Numerical Ecology

Preface

Chapter 1 Complex ecological data sets

1.0 Numerical analysis of ecological data

1.1 Spatial structure, spatial dependence, spatial correlation

1.2 Statistical testing by permutation

1.3 Computer programs and packages

1.4 Ecological descriptors

1.5 Coding

1.6 Missing data

1.7 Software

Chapter 2 Matrix algebra

2.0 Matrix algebra

2.1 The ecological data matrix

2.2 Association matrices

2.3 Special matrices

2.4 Vectors and scaling

2.5 Matrix addition and multiplication

2.6 Determinant

2.7 Rank of a matrix

2.8 Matrix inversion

2.9 Eigenvalues and eigenvectors

2.10 Some properties of eigenvalues and eigenvectors

2.11 Singular value decomposition

2.12 Software

Chapter 3 Dimensional analysis in ecology

3.0 Dimensional analysis

3.1 Dimensions

3.2 Fundamental principles and the Pi theorem

3.3 The complete set of dimensionless products

3.4 Scale factors and models

Chapter 4 Multidimensional quantitative data

4.0 Multidimensional statistics

4.1 Multidimensional variables and dispersion matrix

4.2 Correlation matrix

4.3 Multinormal distribution

4.4 Principal axes

4.5 Multiple and partial correlations

4.6 Tests of normality and multinormality

4.7 Software

Chapter 5 Multidimensional semiquantitative data

5.0 Nonparametric statistics

5.1 Quantitative, semiquantitative, and qualitative multivariates

5.2 One-dimensional nonparametric statistics

5.3 Rank correlations

5.4 Coefficient of concordance

5.5 Software

Chapter 6 Multidimensional qualitative data

6.0 General principles

6.1 Information and entropy

6.2 Two-way contingency tables

6.3 Multiway contingency tables

6.4 Contingency tables: correspondence

6.5 Species diversity

6.6 Software

Chapter 7 Ecological resemblance

7.0 The basis for clustering and ordination

7.1 Q and R analyses

7.2 Association coefficients

7.3 Q mode: similarity coefficients

7.4 Q mode: distance coefficients

7.5 R mode: coefficients of dependence

7.6 Choice of a coefficient

7.7 Transformations for community composition data

7.8 Software

Chapter 8 Cluster analysis

8.0 A search for discontinuities

8.1 Definitions

8.2 The basic model: single linkage clustering

8.3 Cophenetic matrix and ultrametric property

8.4 The panoply of methods

8.5 Hierarchical agglomerative clustering

8.6 Reversals

8.7 Hierarchical divisive clustering

8.8 Partitioning by K-means

8.9 Species clustering: biological associations

8.10 Seriation

8.11 Multivariate regression trees (MRT)

8.12 Clustering statistics

1 Connectedness and isolation

2 Cophenetic correlation and related measures

8.13 Cluster validation

8.14 Cluster representation and choice of a method

8.15 Software

Chapter 9 Ordination in reduced space

9.0 Projecting data sets in a few dimensions

9.1 Principal component analysis (PCA)

9.2 Correspondence analysis (CA)

9.3 Principal coordinate analysis (PCoA)

9.4 Nonmetric multidimensional scaling (nMDS)

9.5 Software

Chapter 10 Interpretation of ecological structures

10.0 Ecological structures

10.1 Clustering and ordination

10.2 The mathematics of ecological interpretation

10.3 Regression

10.4 Path analysis

10.5 Matrix comparisons

10.6 The fourth-corner problem

4 Other types of comparisons among variables

10.7 Software

Chapter 11 Canonical analysis

11.0 Principles of canonical analysis

11.1 Redundancy analysis (RDA)

11.2 Canonical correspondence analysis (CCA)

11.3 Linear discriminant analysis (LDA)

11.4 Canonical correlation analysis (CCorA)

11.5 Co-inertia (CoIA) and Procrustes (Proc) analyses

11.6 Canonical analysis of community composition data

11.7 Software

Chapter 12 Ecological data series

12.0 Ecological series

12.1 Characteristics of data series and research objectives

12.2 Trend extraction and numerical filters

12.3 Periodic variability: correlogram

12.4 Periodic variability: periodogram

12.5 Periodic variability: spectral and wavelet analyses

12.6 Detection of discontinuities in multivariate series

12.7 Box-Jenkins models

12.8 Software

Chapter 13 Spatial analysis

13.0 Spatial patterns

13.1 Structure functions

13.2 Maps

13.3 Patches and boundaries

13.4 Unconstrained and constrained ordination maps

13.5 Spatial modelling through canonical analysis

13.6 Software

Chapter 14 Multiscale analysis

14.0 Introduction to multiscale analysis

14.1 Distance-based Moran’s eigenvector maps (dbMEM)

14.2 Moran’s eigenvector maps (MEM), general form

14.3 Asymmetric eigenvector maps (AEM)

14.4 Multiscale ordination (MSO)

14.5 Other eigenfunction-based methods of spatial analysis

14.6 Multiscale analysis of beta diversity

14.7 Software

References

Subject Index