ALBERT

Note: Contents 1 Introduction 1.1 Why Numerical Ecology? 1.2 Why R? 1.3 Readership and Structure of the Book 1.4 How to Use This Book 1.5 The Data Sets 1.5.1 The Doubs Fish Data 1.5.2 The Oribatid Mite Data 1.6 A Quick Reminder About Help Sources 1.7 Now It Is Time 2 Exploratory Data Analysis 2.1 Objectives 2.2 Data Exploration 2.2.1 Data Extraction 2.2.2 Species Data: First Contact 2.2.3 Species Data: A Closer Look 2.2.4 Ecological Data Transformation 2.2.5 Environmental Data 2.3 Conclusion 3 Association Measures and Matrices 3.1 Objectives 3.2 The Main Categories of Association Measures (Short Overview) 3.2.1 Q Mode and R Mode 3.2.2 Symmetrical or Asymmetrical Coefficients in Q Mode: The Double-Zero Problem 3.2.3 Association Measures for Qualitative or Quantitative Data 3.2.4 To Summarize 3.3 Q Mode: Computing Dissimilarity Matrices Among Objects 3.3.1 Q Mode: Quantitative Species Data 3.3.2 Q Mode: Binary (Presence-Absence) Species Data 3.3.3 Q Mode: Quantitative Data (Excluding Species Abundances) 3.3.4 Q Mode: Binary Data (Excluding Species Presence-Absence Data) 3.3.5 Q Mode: Mixed Types Including Categorical (Qualitative Multiclass) Variables 3.4 R Mode: Computing Dependence Matrices Among Variables 3.4.1 R Mode: Species Abundance Data 3.4.2 R Mode: Species Presence-Absence Data 3.4.3 R Mode: Quantitative and Ordinal Data (Other than Species Abundances) 3.4.4 R Mode: Binary Data (Other than Species Abundance Data) 3.5 Pre-transformations for Species Data 3.6 Conclusion 4 Cluster Analysis 4.1 Objectives 4.2 Clustering Overview 4.3 Hierarchical Clustering Based on Links 4.3.1 Single Linkage Agglomerative Clustering 4.3.2 Complete Linkage Agglomerative Clustering 4.4 Average Agglomerative Clustering 4.5 Ward's Minimum Variance Clustering 4.6 Flexible Clustering 4.7 Interpreting and Comparing Hierarchical Clustering Results 4.7.1 Introduction 4.7.2 Cophenetic Correlation 4.7.3 Looking for Inteipretable Clusters 4.8 Non-hierarchical Clustering 4.8.1 k-means Partitioning 4.8.2 Partitioning Around Medoids (PAM) 4.9 Comparison with Environmental Data 4.9.1 Comparing a Typology with External Data (ANOVA Approach) 4.9.2 Comparing Two Typologies (Contingency Table Approach) 4.10 Species Assemblages 4.10.1 Simple Statistics on Group Contents 4.10.2 Kendall's W Coefficient of Concordance 4.10.3 Species Assemblages in Presence-Absence Data 4.10.4 Species Co-occurrence Network 4.11 Indicator Species 4.11.1 Introduction 4.11.2 IndVal: Species Indicator Values 4.11.3 Correlation-Type Indices 4.12 Multivariate Regression Trees (MRT): Constrained Clustering 4.12.1 Introduction 4.12.2 Computation (Principle) 4.12.3 Application Using Packages mvpart and MVPARTwrap 4.12.4 Combining MRT and IndVal 4.13 MRT as a Monothetic Clustering Method 4.14 Sequential Clustering 4.15 A Very Different Approach: Fuzzy Clustering 4.15.1 Fuzzy c-means Using Package cluster's Function fanny () 4.15.2 Noise Clustering Using the vegclust () Function 4.16 Conclusion 5 Unconstrained Ordination 5.1 Objectives 5.2 Ordination Overview 5.2.1 Multidimensional Space 5.2.2 Ordination in Reduced Space 5.3 Principal Component Analysis (PCA) 5.3.1 Overview 5.3.2 PCA of the Environmental Variables of the Doubs River Data Using rda () 5.3.3 PCA on Transformed Species Data 5.3.4 Domain of Application of PCA 5.3.5 PCA Using Function PCA. newr () 5.3.6 Imputation of Missing Values in PCA 5.4 Correspondence Analysis (CA) 5.4.1 Introduction 5.4.2 CA Using Function cca () of Package vegan 5.4.3 CA Using Function CA. newr () 5.4.4 Arch Effect and Detrended Correspondence Analysis (DCA) 5.4.5 Multiple Correspondence Analysis (MCA) 5.5 Principal Coordinate Analysis (PCoA) 5.5.1 Introduction 5.5.2 Application of PCoA to the Doubs Data Set Using cmdscaleO and vegan 5.5.3 Application of PCoA to the Doubs Data Set Using pcoa () 5.6 Nonmetric Multidimensional Scaling (NMDS) 5.6.1 Introduction 5.6.2 Application to the Doubs Fish Data 5.6.3 PCoA or NMDS? 5.7 Hand-Written PCA Ordination Function 6 Canonical Ordination 6.1 Objectives 6.2 Canonical Ordination Overview 6.3 Redundancy Analysis (RDA) 6.3.1 Introduction 6.3.2 RDA of the Doubs River Data 6.3.3 Distance-Based Redundancy Analysis (db-RDA) 6.3.4 A Hand-Written RDA Function 6.4 Canonical Correspondence Analysis (CCA) 6.4.1 Introduction 6.4.2 CCA of the Doubs River Data 6.5 Linear Discriminant Analysis (LDA) 6.5.1 Introduction 6.5.2 Discriminant Analysis Using Ida () 6.6 Other Asymmetric Analyses 6.6.1 Principal Response Curves (PRC) 6.6.2 Co-correspondence Analysis (CoCA) 6.7 Symmetric Analysis of Two (or More) Data Sets 6.8 Canonical Correlation Analysis (CCorA) 6.8.1 Introduction 6.8.2 Canonical Correlation Analysis Using CCorA () 6.9 Co-inertia Analysis (CoIA) 6.9.1 Introduction 6.9.2 Co-inertia Analysis Using Function coinertia () of ade4 6.10 Multiple Factor Analysis (MFA) 6.10.1 Introduction 6.10.2 Multiple Factor Analysis Using FactoMineR 6.11 Relating Species Traits and Environment 6.11.1 The Fourth-Corner Method 6.11.2 RLQ Analysis 6.11.3 Application in R 6.12 Conclusion 7 Spatial Analysis of Ecological Data 7.1 Objectives 7.2 Spatial Structures and Spatial Analysis: A Short Overview 7.2.1 Introduction 7.2.2 Induced Spatial Dependence and Spatial Autocorrelation 7.2.3 Spatial Scale 7.2.4 Spatial Heterogeneity 7.2.5 Spatial Correlation or Autocorrelation Functions and Spatial Correlograms 7.2.6 Testing for the Presence of Spatial Correlation: Conditions 7.2.7 Modelling Spatial Structures 7.3 Multivariate Trend-Surface Analysis 7.3.1 Introduction 7.3.2 Trend-Surface Analysis in Practice 7.4 Eigenvector-Based Spatial Variables and Spatial Modelling 7.4.1 Introduction 7.4.2 Distance-Based Moran's Eigenvector Maps (dbMEM) and Principal Coordinates of Neighbour Matrices (PCNM) 7.4.3 MEM in a Wider Context: Weights Other than Geographic Distances 7.4.4 MEM with Positive or Negative Spatial Correlation: Which Ones should Be Used? 7.4.5 Asymmetric Eigenvector Maps (AEM): When Directionality Matters 7.5 Another Way to Look at Spatial Structures: Multiscale Ordination (MSO) 7.5.1 Principle 7.5.2 Application to the Mite Data - Exploratory Approach 7.5.3 Application to the Detrended Mite and Environmental Data 7.6 Space-Time Interaction Test in Multivariate ANOVA, Without Replicates 7.6.1 Introduction 7.6.2 Testing the Space-Time Interaction with the sti Functions 7.7 Conclusion 8 Community Diversity 8.1 Objectives 8.2 The Multiple Facets of Diversity 8.2.1 Introduction 8.2.2 Species Diversity Measured by a Single Number 8.2.3 Taxonomic Diversity Indices in Practice 8.3 When Space Matters: Alpha, Beta and Gamma Diversities 8.4 Beta Diversity 8.4.1 Beta Diversity Measured by a Single Number 8.4.2 Beta Diversity as the Variance of the Community Composition Table: SCBD and LCBD Indices 8.4.3 Partitioning Beta Diversity into Replacement, Richness Difference and Nestedness Components 8.5 Functional Diversity, Functional Composition and Phylogenetic Diversity of Communities 8.5.1 Alpha Functional Diversity 8.5.2 Beta Taxonomic, Phylogenetic and Functional Diversities 8.6 Conclusion Bibliography Index