1. Classification

2. Similarity measures Each ordination or classification method is based (explicitely or implicitely) on some similarity measure (Two possible formulations of ordination problem)

3. Similarities (dissimilarities, resemblance functions) based on qualitative/quantitative data Other indices used for sample similarity and for species similarity Similarity of two samples has a meaning by itself: similarity of two species has meaning only in relation to the data set. Species set is „fixed“, samples are random selection from a population

4. Sample similarity based on qualitative data SörensenJacquard d - number of species absent from both samples (usually not used)

5. Species similarity based on presence absence d - number of quadrats without both species - absolutely necessary

6. Transformation is an algebraic function X ij ’=f(X ij ) which is applied independently of the other values. Standardization is done either with respect to the values of other species in the sample (standardization by samples) or with respect to the values of the species in other samples (standardization by species). Quantitative data Centering means the subtraction of a mean so that the resulting variable (species) or sample has a mean of zero. Standardization usually means division of each value by the sample (species) norm or by the total of all the values in a sample (species).

8. Euclidean distance For ED, standardize by sample norm, not by total The samples with t contain values standardized by the total, those with n samples standardized by sample norm. For samples standardized by total, ED12 = 1.41 (√2), whereas ED34=0.82, whereas for samples standardized by sample norm, ED12=ED34=1.41

9. Percentual similarity (quantitative Sörensen)

10. Similarity of species based on quantitative data Correlation coefficients (ordinary, rank)

11. Similarity of samples vs. similarity of communities

12. expected number of shared species in two subsamples taken randomly from the second sample. 22 Normalized expected shared species =

13. Similarity matrices - directly used in Multidimensional scaling (both metric and non-metric) Mantel test

16. Classification

17. Hierarchical agglomerative (cluster analysis)

18. Subjective decissions in the objective procedure

19. Single linkage and complete linkage

20. Single linkage - > chaining

21. Order does not play a role

22. TWINSPAN (Two Way INdicator SPecies ANalysis) Pseudospecies

23. 01 is more similar to 1 than 00