# Numerical Ecology

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.

Audience
Practicing ecologists: professional researchers and graduate students in the fields of ecology, environment, and oceanography.

Paperback, 1006 Pages

Published: July 2012

Imprint: Elsevier

ISBN: 978-0-444-53868-0

## Reviews

• "Pierre Legendreâ¦and Louis Legendreâ¦ 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 interpretationâ¦Numerical Ecology is a definite must-have for any quanti-tative ecologist."--Basic and Applied Ecology, December 2013

## Contents

• 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
2. Matrix algebra: a summary
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
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
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
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
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
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
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
8.6 Reversals
8.7 Hierarchical divisive clustering
8.9 Species clustering: biological associations
8.10 Seriation
8.11 Multivariate regression trees (MRT)
8.12 Clustering statistics
8.13 Cluster validation
8.14 Cluster representation and choice of a method
8.15 Software
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
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
10.7 Software
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
12. Ecological data series
12.0 Ecological series
12.1 Characteristics of data series and research objectives
12.2 Trend extraction and numerical filters7
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
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
14. Multiscale analysis: spatial eigenfunctions
14.0 Introduction to multiscale analysis
14.1 Distance-based Moranâs eigenvector maps (dbMEM)
14.2 Moranâ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
Bibliography
Subject index

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