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Numerical Ecology (Developments in Environmental Modelling): P. Legendre, L. Legendre

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. Compared to the first edition of Numerical Ecology, this second edition includes three new chapters, dealing with the analysis of semiquantitative data, canonical analysis and spatial analysis. New sections have been added to almost all other chapters. There are sections listing available computer programs and packages at the end of several chapters. As in the previous English and French editions, there are numerous examples from the ecological literature, and the choice of methods is facilitated by several synoptic tables.

Review:

This is the best book on numerical ecology available. Legendre & Legendre are already a classical on communities data analysis, and this second edition is a fundamental update. The book should be always around when you are analysing complex data sets and want a correct method and a valid interpretation.

Review:

A great resource for graduate level and above. This book is comprehensive in terms of numerical ecology and is for the more advanced quantitative ecologist. My area of interest is site similarity indices, and I have only begun to tap into the knowledge available in this book on the subject. I am sure I will be returning to it repeatedly through the years.

Review:

This is THE TEXT to have if you use any of the numerical techniques in the field of quantitative ecology. Its scope if exhaustively comprehensive. The authors clearly explain which methods are at your disposal under given circumstances and which are inappropriate to use. Many of the methods described are illustrated with case studies of ecological examples from the literature. In most cases, the authors walk you thru the computational steps involved in using a particular numerical method--this would make it possible for the reader to construct a "home grown" algorithm for methods unavailable in "off-the-shelf" statistical packages. In addition, the book is also thankfully littered with citations and references for those computer programs that are available for each of the methods described...this is very up-to-date material, as many of these references are web sites!

This second English edition of Numerical ecology is a revised and largely expanded translation of the second edition of Écologie numérique (Legendre & Legendre, 1984). Compared to the first English edition (1983), there are three new chapters, dealing with the analysis of semiquantitative data (Chapter 5), canonical analysis (Chapter 11), and spatial analysis (Chapter 13). New sections have been added to almost all other chapters. These include, for example, new sections (numbers given in parentheses) on: autocorrelation (1.1), statistical testing by permutation (1.2), coding (1.5), missing data (1.6), singular value decomposition (2.11), multiway contingency tables (6.3), cophenetic matrix and ultrametric property (8.3), reversals (8.6), partitioning by K-means (8.8), cluster validation (8.12), a review of regression methods (10.3), path analysis (10.4), a review of matrix comparison methods (10.5), the 4th-corner problem (10.6), several new methods for the analysis of data series (12.3-12.5), detection of discontinuities in multivariate series (12.6), and Box-Jenkins models (12.7). There are sections listing available computer programs and packages at the end of several chapters. As in the previous English and French editions, there are numerous examples from the ecological literature, and the choice of methods is facilitated by several synoptic tables. Additional information is available from the Elsevier WWWeb site:

Contents

1. Complex ecological data sets, including: Autocorrelation and spatial structure. Statistical testing by permutation. Computers. Descriptors. Coding. Missing data.

2. Matrix algebra: a summary

3. Dimensional analysis in ecology

4. Multidimensional quantitative data

5. Multidimensional semiquantitative data

6. Multidimensional qualitative data

7. Ecological resemblance, including: Review of similarity, distance, and R-mode coefficients. Computer programs and packages.

8. Cluster analysis, including: Agglomerative and divisive methods. K-means partitioning. Cophenetic matrix and ultrametric property. Reversals. TWINSPAN. Species clustering: biological associations. Indicator species. Seriation. Clustering statistics. Cluster validation. Choice of a clustering method.

9. Ordination in reduced space, including: Principal component analysis (PCA). Principal coordinate analysis (PCOA). Nonmetric multidimensional scaling (MDS). Correspondence analysis (CA). Factor analysis.

10. Interpretation of ecological structures, including: Review of regression methods. Path analysis. Matrix comparison: Mantel tests, ANOSIM, Procrustes analysis, and 4th-corner statistics.

11. Canonical analysis, including: Redundancy analysis (RDA). Canonical correspondence analysis (CCA). Partial RDA and CCA. Tests of significance in RDA and CCA. Canonical correlation analysis (CCORA). Discriminant analysis. Canonical analysis of species data.

12. Ecological data series: time series analysis, including: Trend extraction and numerical filters. Correlogram. Periodogram. Spectral analysis. Detection of discontinuities in multivariate series. Box-Jenkins models. Computer programs.

13. Spatial analysis, including: Scale. Structure functions (spatial correlograms, variograms, multivariate Mantel correlogram). Mapping. Patches and boundaries. Connection networks. Unconstrained and constrained ordination maps. Causal modelling through partial canonical analysis and partial Mantel analysis. Computer programs.

Pierre Legendre is an ecologist and Professor at Université de Montréal, Québec. Louis Legendre is a biological oceanographer and Professor at Université Laval, Québec City. The two brothers are fellows of the Royal Society of Canada (Academy of Science).

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