Biological diversity is the product of the interaction between many species, be they marine, plant or animal life, and of the many limiting factors that characterize the environment in which the species live. Multivariate analysis uses relationships between variables to order the objects of study according to their collective properties, and to classify the objects of study, that is to group species or ecosystems in distinct classes each containing entities with similar properties. The ultimate objective is to relate the observed biological variation to the accompanying environmental characteristics. Multivariate Analysis of Ecological Data is a comprehensive and structured explanation of how to analyse and interpret ecological data observed on many variables, both biological and environmental. After a general introduction to multivariate ecological data and statistical methodology, specific chapters focus on methods such as clustering, regression, biplots, multidimensional scaling, correspondence analysis (both simple and canonical) and log-ratio analysis, as well as issues of modelling and the inferential aspects of these methods. The book includes a variety of applications to real data from ecological research, as well as two detailed case studies where the reader can appreciate the challenge for analysis, interpretation and communication when dealing with large studies and complex designs. Visit www.multivariatestatistics.org
Raul Primicerio, Associate Professor of Ecology, Evolutionary Biology and Epidemiology at the University of Tromsø, obtained his master degree in his country of birth, Italy, and later his doctorate in Norway. His research and teaching focus on quantitative biology, and he has been training graduate students and professionals at several research institutions in scientifi c method, statistical inference and modelling. He has coordinated ecological modelling activities at the High North Research Centre for Climate and the Environment (FRAM, Tromsø), and has collaborated and helped to coordinate several research projects on global environmental change impact funded by the Norwegian and European research councils. He has produced over 50 papers on both basic and applied issues, such as harvesting and climate change impact, including publications in the multidisciplinary journals Science and PNAS.
Preface Michael Greenacre and Raul Primicerio ECOLOGICAL DATA AND MULTIVARIATE METHODS 1. Multivariate Data in Environmental Science 2. The Four Corners of Multivariate Analysis 3. Measurement Scales, Transformation and Standardization MEASURING DISTANCE AND CORRELATION 4. Measures of Distance between Samples: Euclidean 5. Measures of Distance between Samples: Non-Euclidean 6. Measures of Distance and Correlation between Variables VISUALIZING DISTANCES AND CORRELATIONS 7. Hierarchical Cluster Analysis 8. Ward Clustering and k-means Clustering 9. Multidimensional Scaling REGRESSION AND PRINCIPAL COMPONENT ANALYSIS 10. Regression Biplots 11. Multidimensional Scaling Biplots 12. Principal Component Analysis CORRESPONDENCE ANALYSIS 13. Correspondence Analysis 14. Compositional Data and Log-ratio Analysis 15. Canonical Correspondence Analysis INTERPRETATION, INFERENCE AND MODELLING 16. Variance Partitioning in PCA, LRA, CA and CCA 17. Inference in Multivariate Analysis 18. Statistical Modelling CASE STUDIES 19. Case Study 1: Temporal Trends and Spatial Patterns across a Large Ecological Data Set 20. Case Study 2: Functional Diversity of Fish in the Barents Sea APPENDICES Appendix A: Aspects of Theory Appendix B: Bibliography and Web Resources Appendix C: Computational Note List of Exhibits Index About the Authors