatial covariance, semi-variance, correlation, cross-correlation
816(3)
6 Multivariate Mantel correlogram
819(2)
13.2 Maps
821(13)
1 Trend-surface analysis
822(7)
2 Interpolated maps
829(4)
3 Measures of fit
833(1)
13.3 Patches and boundaries
834(15)
1 Connection networks
834(5)
2 Space-constrained clustering
839(5)
3 Ecological boundaries
844(3)
4 Dispersal
847(2)
13.4 Unconstrained and constrained ordination maps
849(3)
13.5 Spatial modelling through canonical analysis
852(5)
13.6 Software
857(2)
14 Multiscale analysis: spatial eigenfunctions
14.0 Introduction to multiscale analysis
859(2)
14.1 Distance-based Moran's eigenvector maps (dbMEM)
861(20)
1 Algorithm
862(2)
2 Numerical examples
864(5)
3 Ecological applications
869(8)
4 Interpretation of the fractions
877(4)
14.2 Moran's eigenvector maps (MEM), general form
881(7)
1 Algorithm described through an example
881(3)
2 Different types of MEM eigenfunctions
884(4)
14.3 Asymmetric eigenvector maps (AEM)
888(6)
1 Algorithm described through an example
888(4)
2 Ecological applications
892(2)
14.4 Multiscale ordination (MSO)
894(6)
14.5 Other eigenfunction-based methods of spatial analysis
900(3)
1 Space-time interaction
900(1)
2 Multiscale codependence analysis
901(1)
3 Estimating and controlling for spatial structure in modelling
902(1)
14.6 Multiscale analysis of beta diversity
903(1)
14.7 Software
904(3)
References
907(62)
References to cited works
907(56)
References to R packages
963(6)
Subject index 969
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