Numerical Ecology

Numerical Ecology

3rd Edition - July 3, 2012

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  • Authors: P. Legendre, L. Legendre
  • Paperback ISBN: 9780444538680
  • eBook ISBN: 9780444538697

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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


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

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


    Subject Index

Product details

  • No. of pages: 1006
  • Language: English
  • Copyright: © Elsevier 2012
  • Published: July 3, 2012
  • Imprint: Elsevier
  • Paperback ISBN: 9780444538680
  • eBook ISBN: 9780444538697

About the Authors

P. Legendre

Affiliations and Expertise

Département de Sciences Biologiques, Université de Montréal, H3C 3J7, Québec, Canada

L. Legendre

Ratings and Reviews

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  • Jim V. Fri Aug 21 2020

    Modelización ecológica, volumen 31 1ra Edición

    Excelente publicación, pero considero que deben realizar traducción en español. Gracias

  • LauraRigacci Thu Sep 26 2019


    This book is very useful both for undergraduate students and for researchers. It is very complete and clear in the explanations.