Numerical Ecology
- 3rd Edition, Volume 24 - August 6, 2012
- Latest edition
- Authors: P. Legendre, Louis Legendre
- Language: English
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… Read more
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
Practicing ecologists: professional researchers and graduate students in the fields of ecology, environment, and oceanography.
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
"Pierre Legendre…and 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 interpretation…Numerical Ecology is a definite must-have for any quanti-tative ecologist."—Basic and Applied Ecology, December 2013
- Edition: 3
- Latest edition
- Volume: 24
- Published: August 6, 2012
- Language: English
PL
P. Legendre
Affiliations and expertise
Département de Sciences Biologiques, Université de Montréal, H3C 3J7, Québec, CanadaRead Numerical Ecology on ScienceDirect