Numerical Ecology - Developments in Environmental Modelling - Volume 24 - 3rd Edition

Numerical Ecology - Developments in Environmental Modelling - Volume 24 - 3rd Edition

Description

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.

Key features

• 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.

Table of contents

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 About the author PL P. Legendre Affiliations and expertise Département de Sciences Biologiques, Université de Montréal, H3C 3J7, Québec, Canada