Numerical Ecology book cover

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.

Paperback, 1006 Pages

Published: July 2012

Imprint: Elsevier

ISBN: 978-0-444-53868-0

Reviews

  • "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


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 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
    Bibliography
    Subject index

     

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