1. Managing Dimensionality (but not acronyms) PCA, CA, RDA, CCA, MDS, NMDS, DCA, DCCA, pRDA, pCCA

2. Type of Data Matrix

3. Ordination Techniques
Linear methods
Weighted averaging
unconstrained
Principal Components
Analysis (PCA)
Correspondence Analysis
(CA)
constrained
Redundancy Analysis (RDA)
Canonical
Correspondence Analysis (CCA)

4. Models of Species Response
There are (at least) two models:-
Linear - species increase or decrease along the environmental gradient
Unimodal - species rise to a peak somewhere along the environmental gradient and then fall again

5. A Theoretical Model

6. Linear

7. Unimodal

8. Alpha and Beta Diversity
alpha diversity is the diversity of a community (either measured in terms of a diversity index or species richness)
beta diversity (also known as ‘species turnover’ or ‘differentiation diversity’) is the rate of change in species composition from one community to another along gradients; gamma diversity is the diversity of a region or a landscape.

9. A Short Coenocline

10. A Long Coenocline

11. Inferring Gradients from Species (or Attribute) Data

12. Indirect Gradient Analysis
Environmental gradients are inferred from species data alone
Three methods:
Principal Component Analysis - linear model
Correspondence Analysis - unimodal model
Detrended CA - modified unimodal model

13. PCA - linear model

14. PCA - linear model

15. Terschelling Dune Data

16. PCA gradient - site plot

17. PCA gradient - site/species biplot
standard
biodynamic & hobby
nature

18. Reciprocal Averaging
Site A B C D E F Species Prunus serotina Tilia americana Acer saccharum Quercus velutina Juglans nigra

19. Reciprocal Averaging
Site A B C D E F Species Score Species Iteration Prunus serotina Tilia americana Acer saccharum Quercus velutina Juglans nigra
Iteration Site Score

20. Reciprocal Averaging
Site A B C D E F Species Score Species Iteration Prunus serotina Tilia americana Acer saccharum Quercus velutina Juglans nigra
Iteration Site Score

21. Reciprocal Averaging
Site A B C D E F Species Score Species Iteration Prunus serotina Tilia americana Acer saccharum Quercus velutina Juglans nigra
Iteration Site Score

22. Reciprocal Averaging
Site A B C D E F Species Score Species Iteration Prunus serotina Tilia americana Acer saccharum Quercus velutina Juglans nigra
Iteration Site Score

23. Reordered Sites and Species
Site A C E B D F Species Species Score Quercus velutina Prunus serotina Juglans nigra Tilia americana Acer saccharum Site Score

24. Arches - Artifact or Feature?

25. The Arch Effect What is it? Why does it happen?
What should we do about it?

26. From Alexandria to Suez

27. CA - with arch effect (sites)

28. CA - with arch effect (species)

29. Long Gradients A B C D

30. Gradient End Compression

31. CA - with arch effect (species)

32. CA - with arch effect (sites)

33. Detrending by Segments

34. DCA - modified unimodal

35. Making Effective Use of Environmental Variables

36. Direct Gradient Analysis
Environmental gradients are constructed from the relationship between species environmental variables
Three methods:
Redundancy Analysis - linear model
Canonical (or Constrained) Correspondence Analysis - unimodal model
Detrended CCA - modified unimodal model

37. CCA - site/species joint plot

38. CCA - species/environment biplot

39. Removing the Effect of Nuisance Variables

40. Partial Analyses Remove the effect of covariates
variables that we can measure but which are of no interest
e.g. block effects, start values, etc.
Carry out the gradient analysis on what is left of the variation after removing the effect of the covariates.