R.H.G. Jongman

Ecological data has several special properties: the presence or absence of species on a semi-quantitative abundance scale; non-linear relationships between species and environmental factors; and high inter-correlations among species and among environmental variables. The analysis of such data is important to the interpretation of relationships within plant and animal communities and with their environments. In this corrected version of Data Analysis in Community and Landscape Ecology, without using complex mathematics, the contributors demonstrate the methods that have proven most useful, with examples, exercises and case-studies. Chapters explain in an elementary way powerful data analysis techniques such as logic regression, canonical correspondence analysis, and kriging.

A global system of harmonized observations is needed to inform scientists and policy-makers.

ABSTRACT Aim To produce a statistical stratification of the European environment, suitable for stratified random sampling of ecological resources, the selection of sites for representative studies across the continent, and to provide strata for modelling exercises and reporting. Location A ‘Greater European Window’ with the following boundaries: 11° W, 32° E, 34° N, 72° N. Methods Twenty of the most relevant available environmental variables were selected, based on experience from previous studies. Principal components analysis (PCA) was used to explain 88% of the variation into three dimensions, which were subsequently clustered using an ISODATA clustering routine. The mean first principal component values of the classification variables were used to aggregate the strata into Environmental Zones and to provide a basis for consistent nomenclature. Results The Environmental Stratification of Europe (EnS) consists of 84 strata, which have been aggregated into 13 Environmental Zones. The stratification has a 1 km 2 resolution. Aggregations of the strata have been compared to other European classifications using the Kappa statistic, and show ‘good’ comparisons. The individual strata have been described using data from available environmental databases. The EnS is available for noncommercial use by applying to the corresponding author. Main conclusions The Environmental Stratification of Europe has been constructed using tried and tested statistical procedures. It forms an appropriate stratification for stratified random sampling of ecological resources, the selection of sites for representative studies across the continent and for the provision of strata for modelling exercises and reporting at the European scale.

Bibliographical notes 26 2.9 Exercise 2.10 Solution to the exercise 27 /f 5 .~\Ordination 91 < \5Jr--/ Introduction 91 §-l-J) Aim and usage 91 \T^Z Data approximation and response models in ordination 93 5.1.3Outline of Chapter 5 5.2 Correspondence analysis (CA) and detrended correspondence analysis (DCA) 95 5.2.1 From weighted averaging to correspondence analysis 95 5.2.2 Two-way weighted averaging algorithm 5.2.3 Diagonal structures: properties and faults of correspondence analysis 103 5,2.4/Detrended correspondence analysis (DCA) 5727$/ Joint plot of species and sites 108 5.2.6 Block structures and sensitivity to rare species 109 5.2.7 Gaussian ordination and its relation with CA and DCA 110 5.3_ Principal components analysis (PCA) QJJJ) From least-squares regression to principal components analysis 116 5.3.2Two-way weighted summation algorithm 5 J,3 Best lines and planes in m-dimensional space 125 ^5.3^) Biplot of species and site scores 127 5.3.5 Data transformation 130 5.3.6 R-mode and Q-mode algorithms ( §A) Interpretation of ordination with external data 132 5.5 Canonical ordination 136 5.5.1 Introduction 136 5.5.2Canonical correspondence analysis (CCA) 5.5.3Redundancy analysis (RDA) 144 5.5.4Canonical correlation analysis (COR) 5.5.5 Canonical variate analysis (CVA) 5.5.6 Interpreting canonical axes 150 5.5.7 Data transformation 151 5.6 Multidimensional scaling 151 5.7 Evaluation of direct gradient and indirect gradient analysis techniques 153 5.8 Bibliographic notes 156 5.9Ordination methods in terms of matrix algebra 158 5.9.1 Principal components analysis (PCA) 5.9.2 Correspondence analysis (CA) 160 5.9.3 Canonical correllation analysis (COR) 5.9.4 Redundancy analysis (RDA) 163 5.9.5 Canonical correspondence analysis (CCA) 5.10 Exercises 165 5.11 Solutions to exercises 169 6 Cluster analysis